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Langdon_Thesis_Rev_Final_ETD_2007

1. Desired Sprung Mass Response Sprung Mass Error Acceleration G 0 100 200 300 400 500 600 Time s Figure 5 18 Sprung Mass Desired Response and Error Convergence The plots in Figure 5 17 and Figure 5 18 show that the error did not converge as well as in the system ID simulation It did occur very rapidly however The RMS value 75 of the unsprung mass response error converged to within 8 4 of the RMS of desired signal Similarly the RMS of the sprung mass response error was 7 5 of the RMS of the desired sprung mass response Figure 5 19 found below is a half second window showing a comparison between the desired and actual responses The controller appears to make the signal shapes and bandwidth match very well 3 010 Desired Unsprung 8 Actual Unsprung a Desired Sprung 6 Actual Sprung 4 i h ni e 1 e O a 5 2 A J E n 2 of AAAS RA 7 1 AMEN DY 5 j 2 oda I 4 6 8 550 550 1 550 2 550 3 550 4 550 5 Time s Figure 5 19 Sample of Desired Compared to Actual Response Similar to the system ID the signal powers of the error and desired responses were investigated Figure 5 20 and Figure 5 21 show the signal powers during convergence Again the criterion for good convergence in vibrations is a 10 dB red
2. 100 10 10 10 10 10 Frequency Figure 6 11 Frequency Response of White Noise Excitation Low Pass Filter 6 3 3 Experimental Results Several tests were run while trying to optimize the balance between fast convergence and stability It was found that tuning the step sizes of both FIR models while running was an excellent way to achieve this The step sizes were set relatively high during the early part of convergence Later on the step size was reduced to help fine 92 tune the weights This offered a great balance between quick convergence and nice results The sizes of the FIR filters were also altered and tested several times to get the best results Ultimately the model size was set at 700 coefficients The step size for each adaptive filter started at around 0 2 and then was fine tuned down to around 0 05 Figure 6 12 and Figure 6 13 contain plots of the quarter car accelerations and the error associated with how well the FIR models identified the plant Unsprung Response Error Acceleration G O Time s Figure 6 12 Unsprung Mass Acceleration Response and Model Error 93 Sprung Response Error 0 4 0 6 0 2 Acceleration G O 0 4 0 20 40 60 80 100 Time s Figure 6 13 Sprung Mass Acceleration Response and Model Error The adaptive fil
3. 63 Unsprung Accelerometer and Error Signal Powers 64 Impulse Response Compared to Converged ID Welt hts 65 Comparison of Model and Adaptive Filter Frequency Responses 66 Basic Construction of Simulink Control Block Diaeram 67 Detail of a DAC Block and b ADC BlockK 68 Detailed Simulink Diagram of Control Block 70 EMS Aleoritamn Detail uuu kotize ooo anun alus us uu asa 71 Sample Desired Acceleration Response Generated with State space Quarter ope 74 Unsprung Mass Desired Response and Error Convergence 75 Sprung Mass Desired Response and Error Convergence 75 Sample of Desired Compared to Actual Response 76 Signal and Error Power for Unsprung Mass del Signal and Error Power for Sprung Mass 717 Convers ed Conirol Weigh uu k u aun ia ai a pe l ke ukasa 78 Frequency Response Function of the Convolved Controller and Plant 79 Accelerometer Installed on Sprung Mass 81 Accelerometer Installed on the Suspension Upri ht 82 Otech Data ACQUIS OI Mr 83
4. Error MWA 514 514 2 514 4 514 6 514 8 515 Time s Acceleration G Oo mb EX eee E aan nen ZA A A _ w Y Figure 6 32 Detail of 30 Hz Unsprung Mass Response and Error Furthermore the quality of the error convergence was again gauged by the signal power levels are plotted in Figure 6 33 and Figure 6 34 20 LI A 22 24 IO 30 Unsprung Desired Signal Error 32 0 100 200 300 400 500 600 Time s Signal Power dB Figure 6 33 30 Hz Filtered Unsprung Desired Response and Error Signal Powers 112 24 Sprung Desired Signal 26 I Error 28 T N A Vt YW Yt Y ll 30 m e o 32 2 a q 734 lt D 36 A A LANNEN 38 40 42 0 100 200 300 400 500 600 Time s Figure 6 34 30 Hz Filtered Sprung Desired Response and Error Signal Powers Table 5 1s assembled below comparing these error and power level results to the control simulation results Again the RMS values of the response and error signals were used to form the error metric for convergence and the decibel levels are directly from the above plots Table 5 30Hz Replication Controller Error Comparison Model M
5. is now replaced with the filtered desired response R in Figure 4 4 The gradient is still estimated in the same manner Only the input vector in the gradient term is changed Therefore the weights are adjusted at each time step by W W se R 10 where R Py ae d1 49 In control the step size still dictates the rate of convergence and determines stability The length of the weight vector can also still be tuned to affect convergence and quality of the inverse model Additionally the amount of delay of the desired response signal may be tuned to help produce a more accurate response 50 5 SIMULATION AND RESULTS The following chapter presents the first step taken to apply the principles discussed in the previous chapter Before proving the worth of applying these control theories to the quarter car rig they were first tested purely in software This was to help understand the process before risking damage to the hardware due to some unforeseen instabilities The chapter begins by discussing the linear quarter car model used to represent the unknown plant in software System ID is then applied and the results of this identification are discussed Finally a desired response 1s produced and the inverse control algorithm 1s applied to replicate this response on the quarter car model The chapter closes with the results of the control study 5 1 Quarter car Model To prove the concept purely in simulation a plan
6. jejeg paddel JOJE MO a 181 14 ejansig zjuep Jd zunu Ja uaye Joyenjoe a3 qe4u3 u uo END SION SUMA link Model for ID 1mu igure 6 8 Detailed Si F 89 The LMS algorithm works to adapt the weights of the FIR filters the same way as in simulation The step sizes z_gain and y gain in this case can be changed form the front panel during simulation in Control Desk The output block labeled Actuator is where the signal is sent out to the DAC block The addition of weight switches Wz and Wy allows for the ability to reset the weights while the real time processor is running This is to perform multiple tests without reloading the software or in the event that the weights become unstable during a test Otherwise the algorithm runs the same way to adapt the weights per equation 8 For the system ID test a front panel in Control Desk was created to have control of the tests An images of two of the layouts from Control Desk are found in Figure 6 9 and Figure 6 10 q_car_to_box_1 ControlDesk Developer Version id layout Ef a x 184 File Edit View Tools Experiment Instrumentation Platform Parameter Editor Window Help b Z EN Dig s UR sm s a wes 4 gt aA PPC combinedid dspace HostService vi f s 100 eon NU Auto Repeat Downsampling 5 Trigger Signal Y On Off Y Level 0 001 Delay 0 Model Root DAC actuator
7. of the specimen to calculate an error denoted by 106 This error is fed into an adaptive filter shown by 34 whose coefficients are adapted by the inverse plant identifier The output of this filter 1s then added to the corrected drive file to create a new corrected drive file at 112 This iteration of the drive file is then collected and stored at 54 Once the entire corrected drive file is played through once it is then overwritten by the newly stored drive file completing an iteration of the control loop This process is then repeated until the corrected drive file converges to create a response of the plant that closely matches the desired response 15 Figure 2 7 Algorithm Presented in U S Patent 5 394 071 This method is also very different from the algorithm applied in this research One primary difference 1s that even though the process is continuously online the changes to the drive signal occur in batches where as the drive signal in this study changes each sample Also the error computed in this algorithm is fed directly in to the adaptive filter rather than to the algorithm that adapts the filter Finally another difference that is apparent is that some base line drive file must first be computed off line to begin the process 2 2 3 Summary of Literature To summarize the literature there are many methods for computing a drive file that will cause the test specimen to replicate signals Acqu
8. y d W X 4 At this point we construct a quadratic cost function which is the instantaneous squared error We can study the optimal solutions and the dynamics of weight trajectories by assuming that d and X are statistically stationary The details of this analysis can be found in the literature 27 28 Taking the expected value of equation 4 we have Ele Eldj W RW 2B W 5 Equation 5 represents the mean square error function Here R is the input auto correlation matrix and B is the cross correlation between the desired response and the input signal It is clear that this equation is a quadratic function of the weights W Thus the mean square error cost function is bowl shaped Naturally this bowl shape has a bottom or minimum value In order to determine this minimum the partial derivative gradient of the cost function is taken with respect to the weight vectors The result of differentiation is set equal to zero to find the minimum error value This minimum is found when the weights are at their optimal values W In practice most adaptive algorithms utilize noisy instantaneous gradients to slowly converge on the optimal value as opposed to single step deadbeat control algorithms In this study the LMS gradient descent adaptation algorithm is utilized to optimize the weights of the adaptive linear combiner 43 4 2 Least Mean Squares The LMS algorithm 1s a steepest descent m
9. Figure 2 7 Algorithm Presented in U S Patent 5 394 071 _ 16 Figure 5 1 Sechematic ot Quarter car Test RI ia 18 Figure 3 2 Solid Model of Quarter car Rig in Design Phase 19 Foure 525 Teslo In Base plate ies 22 Erstte 5 4 Clampine Hato Water 22 Figure 3 5 Finite element Beam Model of Reaction Frame 23 Figure 3 6 Sectionvol LH Ser s BELM essa darias 27 Figure 3 7 ANSYS Sprung Mass Results a Out of plane Deflection b von Mises PS UL Saas an es ec yanusha saus manis a e et n e a e a e e n ee ates ane ob e ake e bio asta 29 Figure 3 8 Porsche 996 Grand Am Cup GS Racecar 30 Figure 3 9 LF Porsche 996 MacPherson Strut Type Suspension 31 Figure 3 10 Detailed View of Modeled Suspension and Mounts 32 Figure 3 11 Detailed View of LCA and Tie rod Brackets Showing Adjustment Dre ON Se ti aa t aks e rt a kt kad tk a e E oi aste 33 Figure 3 12 MTS 248 05 Hydraulic A Ct ator u uuu pin galon bonb d a e bekas 35 Figure 3 13 MTS SilentFlo Hydraulic Power Supply 36 Figure 3 14 MTS Hydraulic Service Manifold 37 Fiore 3 15 JM f Plex Vest SE Controlado ido 37 Figure 3 16 Completed Quarter car
10. This ensures that the rig is very stable and does 25 not flex when clamped to the base plate Next the front 1 in plate was milled to within 0 0003 in flatness This was within the allowable misalignment of the bearing rails per the manufacturer Also the front face was milled to within 0 005 in perpendicularity of the bottom feet This ensured that the forces entering the suspension were well defined by reducing the misalignment of the actuator with the motion of the sprung mass The design of the load frame as a single unit allows it to be placed all over the base plate for various configurations The large cutout in the front face allows for protrusions from the rear of the sprung mass such as added mass plates or motors for an active geometry type of suspension 3 4 Linear Guides The linear guides are LH35 series linear bearings manufactured by NSK This particular bearing design 1s used due to its proven performance in machine tool and automation industries A larger custom variation of this particular design can be found in many Toyoda vertical high speed milling machines 21 These bearings are a high accuracy high load and low friction design 3 4 1 Sizing The bearings were sized with assistance from NSK Corporation engineers and product documentation 22 NSK has a standard sizing practice that is based on life load and load offset among others In this study the driving load was calculated from a simple two mass quar
11. and D are defined by the two equations of motion and are found in Appendix C 53 5 1 2 Parameter Values For the purpose of having a ballpark comparison of experimental results such as frequency response to those in this simulation the parameters were chosen reasonably close to the real Porsche suspension on the test rig A high fidelity parameter identification was not performed for this study The following table is a list of those parameters used in the model Table 2 Quarter car Model Parameters Parameters Value Unit ms 9 H 1480 Ibf in Ibf in zeta HP The values selected are meant to be a fairly accurate representation of the suspension on the quarter car rig The masses were measured directly as the components were in place at the time of this study The suspension spring rate was measured directly The tire spring rate was approximated based on an assumption that a tire spring rate was on the same order of magnitude as a race car suspension spring rate It was not possible to directly measure the damping rate Instead a damping ratio was selected to be around 0 4 The damping coefficient was then calculated from this assumption based on the simple calculation c 254 k m 18 These values were then used to fill in the elements of the state variables to complete the continuous time s domain state space model The parameters were put into a MATLAB parameter file for ease of making changes Th
12. 17 H l ra a a y pra VE L ACCE Li L s A AAA AN lt ze L e NE y i x ey Z ar No AGE as a eae As E u TIDE ASIA IR aN ko CU IRE PA a 3 mai a x EDAD CELI NORMA E Choe Z lt vet z PET E RUAD INPU Xr IQ EDET PHS FEEDBACK SEYE O y KE Figure 3 1 Schematic of Quarter car Test Rig This representation shows the primary components of the rig Those components are the sprung mass adapter plate vehicle suspension tire tire pan actuator and ground or load frame The sprung mass and suspension adapter plate are constrained with bearings to move in the vertical direction The actual suspension of the vehicle is attached to the sprung mass via the adapter plate and fixtures The actuator is fixed to the ground and supports this represented vehicle via the tire resting on the tire pan A displacement command signal is input to the servo hydraulic actuator which then excites the system through the tire contact so that the suspension response matches the measured signal Since the sprung mass is free to move in the vertical direction only the vertical dynamic response of the specimen may be tested To ensure that the requirements of the new rig were fulfilled special attention was paid to the specifications and design of the key components The result of this design was a state of the art quarter car rig that is able to fulfill ma
13. 50 100 150 200 250 300 350 400 Weight Figure 6 16 Experimental FIR Model Weights It is clear from the plot that there are at least two distinct dynamics which the FIR filters successfully identified It is also clear that the FIR model of the unsprung mass transfer function has a much higher amplitude and frequency content than that of the sprung mass transfer function Finally the frequency response of the identified models is investigated in Figure 6 17 97 Transfer Function 180 90 90 180 40 Usprung 99 TT Sprung Phase deg O Mag dB 10 10 10 Frequency Figure 6 17 Frequency Response of the FIR Identified Model The frequency response of the FIR model has two resonances one near 5 2 Hz and one near 29 Hz This closely agrees with the simulation model This agreement with simulation 1s fairly reasonable to expect because the masses and spring rates used were well known when used in the state space model It is curious that the sprung mass 1s sensitive to a wide band of frequencies between the two resonance peaks This is likely due to non linear properties of the bearings suspension bushing and damper and high damping in the system The resonance peak at 29 Hz is more defined for the unsprung mass There also appears to b
14. 6 22 shows why Figure 6 24 is a one second detailed view of a converged part of the unsprung mass error plot Itis clear in this plot that the high magnitude peaks have been captured the best These higher magnitude accelerations are associated with lower frequencies Because this data set was collected with a 15 Hz filter most of the dynamics 105 of the unsprung mass were not really captured Thus the controller has a much harder time replicating any dynamics at the higher frequency Most of the error in this plot appears to be associated with higher frequency excitation 0 8 Desired Unsprung Response Controller Error l AN 43 43 2 43 4 43 6 43 8 44 Time s 0 6 0 4 An o Acceleration G O 2 0 4 0 6 Figure 6 24 Detail of Unsprung Response Controller Error Perhaps the better way to look at the error convergence is based on power levels of the signals Figure 6 25 and Figure 6 26 are the power levels of the desire signals and their respective error signals These plots tell more about how well the controller is actually replicating the signal The power level drop of the unsprung mass error signal from the desired response is nearly 10 dB Considering that the large amplitude low frequency response seemed to be replicated with more accuracy than the higher frequency low amplitude signals indicates that ther
15. Test Rig with Suspension Installed 39 Figure 4 1 The Single Input Adaptive Linear Combiner 41 Figure 4 2 The Adaptive Linear Combiner Compared to a Desired Signal 42 Figure 4 3 Figure 4 4 Figure 5 1 Figure 5 2 Figure 5 3 Figure 5 4 Figure 5 5 Figure 5 6 Figure 5 7 Figure 5 8 Figure 5 9 Figure 5 10 Figure 5 11 Figure 5 12 Figure 5 13 Figure 5 14 Figure 5 15 Figure 5 16 car Model Figure 5 17 Figure 5 18 Figure 5 19 Figure 5 20 Figure 5 21 Figure 5 22 Figure 5 23 Figure 6 1 Figure 6 2 Figure 6 3 Figure 6 4 Figure 6 5 Typical System Identification Block Diaeram 46 Filter X LMS Adaptive Inverse Control Block Diaeram 48 Two Degree of freedom Quarter car Model 52 Frequency Response of the Analytical Quarter car State space Model 56 Simulink Block Diagram of Basic ID Scheme 57 Simulink Block Diagram Model of Simulation ID Aleortthm 59 Model Detail of Filtering the White Noise Exclitation 61 Error Convergence of Sprung Mass Numerical Model Identification 61 Error Convergence of Unsprung Mass Numerical Model Identification 62 Sprung Accelerometer and Error Signal Powers
16. Waltham MA May 5 2003 Wright P Movers and Shakers Article GrandPrix com The Motorsport Company October 19 2000 Personal communication on 7 post test road profile generation methods with Dr Christoph Leser MTS Systems Corporation December 5 2006 Solderling S Sharp M Leser C Servo Controller Compensation Methods Selection of the Correct Technique for Test Applications SAE Technical Paper Series No 1999 01 3000 Warrendale PA 1999 Kowalczyk H Damper Tuning with the Use of a Seven Post Shaker Rig SAE Technical Paper Series No 2002 01 0804 Warrendale PA 2002 Vaes D Souverijns W De Cuyper J Swevers J Sas P Optimal Decoupling for Improved Multivariable controller Design Applied on an Automotive Vibration Test Rig Proceedings of the American Control Conference v 1 p 785 790 2003 Goncalves F Dynamic Analysis of Semi Active Control Techniques for Vehicle Applications Master s Thesis Virginia Tech Blacksburg VA August 2001 118 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Milliken W F Milliken D L Race Car Vehicle Dynamics Society of Automotive Engineers Inc Warrendale PA 1995 PT Labtech Penta Internationa http labtech org website Batam Indonesia 2006 FCS Control Systems B V FasTEST Manager User Manual Issue 1 2 4 Oude Meer Netherlands 2004 MTS Systems Corporation RPC Pro Broc
17. aa ie 74 6 EXERIMENTAL PROCEDURES AND RESULIS 80 O MOSO DI OP bbl lat E 80 6 1 1 SENSOMS ina 80 6 1 2 u Tio ON ios 82 6 2 Basic dSPACEL Ode ed neo 85 Gi sy StemuIGemiiie VI NON ae da iii 88 6 3 1 ISP ACI Mode usura potjel dy ter ta a eti ea 88 6 3 2 EXCifatiOM 51 nal SWA PLIS aia 92 6 3 3 Experimental R O sulis uuu yku nu ola wi ale e epa a a ok ai ke ie 92 OG Adaptive CONTO A a a a a his aie aos lat 99 6 4 1 SP ACI Mode lindos 99 6 4 2 Desired Response G n rallon u u u idas 103 6 4 3 Experimental Results 15 Hz Data uu ica 104 6 4 4 Experimental Results 30 Hz Data 7 aa a 110 7 CONCLUSIONS AND RECOMMENDA TION S 116 O A yun bs besse ad s E uu iss 118 AAPP i tj ll lt a pl BA tr A aaa a a at a kl 121 Appendix A Rie MAN EN YA CG us e 121 Appendix D Ric Specilicalionsu uu uu klete ko v n kt aw ot ad kel k n lar sd al ala 122 Appendix C Linear State Space MatriIces 123 MIA bind 124 Vil m lt q lt z Y Z w gt y u A B C D A B C D 8 n p R List of Nomenclature discrete Input vector at time k Input vector element at time k sample time In seconds n sample delay n sample weight at time k output at time k weight vector FIR model at time k desired response signal at time k error at time k expected value fun
18. and 8 post test rigs Chapter three details the development of the new quarter car test rig completed for this study The functional requirements are stated and achieved Chapter four introduces the reader to the control algorithm concepts utilized in this study The building blocks for the adaptive algorithm are explained in detail Chapter five applies these concepts in simulation with the use of a simplified linear quarter car model The results of this simple study are then discussed Similarly in chapter six the software simulated quarter car model is now replaced with actual hardware The same tests are then run with hardware in the loop The results of this study are provided and compared to those of the simulation work Finally the thesis ends with the conclusions and recommendations provided in chapter seven 2 LITERATURE REVIEW In this chapter a background of the current state of the art in vehicle testing rigs and the controls they utilize 1s reviewed The chapter begins with a survey of the current test rig technology and some of the issues or deficiencies found with them This will lay the groundwork for defining the new requirements of the quarter car rig design presented in this thesis The second half of the chapter reviews the current control algorithms in use on indoor vehicle shaker rigs The differences between these current algorithms and the one used in this study are highlighted These differences will become more obvious
19. are restrictive rules that govern the specifics of a racecar s design or that limit actual track testing that a team may perform in a given season A major trend in both industries is to utilize more indoor lab based test equipment It was noted that it is near compulsory for a Fl race team to have a 7 post shaker at its disposal 2 Testing in a laboratory environment allows for greater control of the experiment less time required which allows for more experimentation and in many cases much lower costs and liabilities 3 Specifically it was noted that a laboratory test generally requires one fourth of the time as a road test and is less expensive per test It reduces the need to have support personnel such as safety crews during a track test Lab testing also reduces the liability as a test driver could be injured during a road test In many cases the driver can be eliminated during a laboratory test One primary mission of the Virginia Institute for Performance Engineering and Research VIPER Lab the research group from which this study stems 1s to develop and evaluate the technology that has the potential to advance the state of the art in 8 post testing The goals of this study seek to support this mission 1 2 Objectives The primary goal for this study is to develop and evaluate technology that can improve the state of the art in indoor vehicle simulation testing on a quarter car vehicle Because this 1s a start up lab an add
20. blocks are also seen in Figure 6 8 Similar to the simulation the decrease in power from the acceleration to the error signals Is very good Here the unsprung mass model error signal converges to around 15 dB lower than the accelerometer signal power The sprung mass error signal has a slightly larger decrease in power of 20 dB Both indicate that the model is doing a fairly accurate job of modeling the dynamics of the quarter car rig NG a NA ATAN 22 24 26 Unsprung Accel Power Error Power 28 Power dB 30 32 40 20 30 40 50 60 70 80 90 100 Time s Figure 6 14 Unsprung Acceleration and Error Power 95 25 Sprung Accel Power Error Power a a A Y A 35 m 2 s 40 O a A5 50 55 10 20 30 40 50 60 70 80 90 100 Time s Figure 6 15 Sprung Acceleration and Power Other interesting results include plots of the FIR model weights These can be found in Figure 6 16 The weights take the shape of an impulse response of the modeled system 96 0 8 Unsprung FIR Model Weights Sprung FIR Model Weights 0 6 0 4 0 2 Magnitude O J 0 2 0 4 0 6 0 8 0
21. distribution in the plate The simulation revealed that the plate would have no more than 0 008 in of deflection out of plane This corresponded to a von Mises stress of 5000 psi 23 This was substantially less than the yield strength of 40000 psi Based on maximum distortion energy theory yielding will not occur 24 The design of the plate is more than sufficient in strength and rigidity The rigidity helps extend the life of the bearings and reduces friction as well a b Figure 3 7 ANSYS Sprung Mass Results a Out of plane Deflection b von Mises Stress 3 5 2 Adapter Plate and Fixturing The latter component of the modular moving mass design is the adapter plate This plate 1s the interface between the suspension mounts and the sprung mass plate The design of this plate 1s specific to the suspension design The idea is to have one adapter plate per suspension tested on the rig For this study the adapter plate is made from Y in thin cold rolled steel plate This plate is designed in conjunction with the suspension 29 mounts to ensure that clearance and fastener issues do not arise The addition of this plate fastened to the sprung mass helps to further stiffen the entire moving mass More detail of the design of this plate is included later in the discussion of the first suspension application 3 6 First Application The first suspension implemented is the left front suspension from a 2004 Porsche 996 Grand Ame
22. eee k ents ta vain e potato ino 28 S 5 2 Adapter Plate and Fix U0 u u kuu suu kaka eka da e ia 29 20 Hi UAppDICaS ON to kt a a a e t t ta n is cet a e n t t a e n is el aa ia 30 3 6 1 996 SUSPENSION uu volo vi adsosas aka vokabile cian 30 3 6 2 EXE Dobi rn 32 3 6 3 Adjustmment S u unu numas a a a a ke au ayau kiya aki 33 wis GWO iOlu uhanay e ee aa e 34 M L latencia 38 3 9 Summary and Future Developments 38 3 9 1 Summary of Functional Requirements Fullilled 38 SRPA Future Enhancements yaya ke a E a sa 39 CONTROL THEORY ona a ks kd ie 41 4 1 The Adaptive Linear CombDbIn eru u al una ita 41 o Least NIC AMS AE ii 44 Ad OY SUC MA Id CAOS O a e l 45 Ak Adaptive Controla ai nun ba e rt eae a are a 47 4 4 1 General DES Crip rr A ek pa n ete a e peni sti 47 4 4 2 EN t r eX VES das 49 SIMULA TION AND RESULTS l l u aia 51 Dale Olmer O n Modelado 51 5 1 1 Mathematical Mode lus 51 3 1 2 Rarameter Valli sis 54 e Le PIC I NA lli p si tro 55 5 1 4 qu ne Y Response 39 Js System Identitication Uds ios 56 3 2 1 SHULD Mode lesir a oi t E aye 57 J22 Excitation senal SWA PLAS ia 60 3 2 5 Numerical Resu liS enn 6l do Adaptive CONnmOl SUICY sis 66 vi 5 3 1 simulink Model a ik an a ik can e tai a n n a e n ee do 67 Za Desired Response General is coa 73 5 3 3 Numerical Rests saussar m at ai n ol a e ia poset a ai po ok
23. local tool and die shop and all of the mounting points were measured with a coordinate measuring machine CMM Data from the CMM was imported directly into Solidworks to create the mating surfaces of the upright The mounting locations modeled on the upright were the strut bore tie rod taper bore lower control arm taper bore and center of the hub to locate the wheel 31 3 6 2 Fixture Design The required mounting brackets and fixtures need to offer at least the same level of adjustability as found on the car Provisions for adjusting camber caster and toe based on the required race setup were considered during the design of these components Figure 3 10 shows the final design of all fixturing for the 996 suspension Extra mass plate Adapter plate Strut mount bracket Y axis LCA mount Z axis LCA mount 2 2 piece tie rod mount Z axis LCA mount 1 Figure 3 10 Detailed View of Modeled Suspension and Mounts The figure shows the lower control arm LCA mount 1s a three piece design Because the LCA is actually a two piece design there needed to be separate brackets for each part of the arm to allow for adjustment in the Z direction when referring to the axis coordinate system in the figure The two ends of the LCA bolt to mounts 1 and 2 respectively The back faces of these mounts have slotted holes for adjustment in the Z direction independent of one another The first two brackets bolt to a third plate that h
24. ni gt a i bis ki ki d a Sl BA j oe id i q k alye i I n a T ON L 3 y 5 x zi a rat Q La I Gn en A n e E Er A AAA a PO a ee TA To ca ie gt 1 4 l 4 1 fa a a i n nan m Dm lay ir Los k e DW kaa Figure 3 5 Finite element Beam Model of Reaction Frame The modal natural frequencies of the structure were investigated with finite element analysis as well Using the same beam model as before the feet of the structure were constrained in all directions and a free vibration modal analysis was performed in ANSYS The results of this analysis showed that the first modal frequency of concern was nearly 200 Hz This is comparable to the results of another study which yielded a 500 Hz first resonant frequency for the test specimen s superstructure 20 These resonant frequencies are much higher than those of interest in vehicle dynamics In many tests the frequency band of interest is only 1 to 25 Hz 2 3 3 3 Functionality The results of the analyses of the frame indicate that it is very rigid compared the rest of the experiment This minimizes sensor noise from excitation of the load frame To make the frame fully functional an 8 in x 8 in x 1 in steel pad was welded to the bottom of each corner These pads are used to clamp the fixture to the base plate Once fully welded the entire load frame was machined as a unit The feet were all milled to within 0 003 in flatness of one another
25. the center section is lightened to increase the natural modes of this constrained membrane Figure 3 5 1s an image from ANSYS showing the finite element beam model created Two analyses were performed to aid in the design of the frame First deflection of the frame in the out of plane direction was simulated with a lateral suspension load Though this rig is not designed to test lateral forces at this point the suspension components will resolve normal forces at the contact patch into some combination of lateral forces on the rig Thus the lateral force used for the deflection analysis was well beyond that which the suspension could create in pure jounce Minimizing the deflection of the frame was necessary to reduce friction created by the bearing rails which mount directly to the frame Just to ensure the strength of the load frame allowed for testing flexibility a steady state lateral force of a 6000 lb vehicle in an extreme cornering event was simulated to be acting on the load frame The result of this simulation showed that the deflection of the frame was less than 0 010 in which was significantly below the allowable misalignment of 375um 500mm rail length specified by the bearing manufacturer This ensured proper low friction bearing operation 24 j m A h i 1 i Mi i f PPY oes i o ai y 7 n Eka rita n iw i TA in A I tine i E Ti Yn L care ke kou k E Y A A n A a et pa LIT A oo ki a em
26. tire attached the representative corner of a car is supported by the actuator via the wheel pan The sections that follow detail the design of many of these major components of the rig 3 2 Base Plate In any laboratory test an engineer wishes to have as much control of the test specimen s environment as possible Particularly in vibrations and control tests any fixturing used must be designed such that the dynamics of the fixture do not affect the dynamics of the test specimen Some studies used a welded steel structure and base plate which weighed in excess of 12 tons 17 18 To this end the base plate needed to be heavy and rigid The base plate was specified and sourced by BayCast Technologies 19 3 2 1 Plate Design The specified base plate is an 84 in x 60 in x 7 in purpose build cast iron plate The plate is hollow with a stiffening rib structure on the under side It weighs approximately 2500 lbs The base plate is anchored floor via four 1 in anchors one for each corner of the base plate The anchoring system works as follows The 1 in all thread anchors were secured to the 8 in thick concrete floor with epoxy With the epoxy cured the base plate was lowered down over the anchors Fixed nuts in the base plate thread the plate down these anchors such that it was actually floating over the floor The full weight of the plate was supported temporarily by the anchors This allowed the plate to be leveled to within 0 1 via BayC
27. to convolve the FIR controller weights with the original unknown plant To do this the frequency responses of the controller weights and the original plant were computed These two frequency responses were multiplied together Also the frequency response of a 115 sample delay was calculated and then divided into the resulting frequency response Both of these calculations were done on an element by element basis at each frequency Division by the delay response function was performed in order to see more clearly the phase response The resulting frequency response of the convolved transfer functions 1s shown in Figure 5 23 78 Phase deg 10 10 10 10 Frequency Figure 5 23 Frequency Response Function of the Convolved Controller and Plant This plot clearly shows how well the adaptive inverse controller works As expected the convolved controller and plant act as a feed through device only over the frequencies of interest This is indicated by the O dB magnitude of the frequency response between 3 60 Hz It is also noted that there Is a zero phase shift in this frequency range as well Below 3 Hz the controller appeared to have some trouble identifying the inverse of the plant This is likely due to lack of power in the low frequency
28. to go through One end of the strap is resting on the object to be held in place and the other is resting on the step block with the teeth of each being meshed The top nut is then turned down to apply a clamping force on the clamped object 21 Figure 3 3 T slots in Base Plate Nut with washer Stud Block Clamp strap Clamped Tit object Figure 3 4 Clamping Hardware The combination of the machined surface and T slot system allows for a vast amount of adjustability and also for precise positioning of the actuator under the tire This adjustability allows the rig to accommodate a wide variety of suspension component sizes like long control arms of up to 22 inches as well as wide racing tires In summary 22 the base plate s functionality lies in it rigid design to reduce unwanted noise in test signals and its ability to accommodate a vast variety of suspension configurations 3 3 Reaction Load Frame For the same reasons as the base plate design the reaction load frame also needed to be extremely strong The reaction frame is the tall triangulated steel structure that 1s clamped to the base plate Together the reaction frame and base plate work to create an excellent rigid ground for the vibration experiment to work on The reaction frame s additional functionality lies in its ability to be placed at various positions on the base plate allowing for a large range of suspension designs and sizes 3 3 1 Frame Desig
29. when the control details are discussed in Chapter 4 2 1 Vehicle Testing Rigs It is clear that the main purposes of a shaker rig regardless of the number of posts are to evaluate noise vibration and harshness NVH perform durability tests and or improve vehicle performance 4 5 6 These goals vary slightly depending on the nature of the industry in which they are applicable The automotive manufacturing segment would primarily be interested in NVH and durability but on some occasions may want to improve the handling of their vehicle without spending countless hours on a proving ground The racing industry 1s slightly different They are not as likely to be interested in NVH however durability and particularly performance metrics such as handling and suspension tuning are critical For these tests knowledge of the road input 1s extremely important especially if the desire is to simulate the surface of the track and characterize vehicle response If complete knowledge of the road profile were known this would undoubtedly improve the efficiency of 7 post software However this information is seldom actually known particularly in the motorsports industry Even if the road profile 1s known precisely it tells the test engineer nothing about other dynamics the vehicle endures such as inertial and aerodynamic loading This information is often calculated based on maps lookup tables or vehicle models running in software such as ADAMS These ty
30. 02 LMS Algorithm 0 001 0 000 Z id leyoutipo k id weights pg control_layo bz control wel x K Log Viewer A Interpreter A File Selector A c documents and settings langdonlid_and_control_dspacelcombinedid_dspace sdf or Help press F1 RUN 12 15 2006 11 58 Figure 6 20 Screenshot of Control Desk Real time Control Interface 102 q car to box 2 power ControlDesk Developer Version control weights 4 File Edit View Tools Experiment Instrumentation Platform Parameter Editor Window Help Mic ed EN WSs S b wht n Bit li y E Xx O Ll A 0 003 0 002 KE A Onl 0 001 PS RA a ak ak ak ak n n a ZON 200 308 500 600 700 800 900 gt 1000 SA 400 1200 1300 an 1500 600 BO ai os oooo N ww y w li am KE ae oe ad me o a ee ow a m a oom foe os 1 ki G ai I 0 010 yes p nis A an AA al x Log Viewer Interpreter A File Selector c documents and settings langdond_and_cortrol_dspacelcombinedid_dspace sdf Y id layoutipo 154 id weights Sd control_layo be control wet or Help press F1 EDIT 12 15 2006 12 01 Figure 6 21 Screenshot of Control Desk Real time Control Weights 6 4 2 Desired Response Generation For the control experiment a desired response was first needed for reproduction The first step in proving this concept was to collect data off of the quarter car rig itself Obviously if da
31. 10 Wa Wi MWER y U ER 23 Thus the adaptive inverse controller for a single path may be adapted by the error signals of several paths in the same dynamic quarter car model This is a very common modification to filtered x LMS gradient descent adaptation algorithms 5 3 2 Desired Response Generation To run this controller simulation some experimentally collected data was required Since this portion of the study was performed purely in simulation the response data was also created using a MATLAB program To produce the response data a filtered white noise was input to the original continuous time quarter car simulation This white noise was shaped in much the same way as the excitation noise used for system identification The filter chosen was a four pole Butterworth filter with a 50 Hz break frequency The break frequency was chose to be slightly lower than the identification white noise filter break frequency It is good practice to use higher identification bandwidth than what the specimen normally sees in a test This 1s to ensure that all of the dynamics are properly captured by the ID model A vector of white noise was created using the randn m function in MATLAB The low pass filter was created and the white noise was filtered through it using the filter m function Finally the filtered white noise input was simulated through the continuous time state space model using the Isim m command The resulting ac
32. 13 ar STE sod U a Ilaso o lawod F oT LI lg AA OL 3013 spu Bunids TRIO z TSUBTS 2 Et peat sap Jo amod ssuod g9l serum bunaids pazt sf THU TE z Tzor 7148 0 isha ur 14 Detailed Simulink Diagram of Control Block Figure 5 70 The desired unsprung mass acceleration signal 1s fed into the adaptive filter which is being adapted with the usual LMS algorithm The output of the filter is a drive profile called drive u in the block diagram This signal then sent out of the control subsystem to the DAC block and thus fed to the state space model The response of the model is then fed back into the control subsystem at the input blocks labeled y_accel The desired signal is also fed into a delay block called Integer Delay This block delays the desired signal before the signal is compared to the output of the quarter car model The error 1s produced by subtracting the actual response with the delayed desired signal A programmable gain or step size mu y is then placed on the error signal which is then fed into the adaptive algorithm The other input to the adaptive algorithm 1s the filtered X signal This signal is the output from the x filter y block This block has two inputs the desired unsprung mass signal and the FIR filter model identified in the previous step This vector of weights is brought into the subsystem at the Wy block in Figure 5 14 Insid
33. 180 90 90 180 50 Phase deg ATEO SS Spurng SS Unsprung Sprung ID Model Unsprung ID Model 40 30 20 Mag dB o 30 10 10 10 10 10 Frequency Hz Figure 5 11 Comparison of Model and Adaptive Filter Frequency Responses Referencing the phase portion of the figure the FIR model for the unsprung path does not match the state space quarter car model below 1 Hz This is because accurate phase measurements cannot be made when the transfer function magnitude is so small In any case the FIR adaptive filter does still replicate the dynamics of the quarter car analytical model very well 5 3 Adaptive Control Study The second half of the simulation study was to control the quarter car model such that it replicated a pre made acceleration signal Again a Simulink model was created to implement the simulation The adaptive inverse control algorithm also introduced in Chapter 4 was implemented to accomplish this task The identified FIR filters from the previous section were used in the filtered X LMS algorithm 66 5 3 1 Simulink Model The Simulink model was designed to take the basic shape of the model whic
34. 4 Wodh IH A 0 10 20 30 40 50 Time s Figure 5 6 Error Convergence of Sprung Mass Numerical Model Identification 61 Unsprung Acceleration Model Error hil Acceleration G O 0 10 20 30 40 50 Time s Figure 5 7 Error Convergence of Unsprung Mass Numerical Model Identification Figure 5 6 and Figure 5 7 are plots showing how the error converges with time The error is placed over top of the mass acceleration response for both the unsprung and sprung masses The error convergence happens quite quickly For the sprung mass identified model the error 1s minimized in about thirty seconds It takes up to about fifty seconds for the error to converge to a comparable level for the unsprung mass path The root mean square RMS of a converged section of the error signal for the unsprung mass was compared to the RMS of the unsprung response signal This comparison showed that the RMS value of the error converged to within 2 3 of the RMS of the unsprung acceleration signal Likewise the RMS value of the error signal for the sprung mass converged to less than 1 of the RMS value of the sprung mass response Another way to interpret error convergence 1s by looking at the accelerometer signal power versus the error signal power The signal in either case 1s calculated by squaring the signal and the filtering 1t with a low pass filter Again a B
35. Design and Adaptive Control of a Lab based Tire coupled Quarter car Suspension Test Rig for the Accurate Re creation of Vehicle Response by Justin D Langdon Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Mechanical Engineering Dr Steve Southward Chairman Dr John Ferris Dr Corina Sandu January 31 2007 Danville VA Keywords quarter car test rig adaptive inverse control system identification suspension vehicle response replication Design and Adaptive Control of a Lab based Tire coupled Quarter car Suspension Test Rig for the Accurate Re creation of Vehicle Response by Justin Langdon Dr Steve Southward Chairman Abstract The purpose of this study has two parts directed toward a common goal First a state of the art quarter car test platform has been designed and constructed to offer increased testing flexibility at a reasonable cost not found commercially With this new test rig completed the second objective is a proof of concept evaluation of a well known adaptive control algorithm applied to this new quarter car test rig for the purpose of replicating the dynamic suspension response such as a response that was recorded during aroad test A successful application of this control algorithm on the quarter car rig 1s the necessary first step toward its application on an 8 post t
36. Ry 22 Again this equation 1s similar to that of 10 The filter is then sent through a unit delay and then dotted with the tapped delayed desired signal The product of this dot product is the output of the adaptive inverse control filter This output signal is also considered the new drive signal for the quarter car model This process continues to adapt the FIR filter until the error between the desired response and actual response 1s minimized Closer examination of Figure 5 14 and Figure 5 15 reveal that there is an additional error loop There is not an additional set of control filter weights but this is not a problem The aforementioned control filter may also be adapted using the error between the sprung mass desired response and actual response from the quarter car model Referring back to Figure 5 14 the desired sprung mass response data is introduced into the control subsystem the same way but this time it is only used to produce an error signal and not fed into the controller This signal is routed into the adaptive LMS algorithm the same way as the unsprung error signal This signal is run through the identified input to sprung mass output model at the x filter z block The 72 resultant Rz Is fed into the adaptive algorithm and the same tapped delay and multiplication process takes place to help adapt the FIR controller weights The resulting equation for the weight adaptation shown below is a slight modification of
37. S engineers The functional requirements of this system were to have a high load capacity for a wide range of vehicles and a high actuation bandwidth to allow for a wide range of tests The actuator is an MTS Model 248 03 linear hydraulic actuator capable of 5 5 Kip force It has a dynamic stroke of approximately 3 in The actuator shown in Figure 3 12 has hydrostatic bearings to give 1t high side load capability should some lateral force become generated in the tire contact patch The piston was custom made to be light weight and strong to provide a bandwidth of over 150 Hz at low amplitude The actuator 34 has an inline linear variable displacement transducer LVDT and a delta pressure cell for position or force feedback to the controller respectively A wheel pan was custom made from 6061 aluminum to keep the working mass low The first natural frequency of the wheel pan was found to be over 200 Hz using finite element analysis This ensures that unwanted excitation does not appear in a test Figure 3 12 MTS 248 03 Hydraulic Actuator The flow of hydraulic o1l is regulated by two Moog Model 252 25G 01 4 Port servovalves These valves seen in Figure 3 12 are two stage valves giving them a bandwidth of nearly 300 Hz Each valve is rated at 15 gpm flow rate These valves work together to increase the response of the actuator and yield as much bandwidth as possible Hydraulic power 1s supplied by an MTS Model 505 03 SilentFlo hydraulic po
38. The goal is to match this to the desired response Meanwhile the same desired response 1s delayed through a delay element This delayed desired signal 1s then subtracted from the output of the plant to give the error This error is then fed into the LMS algorithm which adapts the weight coefficients of the adaptive filter The other input to the LMS algorithm 1s the filtered X signal This signal 1s created from concurrently sending the desired signal through a plant model The adaptive filter is adjusted until 1t creates an input to the plant that causes the plant to respond as desired This minimizes the error between the plant response and the desired response This process is discussed in detail in the following section V jes Adaptive Filter Ug Plant Desired Plant Input W P Response drive file a Identified plant R a model from E LMS Algorithm K e System ID filtered X Error Yaelayed Figure 4 4 Filter X LMS Adaptive Inverse Control Block Diagram In this study the input to the plant or drive file needed to create this desired response is unknown but it is known that the input is correlated to the desired response In order to create this drive file the desired response is fed to the adaptive filter as it is adapting While it converges the drive file signal converges as well This optimal Input drives the plant to produce the desired response Upon convergence the adaptive filter 1s actually an inverse of t
39. _on off Outl Reference Capture Capture Variables Take Save TA 0120t012 ID ID enabled Enable Disable Actuator Actuator signal strenght On 0 150 a RZ idlayout id_weights B control_layout K control wei de El K Log Mewer A Interpreter A File Selector c Wocuments and setingslangdon id and control dspace eombinedid dspace sdf fi For Help press Fl RUN SCRL 12 14 2006 17 05 Figure 6 9 Control Desk Layout for System ID Accelerometer Error Plots and Control Panel 90 o E q_car_to_box_2 power ControlDesk Developer Version id_weights bz File Edit View Tools Experiment Instrumentation Platform Parameter Editor Window Help o x ws Z BY wes UR ate a FEB 48 gt e MA 300 400 Wy_weights 400 Wz_weights File Selector c idocuments and settings langdonid_and_control_dspacelcombinedid_dspace sdf For Help press F1 RUN SCRL 12 14 2006 16 53 Figure 6 10 Control Desk Layout for System ID FIR Weight Vector Plots These panels allowed for ease in knowing when the system ID weights converged The weights continuously updated as they were adjusted The control panel has the ability to adjust the step size and the amplitude of the excitation signal It was also possible to toggle the low pass filters on the accelerometer signals on and off as well as capture all of the signals Also included were buttons for enabling and disabling the ID subsystem as well as
40. adaptive model The output of this model Wx is then fed to the unknown plant in this case a vehicle suspension The output of the unknown plant y which equals TWx is then fed into a copy of the adaptive filter The outputs of each adaptive filter are then compared to create an error The error is e 1 TW Wx 1 This error is then fed into the LMS algorithm which then updates both adaptive filters identically This method is different from that presented in this study for several reasons First the data used to update the filters via LMS 1s different Second the algorithm here uses two identical adaptive filters where as that presented in this research only uses one adaptive control filter and one identified model Finally the error calculated in this control scheme is compared from the outputs of two adaptive filters rather than comparing the response of the unknown plant to the desired response directly The second algorithm presented in this patent is shown in Figure 2 7 In this algorithm a different approach is taken A derived or corrected drive file indicated by 102 is fed directly to the unknown plant The output of this plant is then fed to an inverse plant identifier 36 which contains the LMS algorithm At the same time this corrected drive file is also fed into this same plant identifier Meanwhile the output of the unknown plant shown as 52 is then compared to the actual desired response 12
41. amically controllable roll degree of freedom on the sprung mass This additional degree of freedom would allow the suspension geometry to be changed by simulating a low frequency body roll as would occur in a cornering event The body roll changes the suspension geometry and replicates a non linearity that most other single post rigs do not account for Many of the findings that may result from these potential studies could be applied to more complex testing rigs 40 4 CONTROL THEORY The control of this test setup is based on two well known principles These are the adaptive linear combiner ALC and the least mean squares algorithm LMS Chapter 4 introduces these two concepts in detail The chapter then discusses the application of LMS and the ALC to system identification The chapter ends with a similar discussion of application to adaptive control This will familiarize the reader with the control concepts used in this study 4 1 The Adaptive Linear Combiner The ALC is an adaptive finite impulse response FIR filter that is a fundamental building block in adaptive signal processing This time varying filter is shown in Figure 4 1 In this instance the ALC is represented for a single input X Figure 4 1 The Single Input Adaptive Linear Combiner For the single input case the ALC functions as follows The input X is sampled by a tapped delay line which creates a sequence of delayed values from the same source sample
42. and maintain They also present other difficulties These rigs are very sophisticated muli input multi output MIMO systems which require a high degree of control knowledge and understanding to use properly Often the complex nature of these multivariable problems requires multi step iteration to obtain a suitable drive file for commanding each of the actuators Once converged data is extracted from tests run on these systems it is often very difficult to interpret and correlate to the real world counterpart Some reasons for these issues with more complex test rigs are the lack of literature and other available documentation 7 8 To the authors knowledge only a handful of papers that discuss multi post test to any detail exist 2 4 9 10 It is likely that the lack of available information is partially due to race teams and automotive companies trying to protect their competitive advantage 2 1 2 Current Quarter car Rigs As an answer to the high complexity and expense of these systems simpler test beds such as the quarter car test rig are used A rig such as this reduces the complexity greatly by only focusing on one corner or quarter of the vehicle These may be considered one post or two post systems Often these systems can be viewed as a single input single output SISO This greatly reduces computational time and complexity and often a closed form solution may be reached This allows for much better understanding of both the proble
43. as holes slotted for adjustment in the Y direction This plate mounts to the adapter plate A detail of the adjustment motions of this three piece design 1s shown in Figure 3 11 32 Figure 3 11 Detailed View of LCA and Tie rod Brackets Showing Adjustment Directions A similar design for the inner tie rod mount allows for two axes of adjustment of the inner tie rod pivot The tie rod threads into the Z axis mount which bolts to the Y axis mount which bolts to the adapter plate This two piece bracket design 1s shown in the previous figure as well The strut mount bracket seen in Figure 3 10 offers two axes of adjustment This bracket mounts to the adapter plate and has slotted holes allowing for Z axis adjustment The strut mount seen in Figure 3 9 has three studs that go through slotted holes in the bracket These holes are slotted in the X axis direction The strut mount connects the strut to the strut bracket which then fixes the assembly to the adapter plate With all of the brackets designed and modeled everything was assembled in Solidworks along with the suspension Once assembled the components were adjusted until the actual 996 suspension geometry was replicated At this point the appropriate holes were positioned in the adapter plate such that the plate could bolt to all of the brackets and the sprung mass plate in order to complete the adaptation 3 6 3 Adjustments With the manufactured parts i
44. ast s proprietary Level Tite system Once the plate was leveled jam nuts fixed the position of the plate With the plate fixed in place it was then filled with a non shrinking grout The grout filled the underside completely and 20 allows the plate to distribute loads over its entire footprint on to the floor The fully anchored plate 1s actually an extension of the concrete floor The working face of the plate is machined flat to within 0 005 in and has cast in 7 8 in T slots 3 2 2 Functionality The anchoring system and structural design of the plate makes it extremely heavy and rigid This gives the plate much higher natural modes than the test specimen which helps to reduce error in tests The extremely flat surface ensures that the forces being introduced into the suspension are well defined Misalignment of the actuator to the motion of the sprung mass would introduce undesired forces such as lateral force when only vertical response is of interest These lateral forces can cause extra non linearities between the input to output relationships of the system The load frame and actuator are secured to the base plate via the T slots in Figure 3 3 and the appropriate hardware shown in Figure 3 4 The hardware uses a T nut that is designed to fit in the T slots in the base plate The stud threads into the T nut The block has stepped teeth and the clamp strap has the same teeth as well The clamp strap has a slot in the middle for the stud
45. at example of what makes a quality person in life For those that don t know you lettered in three major sports in college obtained a Master s degree and served your country Thanks for the lessons in calculus and in life I would like to thank all of my friends at home and at school for being there along the way Tom Jimmie Wilbur and Matt at home you guys provided the wrenching gaming beer drinking shenanigans type of fun which was a great escape from being stuck in an apartment in Danville Here s to more in the future I also want to thank all of my friends at school The jam session gatherings were awesome I expect more in the future 111 I really want to thank my girlfriend Stephanie for putting up with so much crap You supported me in ways that I would never dream of asking anybody You handled my traveling and stress way better than I ever could Most of all I want to thank God and my parents Bonnie and Dave Without you none of my achievements in both school and life would be possible I will never be able to repay you for the doors you have been able to open up for me Without you guys I would probably be looking up car parts behind a counter in town I don t think a person could ask for better parents I want to thank all of my family for their support in my school and work endeavors 1V Contents Acknowledo ments AAA o io e bean an code ea aks ke visa kaa nas ede saaa ill List OF Nomenclature ices a w da uu ki ja
46. at the beginning of the chapter The outputs are then separated or demuxed and output to the ID and controller Inside the ID subsystem are the exact same inner workings discussed in the previous section The only exception is the relocation of the state space model such that 68 the controller is able to have access to it The details of the controller are illustrated in Figure 5 14 The goal of this simulation 1s to replicate a pre defined acceleration signal on the previously identified quarter car model When viewing Figure 5 14 in a landscape format the block diagram will be discussed starting with the desired signals on the far left For this problem there are actually two signals for which replication 1s desired This is obvious because there are two moving masses in the quarter car model Unfortunately there is only one input to the system Therefore there can only be one controller Only one of the desired signals can actually be input to the controller as the reference signal The controller is an inverse of the plant being controlled Since the plant actually has two transfer functions associated with 1t only one path can be inverted The unsprung mass signal was chosen as the reference due to 1ts higher frequency content and what would likely be a more interesting result in the racing industry To begin the discussion the focus will be on shaded portion of the diagram 69 Ti a Bunids kal E UTE 303 2148
47. ated in the shaded box The input to the in this case 1s a filtered white noise excitation This signal is fed to the adaptive filter and also to the discrete state space model of the quarter car The 57 state space system outputs an acceleration signal for the unsprung mass At the same time the adaptive filter block is adapting weights of the ALC using the LMS algorithm introduced earlier The output of the filter is also an acceleration signal To understand the mechanics of implementing the algorithm in a Simulink model the adaptive filter blocks labeled Sprung mass adaptive filter and Unsprung adaptive filter are expanded from Figure 5 3 This detailed representation 1s in Figure 5 4 Here the same unsprung mass adaptive loop 1s still highlighted by the shaded box Following the input to the filter more closely the input signal goes to a tapped delay block This block samples the input signal and files 1t into a vector format such that the first entry 1s the most recent signal and then the one before and so on This is block performs the exact function of the tapped delay line discussed in section 4 1 This vector of tap delayed inputs X k is then split The signal is then dotted with the vector of weight coefficients labeled Wu k This dot product is the same mathematical process as in equation 3 The result of which is the output acceleration of the adaptive filter 58 TPPW siuetotjjeod YTW bunads Tyon
48. atform The mechatronics test system provides an accurate repeatable and highly efficient means of performing software and hardware development and validation tasks currently executed with prototypes on the proving grounds This quarter car rig has much of the flexibility seen in the rig developed for this study A picture of this rig is found in Figure 2 4 This quarter car rig has a sprung mass loader based on a force feedback servo hydraulic actuation system It also incorporates an actual vehicle suspension This test bed is only a prototype and is not commercially available 10 Figure 2 4 MTS Mechatronics Development and Validation Bench reproduced with permission A short video of another quarter car rig developed by ServoTest was found This example is captured in Figure 2 5 Here a MacPhereson strut type suspension from a World Rally Championship Car 1s being tested The details of this rig and origin of the video were not disclosed however 11 Figure 2 5 ServoTest Quarter car Rig reproduced with permission 2 1 3 Functional Requirements After reviewing the operational functions offered by the current state of the art the following requirements were proposed for a new quarter car test rig e Design for a variety of different actual suspension hardware to be mounted and tested thus including the kinematics and dynamics of the vehicle s suspension geometry e Design for a large range of vehicle corner weights ra
49. bearing side of the plate was pocketed heavily leaving a ribbed support structure The plate has an array of threaded thru holes which are used to fasten the adapter plate to the sprung mass Not all holes are used at the same time as some suspensions may block certain holes depending on their locations The finished plate weighs approximately 150 lb Though this is extremely light for the corner weight of a vehicle the mass increases with the addition of the adapter plate fixturing and fasteners Extra weights have been made that can bolt to the back of the sprung mass to adjust the mass according to the corner weight of the vehicle in increments of 30 lb As much as 270 lb can be added to the back side alone Again ANSYS was utilized as a design tool for the sprung mass The plate was loaded as a quasi simply supported beam to find the maximum deflection and stress in the plate For this study it was assumed that the rig could be used for lateral loading 28 some point in the future Therefore a large vehicle weighing 6000 lbs was assumed to be in a tight steady state turn The assumption is that a single wheel might be supporting as much as half the weight of the vehicle Thus a lateral force of 3000 lbs was chose for the deflection load case This load was applied to a small pad in the middle of the plate and the plate was constrained in all degrees of freedom as the bearing carriers Figure 3 7 shows the out of plane deflection and stress
50. cation on Porsche 996 suspension setup and Grand American Racing regulations with Greg Jones and Richard Binzer Synergy Racing 2006 119 27 28 29 30 31 32 33 34 35 36 Widrow B Stearns S D Adaptive Signal Processing Prentice Hall Inc Englewood Cliffs NJ 1985 Widrow B Walach E Adaptive Inverse Control Prentice Hall P T R Upper Saddle River NJ 1996 dSPACE digital signal processing and control engineering GmbH User s Manual Control Desk 2005 Vaes D Swevers J Sas P Experimental Multivariable Tracking Control on an Automotive Vibration Test Rig ISMA Proceedings of the 2004 International Conference on Noise and Vibration Engineering ISMA p 311 323 2004 Oral H A A Tool for Control Algorithm Development of an Active Vehicle Suspension Using Hardware in the Loop SAE Technical Paper Series No 2002 01 1597 Warrendale PA 2002 Fricke D M Hansen M D Chabaan R C Ford Motor Company Effective Road Profile Control Method for a Spindle coupled Road Simulator US Patent No 5 610 330 1997 Kino H Iwai M Tamura M A Study of Road Load Severity Prediction in Market for Power Spectrum Density SAE Technical Paper Series No 2003 01 2867 Warrendale PA 2003 Moran T Sullivan M Menmuir D Mahoney J Replication of Heavy Truck Dynamic Wheel Loads Using a Road Simulator Road Transport Technology 4 University of Michigan Tran
51. cecar to HMMWV e Design for sprung mass external forces such as aerodynamic loading and or weight transfer e Design in flexibility to add future functionality such as vehicle roll or rotating and or steering the tire These functional requirements are made such that a new state of the art test rig would be as flexible as possible allow for more accurate and realistic representation of the test vehicle and achieve these goals as inexpensively as possible 12 2 2 Control of Rig Response A literature review was performed on the control of vehicle shaker rigs All servo hydraulic actuation systems have displacement feedback control loops at the innermost level These loops accept a displacement input reference command which the servo hydraulic system tracks within the designed PID inner loop bandwidth Here interest 1s in placing an additional feedback control loop around this inner loop Particularly the application of adaptive inverse control was searched The usual function of a control system on such test rigs 1s to identify a drive file such that the response of the specimen recorded during a road test is replicated on the rig Several methods for performing this task on quarter car and complex shaker rigs exist however none utilize the particular algorithm implemented in this study In this study a proof of concept 1s being evaluated to find another viable method for controlling these shakers Once proven feasible the algorithm u
52. celerations were stored for later use A sample of the desired acceleration signals are plotted in Figure 5 16 The acceleration magnitudes of the desired signals are somewhat small This is not an issue in practice because the system is linear 73 10 Unsprung Sprung a Acceleration G N A VAN NA MAN l VAN NO IV 8 550 550 2 550 4 550 6 550 8 551 Time s Figure 5 16 Sample Desired Acceleration Response Generated with State space Quarter car Model 5 3 3 Numerical Results The results of this numerical study indicate that adaptive inverse controller was able to produce an input to the quarter car model that reproduced the desired accelerometer signals very well The usual tuning parameters were adjusted to improve the convergence and results For the final configuration the number of inverse adaptive control filter weights was set to 350 The step size for the unsprung mass was set to 1 3e 8 and twice that for the sprung mass loop The z delay on the desired signal was set to 115 samples 74 0 015 Desired Unsprung Mass Response Unsprung Mass Error 0 01 0 005 Acceleration G O 0 005 0 01 0 015 0 100 200 300 400 500 600 Time s Figure 5 17 Unsprung Mass Desired Response and Error Convergence
53. cle response signals Finally the last goal 1s to be the first to publish results such as convergence rates of such a study 1 3 Approach To achieve these goals the following approach is taken Current quarter car test rigs and the state of indoor testing in general are first evaluated The approach is to develop a quarter car test rig that addresses many of the shortcomings found with the state of the art while trying to minimize expense In the future the design will allow for expanded functionality as defined in this paper Having constructed a quarter car test rig the next step 1s to evaluate an adaptive inverse control AIC algorithm as it applies to vehicle dynamics testing Specifically a least mean squares LMS algorithm 1s utilized to reproduce vehicle acceleration response from a previous test This algorithm is first simulated purely in software to evaluate its effectiveness Finally a real time implementation of the algorithm is applied to the quarter car test bed for hardware in the loop testing to validate the control scheme Actual acceleration response will be reproduced on the sprung and unsprung mass of the quarter car rig 1 4 Outline The following is a brief outline of the chapters to come Chapter two provides the background for this study which includes a literature review of current quarter car test rigs Also reviewed are the current control strategies used on more complicated rigs such as 4 post 7 post
54. ction Input auto correlatlon matrIx cross correlation between desired and input signals optimal weight vector small gain constant or step size gradient linear transfer function matrix state space state vector state space output state space input continuous time state space matrices discrete time state space matrices unknown plant output plant noise unknown plant filtered x desired signal Vill e S lt N identified plant FIR model sprung mass unsprung mass suspension stiffness suspension damping coefficient tire stiffness damping ratio sprung mass degree of freedom coordinate unsprung mass degree of freedom coordinate road input to tire patch kinetic energy function potential energy function damping pseudo energy function th 1 degree of freedom coordinate IX List of Figures Figure 2 1 Image of ServoTest 7 post Test Rig reproduced with permission 6 Figure 2 2 Simplified Quarter car Test Rig VT AVDL 9 Figure 2 3 Quarter car Rig for Component Testing adopted from http labtech org 13 iaa E ken 10 Figure 2 4 Mechatronics Development and Validation Bench reproduced with Dei nis iO AM it E a e a a ko ane a ad pata 11 Figure 2 5 ServoTest Quarter car Rig reproduced with permitssion 12 Figure 2 6 Prior Art Algorithm from U S Patent No 5 394 071 14
55. ction details the process of system identification in the hardware environment The test performed was virtually the same as in simulation but now the quarter car state space model was replaced with the real hardware 6 3 1 ASPACE Model The Simulink model compiled for dSPACE was virtually the same as the code for the simulation environment seen in Figure 5 4 Figure 6 8 is the system ID enabled subsystem in Figure 6 6 expanded Again two identical blocks were used for each of the input to output paths All of the output blocks seen in Figure 5 4 are no longer necessary as the code is running on the stand alone control box Instead the data can be collected using capture functions in the dSPACE Control Desk Software The product and low pass filter blocks which are terminated are to compute the power level of the accelerometer and error signals These power levels along with the regular signals can be viewed in and saved with Control Desk 88 Jous SIN 104e U IU cloJeu ua Loue nw poul pole una ES Lonpolg 100 apoul z Jamod jane z P Jemod ole A pPnpolg 100 Jamod jade A YOJIMS ZAA conpold T GPNnpOld Joa sew Gunidsun oJaz JUblam A UMS A elonpolq 10119 SSE oaz Jyblam Z siybiam Z jae Z LAB eq nun slybiam A Aejaq yun ZJOJEU ILLUS UW Jamod joue Z Pnpold pnpoid PNP Ae jag pedde
56. cy Response of FIR Controller Convolved with Plant for 30 Hz Unsprung Mass Response Data xiii List of Tables TaBe Setup fan SE TON 996 oia n e a ka rt a in an kaa a 34 Table 2 Quatter car Model Parameters uyu uu u uy un toke kaka dead ske 54 Table LD Error Omi AN SON a 94 Table 4 15Hz Replication Controller Error Compartison 108 Table 5 30Hz Replication Controller Error Compartison 113 X1V 1 INTRODUCTION This chapter provides motivation for the research presented in this thesis by describing some of the difficulties inherent in vehicle development Next the objectives and approach to achieve the goals of this study are explained The chapter ends with an outline of the thesis 1 1 Motivation For as long as products have been under development engineers have struggled with the trade off between research and development time and quality or performance of the product under development This is especially true in the automotive and motorsports industries In the automotive industry it was said that the necessity to continuously improve the efficiency of research and development was due to things such as changing market demands 1 In the motorsports industry the same 1s true although the market in this case 1s dictated by the performance of one s competition Other constraints in motorsports
57. d every T seconds The z blocks in the figure represent a unit or sample delay Thus the input is successively sampled and multiplied by a gain w which multiplies the n input sample at time k In other words an input can be thought of as a vector with 41 the first element being the most recent sample x followed by the previous sequence of data Xx X _ going back in time The weights are also contained in a vector that when dotted with the input vector yields the output at that particular moment in time This can be expressed as E E gt Wik Xk 2 l 0 This can also be represented in vector form in 3 YE W X 3 If the weights were constants this would be a linear system However the adaptive part of the filter is the time varying weight vector The weights are time varying because they are continuously changed to meet some performance criteria Normally the goal of changing the weights is to reduce the error between the output of the FIR filter and some known signal This desired signal is added to the ALC shown in Figure 4 2 Desired Signal d j OE gt Output Error Signal Figure 4 2 The Adaptive Linear Combiner Compared to a Desired Sienal 42 The output of the filter y is normally subtracted from this desired signal denoted by d to produce an error at time k This error is denoted by Thus the error signal is given in 4 when a substitution Is made from 3 ed
58. dSPACE AutoBox Control Prototyping Box 83 nstrumentation LA YOU AAA 84 Xi Figure 6 6 High Level Simulink Model Modified for dSPACE 86 Figure 6 7 Detail of DAC and ADC and Connection to External Hardware 87 FEis re 6 9 Detailed Simulink Modertor UD esse arab dida 89 Figure 6 9 Control Desk Layout for System ID Accelerometer Error Plots and Control A S E E PAE E hapasta seared aac E E tates agama aes e ate ian 90 Figure 6 10 Control Desk Layout for System ID FIR Weight Vector Plots 91 Figure 6 11 Frequency Response of White Noise Excitation Low Pass Filter 92 Figure 6 12 Unsprung Mass Acceleration Response and Model Error 93 Figure 6 13 Sprung Mass Acceleration Response and Model Error 94 Figure 6 14 Unsprung Acceleration and Error Power 95 Figure 6 15 Sprune Acceleration and PO Wa 96 Figure 6 16 Experimental FIR Model Weiphts 97 Figure 6 17 Frequency Response of the FIR Identified Model 98 Figure 6 18 Real time Control Simulink Block Diagram 100 Figure 6 19 Details of the Real time Filtered X LMS Aleortithm 101 Figure 6 20 Screens
59. e a small spike near 55 Hz This could be an un modeled resonance within the suspension such as a second mode of the tire or wheel 98 6 4 Adaptive Control In this chapter the outer control loop is closed on the quarter car rig to recreate acceleration data on the rig This section discusses the software developed to close this loop in the real time analysis A discussion follows detailing the generation of desired response for the adaptive control tests Finally the section closes with a discussion of the experiment and results 6 4 1 dSPACE Model The Simulink model compiled for the closed loop control was very similar to that used in the simulation Figure 6 18 is the expanded Control block from Figure 6 6 detailing the control algorithm used Like the simulation program the to workspace blocks have been removed as all signals were access directly by Control Desk The addition of the product and discrete filter blocks were used to calculate the power of the signals for later viewing These blocks were set up the same way as those in the ID software The desired signals are loaded into dSPACE as a set when the code is compiled Again the usual tuning parameters were accessible The step sizes could be altered while the real time test was running to fine tune the convergence rate and maintain stability The number of FIR filter weights and desired response delay had be set up front and recompiled each time Like the control algo
60. e is a lot of signal power associated with the higher amplitude response 106 Signal Power dB oo O Unsprung Desired Signal Error 38 0 50 100 150 200 Time s Figure 6 25 15 Hz Filtered Unsprung Desired Response and Error Signal Powers Signal Power dB FA O 42 Lp l 44 Sprung Desired Signal Error l l l l 50 100 150 200 250 300 350 400 Time s Figure 6 26 15 Hz Filtered Sprung Desired Response and Error Signal Powers The RMS values of the error and desired signals were computed over a converged section of data An error was calculated from these RMS values in a similar fashion as the identification error This error along with the power level reduction is compared to the results from the simulation analysis in Table 4 107 Table 4 15Hz Replication Controller Error Comparison Model Metric Unsprung TF Sprung TF 8 40 7 50 xperimental Error 36 20 23 40 B Reduction Sim 22 dB 23 dB B Reduction Exp 13 dB Figure 6 27 is a plot of the converged weights of the inverse adaptive controller for the 15 Hz reproduction data These weights represent the inverse impulse response of the quarter car test rig It is clear in the plot that there is a lot of low frequency content This 1s expected as the controller was only tryin
61. e state space variables were set up in a MATLAB script as well With the variables filled the state space was created using the ss m MATLAB function 54 5 1 3 Discretization Because the programs are simulated in Simulink and later implemented in a dSPACE rapid prototyping environment the state space system was discretized The Simulink simulation environment will automatically discretize equations of motion however if continuous elements are used in the code there 1s little control over how the software discretizes them For this reason all of the code was discretized up front to have full control on how this process takes place Thus the state space system was discretized using a bilinear Tustin transform Before discretizing the system a sample rate and corresponding sample period was chosen The frequency was chosen to be 1000 Hz which corresponds to a sample time of T 0 001 s In MATLAB the function used for discretizing the state space system 1s called c2dm m This function was run using the Tustin transformation This type of transformation transforms a filter from the continuous time s domain to the discrete time z domain such that ge e 19 Here T is still the sample time in seconds The c2dm m function also allows one to input the state space matrices A B C and D The resulting discrete state space system 18 X A X B u 20 y C x D u 5 1 4 Frequency Response For later comparison
62. e the x filter_y block the desired signal is run through a tapped delay to create a vector the same size as the identified model This desired response vector is then dotted to the vector of FIR weights to create a single r value This value is later fed through a different tapped delay to create the vector of filter X coefficients R in equation 10 200 C O Rk_z RZ Tapped Delay2 a Co Figure 5 15 LMS Algorithm Detail 71 The LMS Algorithm subsystem from Figure 5 14 is expanded in Figure 5 15 Again only the loop containing the unsprung mass shown in the shaded area 1s the current focus In this figure the r signal comes in towards the bottom of the figure at block Ry The signal is tapped delayed and then multiplied by the gained error ue y To make tuning the step size easier an option to attenuate the error signal with the signal power of the desired signal is included This power signal is calculated and fed into a division block thus attenuating the signal For this discussion the assumption 1s that the attenuation 1s unity Thus the error signal 1s not actually affected by signal power The weights of adaptive inverse control work on the same ALC principals as before The weight at step k 1 1s defined by adding the previous set of weights to the product of the filtered X signal step size and error signal This is represented by equation 22 referencing Figure 5 15 W k 1 W k u e_y
63. elationship of the physical system The adaptive linear combiner used to perform this task works best identifying a linear system or a non linear system operating in some linear range The ALC does do a relatively good job of identifying a linear approximation of a non linear system The algorithm 1s extremely robust and lends itself to various forms of implementation in a controls problem The identification process may be continuously updated to track non linear changes in a system For this research the system ID algorithm presented will be used in the subsequent steps to assist in controlling the quarter car rig to replicate a desired response 4 4 Adaptive Control The final processor used in this study is an adaptive controller This controller 1s based on the same building blocks as the system identifier The only real differences are the signals fed to the adaptive filter and LMS algorithms Specifically the controller used in this study 1s an inverse adaptive controller using the filtered X LMS algorithm 4 4 1 General Description Figure 4 4 shows the basic block diagram for filtered x LMS adaptive inverse control In this diagram the LMS algorithm is separated from the adaptive block to explicitly show the inputs to the algorithm One channel of the desired response of the plant is fed into an adaptive filter W The output of the adaptive filter is fed into the 47 plant P The output of the plant is the measured response
64. ement of the state space quarter car model with DAC and ADC dSPACE blocks and the physical quarter car hardware A detailed of view of the DAC and ADC blocks are represented with along with the connection to the hardware in Figure 6 7 86 Hardware Figure 6 7 Detail of DAC and ADC and Connection to External Hardware In this image the dSPACE specific blocks are the DS2101 BI DS2004ADC BLI and DS2004ADC_BL2 The DS2101 block is the DAC configuration block Once compiled this block tells dSPACE how to configure its analog outputs Each analog input to dSPACE has its own DS2004 block These blocks configure the ADC and tell the software where to route the signal to The DAC block contains the switch described earlier to control what part of the software 1s outputting a drive signal to the actuator Also to protect the hardware the saturation blocks were installed to limit the magnitude of the signal output The ADC block contains two filters and a zero order hold The ADC and low pass filters run at a higher rate than the rest of the software This helps filter line noise picked up between the WaveBook and dSPACE The zero order hold block down samples the data to the 87 appropriate 1000 Hz frequency The filters on the right side of the ADC are high pass filters These work like AC coupling filters to remove any DC component in the signal picked up by the wiring or equipment 6 3 System Identification This se
65. ersonal communications with engineers in both the racing industry and the test equipment industry there is a need to make indoor testing more efficient by reducing time on the rig Most manufacturers of indoor test equipment like a 7 post or now an 8 post supply software that allows for the replication of vehicle response Very little information 1s available in the public domain that discusses the details of how these software tools function After a review of the literature an application of a different control algorithm not currently in use 1s merited However to simplify the proof of concept evaluation of its application to indoor vehicle testing this control scheme has been applied to a quarter car rig as opposed to the more complex test beds Because of this simplification a true comparison of the performance of this algorithm to existing software on the more complex test rigs 1s not yet possible However value can still be gained since the more complex systems implement an extension of the same principles Thus with this concept of application proved a future study will be to apply these principles to an 8 post rig for a direct comparison of performance between the proposed method and those that are currently in use In summary a new quarter car test rig has been designed and built In an attempt to prove the concept a well known control scheme not currently used for this application 1s applied to the problem of replicating vehi
66. ervo hydraulic controller The data acquisition box is an IOtech WaveBook 516E This is an expandable data acquisition unit For this study an IOtech model number WBK18 8 channel high speed signal conditioning module was added This expansion unit is capable of powering the accelerometers and has programmable signal conditioning such as low pass filtering and AC coupling filtering built in The main unit has an Ethernet connection for direct communication with the lab PC An analog break out box was built to allow the acquisition system to output the analog accelerometer signals to the control box The data acquisition system is shown in Figure 6 3 with two of these expansion units 82 Figure 6 3 IOtech Data Acquisition System The real time control software was run on dSPACE AutoBox see in Figure 6 4 This unit is a high speed real time control prototyping box The nice feature of this unit Is the ability to communicate directly with MATLAB and Simulink on the lab PC All of the software was written as Simulink models and then uploaded directly to the AutoBox via a special network adapter The AutoBox has 16 analog inputs linked to high speed analog to digital converters and it also has 6 analog outputs that can output up to 10 V Figure 6 4 dSPACE AutoBox Control Prototyping Box While running a test all of the real time software is running on board dSPACE A PC user interface was designed using dSPACE Control Desk software This sof
67. est rig for a direct comparison to current practices Before developing a new test rig the current state of the art in quarter car rigs was first evaluated as well as indoor vehicle testing in general Based on these findings a list of desired functional requirements was defined for this new design to achieve The new test rig was built and evaluated to determine how these goals were met and what the next steps would be to improve the rig The study then focused on evaluating control policies used for reproducing dynamic responses on vehicle road simulators such as 4 post and 7 post shaker rigs A least mean squares LMS adaptive algorithm 1s introduced and applied first in software using a linear two mass quarter car model and then to the actual hardware in the loop quarter car rig The results of the study show that the resulting quarter car test rig design 1s quite flexible in its ability to test a multitude of suspension designs and also its ability to accommodate new hardware in the future such as a body loaders The study confirms that this particular implementation of the LMS algorithm 1s a viable option for replicating test vehicle response on an indoor quarter car test rig Thus a future study to compare the use of this algorithm to the current industry standard batch processing method is possible Acknowledgments I would like to start by thanking my advisor Dr Steve Southward I truly appreciate his willingness to bring me in give
68. ethod for finding the minimum value of a function That is it estimates the gradient of a function and then travels in the opposite direction of the positive slope The algorithm 1s extremely useful for applications that use the ALC because computations are relatively simple which make it very useful for on line applications Many identification or optimization processes that are more complicated require some form of off line adaptation The LMS algorithm begins with the definition of the error signal given by 4 Typically equation 5 1s used to define the error function Instead the squared error is used as the estimation of the error function rather than Taking the square of 4 yields the following E d X W W X 2d W X 6 Next the gradient is estimated by taking the partial derivative of the squared error with respect to the weight vector In vector form this appears as dE DE T OW OW 2 e e xX T ow A k kok DE OE OW OW The second partial derivative shown comes from the derivative of the error function in 4 The negative value indicates that the algorithm is descending the performance surface The resulting gradient in 7 is attenuated with a small gain constant or step size 4 Finally the attenuated gradient is then added to the weight vector to yield the weight vector at the next time step This is shown in 8 W W av W 2ue X 8 44 The a
69. etric Unsprung TF Sprung TF 8 40 7 50 xperimental Error 34 40 31 10 B Reduction Sim 22 dB 23 dB B Reduction Exp 10 dB 12 dB The error of the controller in replicating the unsprung mass dropped slightly compared to the 15 Hz data however it ability to replicate the inverse of the sprung mass path was degraded The power level drops are still considered very acceptable The inverse controller weight coefficients are plotted in Figure 6 35 These represent the inverse impulse response dynamics of the unsprung mass to road input of the quarter car These weights do not appear to have much more high frequency content 113 than the controller weights from the 15 Hz experiment This may help explain why the error for the unsprung mass path 1s not improved that much x 10 Magnitude a 10 12 0 200 400 600 800 1000 1200 1400 1600 Time s Figure 6 35 30 Hz FIR Controller Weight Coefficients These controller weights were convolved with the unsprung mass identified model The frequency response of these convolved weights is found in Figure 6 36 This plot explains why the error convergence and power level drop is not as good as was expected The inverse FIR model does not create a feed through transfer function over enough bandwidth The convolved filters only have a unity transfer between 2 8 Hz This is only enough to do a fair job for the filter to i
70. f noise from the unshielded break out box To correct this dSPACE was run at a high sample rate and the accelerometer signals were low pass filtered in the digital domain With the sample rate high enough this would effectively perform anti aliasing with a conventional multi rate approach 6 2 Basic dSPACE Code The Simulink model that was compiled for running in dSPACE was a slightly modified version of the code used in Chapter 5 The basic format of the code 1s similar to that introduced in Figure 5 12 in section 5 3 Only slight modifications were made on this primary structure to aid in some signal routing as there are small discrepancies when moving from the simulation environment into dSPACE Figure 6 6 is block diagram of this modified code This high level code in the program 1s basically the same setup as in Figure 5 12 In this instance the ID weights have been routed directly into the control algorithm rather than being stored for later use Also there 1s a Goto block labeled ID state which controls a switch inside the DAC block This switch controls whether the system ID or control algorithm controls the actuator 85 ID enable ID state ID enable ID state O en y accel ADC I Actuator System ID cont_enable control_enable DAC Actuator Control Figure 6 6 High Level Simulink Model Modified for dSPACE The major difference between this code and that used in simulation Is the replac
71. f the mass making it an ideal location for this measurement The installed sensor is pictured in Figure 6 1 80 Figure 6 1 Accelerometer Installed on Sprung Mass The installation on the unsprung mass was a bit more difficult The wheel and rotor were removed to expose the suspension upright The top of the upright just over the wheel bearing was filed flat such that the surface was perpendicular to the motion of the suspension This surface was then drilled and tapped and a threaded stud was installed to secure the other accelerometer to the upright This was an ideal location because it allows the accelerometer to have the most sensitivity to the motion of the suspension while being as isolated as possible from the motion of the sprung mass Figure 6 2 shows the installed sensor on the assembled suspension Care was taken insure that the signal cables were protected from being pinched kinked vibrated or rubbed by sharp or rough edges The only other sensors used in this test setup were the LVDT and delta P transducers used in feedback control of the servo hydraulic actuation system Access to these signals was possible using analog outputs on the servo controller 81 Figure 6 2 Accelerometer Installed on the Suspension Upright 6 1 2 Instrumentation Several lab instruments were implemented during the experiment The primary pieces of equipment were a data acquisition box real time control box oscilloscope lab computer and s
72. fed into the unknown plant This input signal is usually a filtered white noise with a high spectral content in the frequency range of interest The output of the adaptive filter 1s subtracted from the output of the unknown plant to form an error This calculated error looks identical to that defined in equation 4 The calculated error is then used to adjust the weights of the adaptive linear combiner This process may occur with several different methods However the LMS algorithm 1s selected for this study The LMS algorithm uses the approximated error gradient to incrementally adjust the values of the weights Again the step size and the size of the weight vector are the adjustments 46 These knobs control the convergence rate stability and quality of the identified model With the weights of the adaptive filter converged to values that minimize the error the adaptive filter will replicate the input to output relationship of the unknown plant Thus the adaptive filter has identified the plant The difference between this and other plant models is that this is not a parametric model with coefficients that have physical meaning It requires virtually no knowledge of the plant In the scope of this project a rough physical model of the quarter car suspension and test rig is not needed to correctly identify the system The model created by this method is purely empirical and is in fact an FIR filter that replicates the input to output r
73. g to replicate the inverse of a plant that was creating 15 Hz and lower responses Magnitude 10 12 14 Oo 200 400 600 800 1000 1200 1400 1600 1800 Weight No Figure 6 27 FIR Adaptive Control Filter Weight Coefficients for 15 Hz Data Because the unsprung mass acceleration was the desired response being input to the controller this plot represents the inverse of the transfer function between the road input and the unsprung mass acceleration 108 To better understand how well the filter performed this task the FIR controller was convolved with the identified model of the unsprung mass transfer function A frequency response of this new convolved filter is plotted in Figure 6 28 Again the frequency response of the 550 sample delay was divided into the response of the convolved filters This removes the phase warping caused by the delay Transfer Function 180 90 90 180 10 Phase deg O 10 20 30 Mag dB 40 50 60 1 0 1 10 10 10 Frequency Figure 6 28 Frequency Response of FIR Controller Convolved with Plant for 15 Hz Unsprung Mass Response Data The frequency response shows that the controller does a good job as an inverse
74. ght be a measurable quantity However the matrix H which represents the transfer function of the system 1s unknown This means that knowledge of only the input will not allow one to calculate the output and visa versa The system ID algorithm used in this study solves this problem using the ALC algorithm adapted using the LMS algorithm described in the previous sections Figure 4 3 1s a block diagram of a typical system ID scheme In this diagram the LMS 45 algorithm is included in the adaptive filter block The LMS algorithm uses the same input signal for adaptation as that which is fed into the adaptive filter Plant Noise Pk Unknown Plant P Input Adaptive Filter W Figure 4 3 Typical System Identification Block Diagram In this block diagram it is desired to learn the Input to output relationship of the unknown plant P The adaptive filter W is a form of the adaptive linear combiner introduced in the first section of this chapter Referring back to Figure 4 2 the desired signal d is now actually a combination of the unknown plant output and noise The noise might be measurement noise for example The noise does not have any effect on the convergence of the adaptive filter if it is not correlated to the plant input The input to the adaptive linear combiner is the same in both the system ID problem and the ALC discussed earlier In the system ID problem the same input that is fed to the adaptive filter is also
75. h would eventually be run in dSPACE This was to help the transition into real time control easier Figure 5 12 shows a block diagram illustrating the basic setup of the control software The control model was broken up into four distinct blocks analog to digital converter ADC digital to analog converter DAC system ID and control meme Constant JI Actuator System I Terminatorl cont_enable Constantl Actuator Wk_s Constant2 Control Wk_u Constant3 Figure 5 12 Basic Construction of Simulink Control Block Diagram Of course in a pure simulation study there are no analog to digital or digital to analog converters Inside these blocks there is basically just a wire to feed the signals through These wires will later be replaced with the appropriate converters such that dSPACE can route the signals properly Thus actuator signals that are fed into the DAC block in simulation are simply fed through directly to the ADC block where the model of the plant resides The system ID and control blocks are enabled subsystems The ID_ enable and cont_enable blocks are constants with either a 1 or O value These constant blocks are used to turn the respective subsystems on or off Thus when the simulation is running the quarter car model is first identified using the system ID 67 subsystem Once the model is identified the system ID is switched off and the control
76. he newly designed quarter car test rig and how it has fulfilled the functional requirements laid forth Next a brief discussion of future developments for the test bed is provided 3 9 1 Summary of Functional Requirements Fulfilled Due to the modular design of this new quart car test rig it is able to accommodate a multitude of different vehicle suspension designs A photograph of the fully assembled test rig is shown in Figure 3 16 with the Porsche 996 suspension installed The design of the sprung mass to receive an adapter plate rather than a single specific suspension keeps the rig from being purpose built for one suspension design and corresponding car mass The configurability allotted by the base plate design and the single piece design of the reaction load frame allow for a large window of placement of the tire relative to the sprung mass The moving mass has provisions for adding mass which allows for vehicles of various welghts to be replicated Finally provisions for additional functionality are designed into the rig making it useful for future studies A set of specifications for the rig are included in Appendix B 38 4D m Figure 3 16 Completed Quarter car Test Rig with Suspension Installed 3 9 2 Future Enhancements Future additions in functionality will occur in steps The first of which is to add force loading capability on the sprung mass The results of this research effort can only be improved by replicating ine
77. he plant over the frequency range covered by the desired response spectrum In an ideal system the converged filter convolved with the plant will give a 48 perfect unity or feed through input to output relationship over the frequency range of interest 4 4 2 Filtered X LMS The adaptation of the inverse adaptive filter occurs in much of the same way as the adaptive filter used in system identification Unlike system ID the adaptive filter is now matching the inverse dynamics of the plant The filter weights are adapted using a virtually identical LMS algorithm The adaptation is based on the error between the desired and measured system responses and also the filtered X signal The filtered X signal is created by playing the desired response through an FIR filter model of the plant In this study the model is identified using the system ID technique described in the last section A nice feature of this method is that the identified model does not need to be extremely accurate for the controller to work well 27 This speaks to the robustness of the algorithm The filtered X version of LMS works exactly the same as in system ID with the exception of the input vector used in the gradient term In system ID the input to the adaptive filter was the same input going into the plant being identified In the case of filtered X the input signal 1s first filtered through the identified plant model Referring to equation 8 the input vector X
78. hot of Control Desk Real time Control Interface 102 Figure 6 21 Screenshot of Control Desk Real time Control Weights oooooonnnn 103 Figure 6 22 15 Hz Filtered Unsprung Mass Desired Response Controller Error 105 Figure 6 23 15 Hz Filtered Sprung Mass Desired Response Controller Error 105 Figure 6 24 Detail of Unsprung Response Controller Error 106 Figure 6 25 15 Hz Filtered Unsprung Desired Response and Error Signal Powers 107 Figure 6 26 15 Hz Filtered Sprung Desired Response and Error Signal Powers 107 Figure 6 27 FIR Adaptive Control Filter Weight Coefficients for 15 Hz Data 108 Figure 6 28 Frequency Response of FIR Controller Convolved with Plant for 15 Hz Unspr ns MASS Response Dn uuu lu aan 109 Figure 6 29 Detail of Actual Response Over Desired Response 110 Figure 6 30 30 Hz Filtered Unsprung Mass Desired Response Controller Error 111 Figure 6 31 30 Hz Filtered Sprung Mass Desired Response Controller Error 111 Figure 6 32 Detail of 30 Hz Unsprung Mass Response and Error 112 Figure 6 33 30 Hz Filtered Unsprung Desired Response and Error Signal Powers 112 Figure 6 34 30 Hz Filtered Sprung Desired Response and Error Signal Powers 113 XII Figure 6 35 30 Hz FIR Controller Weight Coefficients Figure 6 36 Frequen
79. hure Eden Prairie MN 2003 Thoen B K MTS Systems Corporation Control Network with On line Iteration and Adaptive Filter US Patent No 5 394 071 1995 Lauwerys C Swevers J Sas P Robust Linear Control of an Active Suspension on a Quarter Car Test Rig Control Engineering Practice 13 p 577 586 2005 Vandersmissen B Kennes P Maes M Reybrouck K Skyhook Control and Performance Evaluation of an Active Suspension System on a Quarter Car Test Rig Proceedings of the 2004 International Conference on Noise and Vibration Engineering ISMA p 103 114 2004 Bay Cast Technologies http baycasttech com website Bay City MI 2006 Gobbi M Giorgetta F Guarneri P Rocca G Mastinu G Experimental Study and Numerical Modelling of the Dynamic Behavior of Tyre Suspension while Running Over an Obstacle Proceedings of IMECHE2006 2006 ASME International Mechanical Engineering Congress and Exposition No IMECHE2006 14804 Chicago IL 2006 Toyoda Machine Works Ltd PV4 ITA High speed Vertical Milling Machine User s Manual and Technical Drawings Okazaki City Japan 1996 NSK Ltd Technical Journal Linear Rolling Guides Ann Arbor MI Ansys Inc User s Manual ANSYS 9 Canonsburg PA 2004 Marshek K M Juvinall R C Fundamentals of Machine Component Design gr Edition John Wiley amp Sons Hoboken NJ 2003 Synergy Racing http www synergyracing com website Alton VA 2006 Personal communi
80. iring the specific technical details of how these algorithms work 1s very difficult The methods appear to have many small discrepancies among one another It is quite clear that the methods presented in this literature review are different than that which 1s used in this study These distinctions will be become more apparent as the details of the algorithm presented in this study are discussed 16 3 HARDWARE DEVEOLPMENT Chapter 3 discusses the engineering approach to the design and construction of the quarter car test rig used in this research It begins with a general discussion of the quarter car rig s design Following are detailed discussions of how each major component was developed and or specified Included is discussion of the implementation of the first suspension tested with the new rig The chapter closes by summarizing the functionality of the new quarter car rig and presents some future developments being planned 3 1 General Description The quarter car test rig 1s designed to represent one corner of a test vehicle The design of the rig 1s such that the rig will go through several configuration phases to achieve the full functionality desired For this study the rig is in Phase 1 The number of phases 1s not actually a set number but progress as time and funding dictate There will be a brief general discussion of these configuration developments at the end of the chapter Figure 3 1 is a schematic of this new design
81. itional necessary objective 1s to develop a state of the art quarter car test bed for this research Currently the desired functions of a quarter car rig include the ability to mount several different designs of actual car suspensions have the ability to perform a wide range of tests which include body loads on the sprung mass and still have the ability to expand for future developments There are several quarter car test rigs that are currently available Many of those rigs do not have the functionality desired for the current and future research projects The commercially available rigs are quite expensive and yet most still do not offer the amount of flexibility needed In order to meet the combination of functional requirements necessitated by VIPER a commercially developed rig from a company such as MTS or ServoTest would require close development with the researchers This would prove to be an even more expensive proposition Thus the goal of this research was to develop the new rig in house in order to achieve the desired functionality at a reasonable expense With a competed test rig the other goal 1s to perform a study on the application of a control system to the rig for reproducing test vehicle response This is not a new concept In fact much of the literature suggests that several methods have been attempted and commercial solutions are available However most of the literature 1s vague in terms of the technical details Based on p
82. ka kal ll a la kl k la kl kk aka ka ake ko ap asss viii BREA A lide u bade ss oti ooo uqun u be de am a ia oo kin dekad A eka dio soos s X List ON Tables iia id xiv LE INTRODUCTION 2 l na a u EEEa EN REETA REENE 1 die IVIOUV ANON sarita l 2 A DIC CUES de fois apa te pab a ik e aS e A ia a oo n ket 2 ko 0 A A a NA 3 LA OYulliikuu anu a ank ko aka e da aste kok stad taa da base 3 2 GITEKATURE REVIEW AAA F ou u sasa uuu Guss 2 5 2 Chir AN NO uyu oie ree otan ey ROTO 3 ZN Complex SHAK CUS aa E e da ke je saaa a leti 6 ZA Cunen OU Arter Cat FA S cota kr kk kata ya ka u ri e kata pa kk e t n e 7 21 3 Functional Requirements aia 12 2 2 Control of Rig RESPONS Cursor 13 22 1 udiisui y standard k l a O 13 Doda On line Adaptive Aleorilthm 14 2223 S mmary of Literat re e ii bl ai tk a ki A 16 3 HARDWARE DEVEOTPMEN T citando ssseoskbsasso ase sas sas 17 Sly General MI L AN PANO iu a a e an a nee a n anl e A au nape sana 17 Bs A CAN MO e ot se anasu e se ty ti en a tes ER 20 3 2 1 Prite YE SATAN f pe ua ke a de kk a a nee kr ye ako eka 20 e ON PUNCHONAIIEY tait aaa sab tal ans a a n aid 21 3 Reaction LO Bia arde 23 3 l Brame Desnuda t Q a Sua bapa a n N 23 Sio PA Prine YANN A A n Dahi A N 23 3 3 3 Punctional rr oda 25 Ike GN 26 3 4 1 SIAM nn 26 3 4 2 Desien and F BC ONA Vd 27 Dede MOVE NI S arar 28 Dili Spin Mass Plate
83. l indicated that the system had two resonances which did not exceed 30 Hz Therefore exciting the system at frequencies much higher than this frequency does not really help the model converge Also because the sample rate was set at 1000 Hz care was taken not have high power signal near the Nyquist frequency of 500 Hz which would cause aliasing problems in the data The solution was to use a fourth order low pass Butterworth filter with a 60 Hz break frequency Coefficients for the numerator and denominator of the filter were created with the butter m function in MATLAB A discrete filter block was then used in the Simulink model to actually filter the white noise before it was fed into the rest of the model The two blocks are cut from Figure 5 4 and shown below in Figure 3 5 60 lpf_num z x k lpf_den z White Noise Discrete Filter Excitation Figure 5 5 Model Detail of Filtering the White Noise Excitation 5 2 3 Numerical Results Several tests were run to achieve the best error convergence possible The tuning knobs noted in the previous chapter were used to control the convergence and quality of the model For system ID the same model size and step sizes were used for both identification paths The best results occurred with a step size of 0 0002 and a model size of 150 coefficients Sprung Acceleration Model Error x A IM a ul Acceleration G O
84. ler Is turned on to allow for replication of signals on the model The identified FIR models are stored in the two blocks labeled as Wk_s and Wk_u for the sprung and unsprung masses respectively When required these weights can be fed into the controller subsystem The quarter car state space model has been placed inside the ADC block In a real time simulation the plant would obviously be hardware and the ADC and DAC blocks would be the means to get signals from the software environment to real signals in the hardware environment This software design mimics this by simply keeping everything in a software environment Detail of the DAC block is shown in Figure 5 13 a and the ADC block is shown in Figure 5 13 b PLANT O car model Discrete State Space vo ace b Figure 5 13 Detail of a DAC Block and b ADC Block Following the figures from left to right the feed through nature of these blocks is now apparent An actuator signal 1s fed into the DAC block There is a one sample delay on the actuator signal to break an algebraic loop in the software This is a simulation anomaly and is not required in the real time implementation The actuator signal is then fed directly from the DAC block to the ADC block via Goto and From blocks These blocks are Simulink s way of transmitting signals without using wires The actuator signal is then fed to the discretized state space quarter car model developed
85. lgorithm is simplistic because a process such as averaging is not necessary for good convergence The gradient is taken at each time step which can be noisy at times This is not a problem as the LMS method will still generally move towards the steepest descent on the performance surface Normally the 2 in 8 is dropped leaving only the gain constant y Also called the step size this constant is a tuning variable that is used to control the rate of convergence and stability of the adaptation If the step size is set too high overshoot can occur causing an unstable system and excessive error In a physical sense this could lead to loss of control of the inputs to the specimen The other tuning knob in LMS is the length of the weight vector This generally depends on the physical system being optimized but can also be used to aid in the quality of the error s convergence towards a minimum value 4 3 System Identification The concept of system identification or system ID is relatively straight forward The process begins with an unknown system This can be a physical plant such as a vehicle or quarter car suspension test rig It can also simply be a software FIR filter or model Typically being an unknown system means the user does not know the input to output relationship or transfer function of that system An example is represented as a linear system such as y Hx 9 Here the input x might be known and the output y mi
86. ll in turn alter the kinematics and dynamics of the suspension Rigs that do not incorporate actual or equivalent suspension geometry do not accommodate such dynamics at all Some rigs primarily those used in durability testing may incorporate some of the actual vehicle components This often limits the use of the testing to component tests only One such platform provided by Labtech International is shown in Figure 2 3 In this example the tire 1s supported by a rotating drum with a bump excitation The suspension is simplified such that the engineer can concentrate on the analysis of the spring and damper performance Also the rotating drum only allows for simple cyclic road inputs to the suspension Thus a simulated non periodic road profile excitation on this rig would be impossible Permission could not be obtained as the company would not respond to request Virginia Tech and the authors could not reproduce without permissions Figure 2 3 Quarter car Rig for Component Testing 13 A couple of commercially developed rigs that offer some of same capability were found in the literature search MTS Systems Corporation in cooperation with dSPACE has developed a proof of concept mechatronics development and validation MDV bench The proof of concept combines MTS Modeled and Mechanical Simulation Technology with dSPACE hardware in the loop simulation to permit real time integrated physical and electronic development validation pl
87. m and results There are some inherent deficiencies with many of the existing test rigs Often the suspension components of the vehicle are simplified or removed altogether To the author s knowledge the literature does not discuss a test rig that can incorporate multiple suspension designs This may be desired to reduce the expense and to add flexibility Several companies such as MTS and ServoTest are capable of developing such rigs but the expense and time required for such designs would be high Many times the tire dynamics are omitted altogether and represented by a simple linear spring Removing the non linear geometry does make the analysis simpler This can allow for reduced computations and easier implementation into simulation with the quarter car as hardware in the loop While this does tend to simplify the understanding of the problem it introduces a new issue Good correlation of the results from a quarter car test with real data from the represented vehicle is difficult to obtain This is often due to the choice of sprung and unsprung masses being represented as linear moving masses To constrain this linear motion guide bearings are used which are often insufficient If the bearings have a highly non linear friction this can create problems in the dynamics of the represented response Often the suspension and tire are represented by equivalent springs which likely do not have the same overall non linear characteristics or may no
88. mass desired response to the adaptive filter During this study the unsprung acceleration was exclusively used as a reference signal Even so the sprung mass signal was replicated better than the unsprung mass signal It would be interesting to see 1f using the sprung mass signal as reference would further improve the error convergence of the sprung mass replication Finally the next step in a future study would be to attempt to implement this algorithm on a more complex system such as an 8 post shaker to yield a fair comparison of this method to existing art 117 REFERENCES 10 il Bigliant U Piccolo R Vipiana C On Road Test vs Bench Simulation Test A Way to Reduce Development Time and Increase Product Reliability SAE Technical Paper Series No 905207 Warrendale PA 1990 Kelly J Kowalczyk H Oral H A Track Simulation and Vehicle Characterization with 7 Post Testing SAE Technical Paper Series No 2002 01 3307 Warrendale PA 2002 Mianzo L Fricke D Chabaan R Road Profile Control Methods for Laboratory Vehicle Road Simulators Proceedings of the 1998 IEEE AUTOTESTCON Salt Lake City UT p 222 228 1998 Vetturi D Magalini A Road Profile Excitation on a Vehicle Measurements and Indoor Testing Using a Four post Rig Dipartimento di Ingengeria Meccanica Universita degli Studi di Brescia 2002 Castor A Tune Up At Jaguar Article Design News Reed Business Information
89. motion of the carrier Each carrier can handle an actuator induced moment of 1120 ft lb static loading e Linear rail parallelism 1s 0 003 in over the entire length of the guide rails 122 Appendix C Linear State Space Matrices a ne O OOOO AAA A e E A 123 VITA Justin Langdon was born in Bristol Pa on June 2 1981 He grew up in Morristown TN graduating from Morristown Hamblen High School West in 1999 One strong influence on his career path becoming engineering related was Gene Quarles an excellent math teacher and great person at West High From there Justin went to Tennessee Technological University to pursue a degree in Mechanical Engineering While at TTU he developed a strong interest in the automobile and decided to pursue a career in the automotive industry with hope of one day racing professionally Part of this desire stemmed from working on the Formula SAE team at TTU Many summers and off time from school was spent working for an automotive supplier in Morristown Justin a KA graduated from Tech in 2004 After finishing a Bachelor s degree Justin decided that he just couldn t get enough and came to Virginia Tech to work on a Master s Degree in Mechanical Engineering He spent the first year taking classes in Blacksburg and helped the VT FSAE team compete in 2005 He ended up in Danville VA and teamed up with Dr Steve Southwa
90. n The first step in the frame design was deciding on the material and construction of the frame In several cases an extruded aluminum frame was assembled using bolts nuts and brackets to connect the pieces First hand accounts of this type of structure indicate that this type of joining can lead to some unwanted flexibility in the structure The goal Is to reduce excitation of the sensors from outside sources including the rig s structure Thus a welded low carbon steel space frame design was chosen The overall dimensions of the frame are 84 in tall with a 28 in x 42 in foot print The rig is made from 4 in x 4 in steel square tubing with a 3 8 in wall thickness The tubes create a triangulated frame seen in Figure 3 2 A 1 in thick steel plate is welded to the front of the space frame as a location for mounting the bearing rails Completed the frame weighs approximately 1500 lbs 3 3 2 Frame Analysis To optimize the rigidity of the frame a finite element model of the rig was created in ANS YS using beam elements This model was simplified in that the steel plate on the front was not modeled due to computational restrictions with this particular license of the software This was not a problem as 1t merely added a safety factor to the analysis 2 If the welded frame was strong enough and had a high enough first mode then welding a steel plate to the front would only strengthen the design The plate has a window cut into it as well so
91. n hand and the quarter car rig assembled some adjustments of the suspension were necessary The adjustments are meant to match the 33 suspension set up of the represented 996 Synergy Racing was the source for the front end alignment figures To protect their setup information ranges were provided rather than actual specific numbers Table 1 is a list of the geometry setup numbers Table 1 Setup range for 996 Setting Camber Caster _ TO ON 89 7 Toe 1 8 out to 1 8 in 0 Corner weight LCA Ride height angle Based on the figures in Table 1 the suspension 1s set up to meet to attempt to meet the median of these ranges The camber 1s adjusted by sliding the location of the strut mount on the strut mount bracket in the X direction and by adjusting the Y position of the LCA inner mounts Care 1s take here as changing the LCA mount position also has some affect on the angle of the LCA at ride height The caster was set by adjusting the Z positions of the LCA mounts and also of the strut mount bracket Finally the toe 1s set by adjusting the position of the inner tie rod mount and the length of the tie rod 3 7 Actuation Road input to the suspension 1s supplied via a tire coupled servo hydraulic system manufactured by MTS Systems Corporation The servo hydraulic system is comprised of an actuator with position feedback pump manifold servo valves and PID controller The hydraulic actuation system was specified with help from MT
92. n the circumstances when I first arrived in Danville Dr Southward s guidance during this research was invaluable Also the hockey games and track data collection at VIR were fun I want to thank Drs Charlie Reinholtz and Harry Robertshaw and also Bruce Billian for helping to guide me through adversity in graduate school I would also like to thank Dr Bob West for letting me sit in on some FEA classes to get back up to speed on some modeling techniques Many thanks go to Synergy Racing for their generous donation of a Porsche suspension for this and future research Particularly thanks to Cole Scrogham Greg Jones and Richard Binzer for allowing us the time to discuss the project and gain insight into Grand Am Cup race cars Also thanks to Dr Christoph Leser of MTS for the extremely insightful phone conversation His knowledge of indoor vehicle testing was extremely valuable I would especially like to thank Jim Belcher at JTEKT Automotive Tennessee Morristown Inc for allowing me to VPN into their network to use a licensed copy of Solidworks Also thanks for being so flexible by allowing me to come to work only when off time at school would allow it The real world experience was invaluable Without your help in both respects this project would have moved much more slowly and difficult I would like to thank my high school math and physics teacher Coach Gene Quarles You were an incredible influence not just as a teacher but as an all around gre
93. nd Figure 6 31 show the error and desired responses for each path These plots are somewhat surprising The error still does not appear to converge well for the unsprung mass although it does converge very fast Of course the scale does much to distort the look of the error The fact that it still has a fair amount of error may be attributed to non linearity or other dynamics not in the frequency range of interest The sprung mass error converges relatively slowly but do seem to do a nice job once converged 110 Error Unsprung Desired Response Acceleration G e woo o l 0 100 200 300 4 Time s 500 600 Figure 6 30 30 Hz Filtered Unsprung Mass Desired Response Controller Error 0 8 _ Error Sprung Desired Response 0 6 0 4 0 2 Acceleration G 0 2 0 4 0 6 0 8 0 Tme s l l 100 200 300 400 500 600 Figure 6 31 30 Hz Filtered Sprung Mass Desired Response Controller Error Again to get a better understanding of the unsprung mass response a zoomed in look at the desired response and error is found in Figure 6 32 Here it 1s clear that the controller 1s still capturing the majority of the high power signals 111 1 5 Unsprung Desired Response l
94. ng mass response was fed directly to the controller as the desired response Thus the adaptive inverse controller was ideally trying to represent the inverse of the path from the tire input to the unsprung mass acceleration The first set of tests was performed to recreate the 15 Hz filtered data After several tests the controller size was set to 1700 weights and the sample delay was set to 550 samples For the low frequency data replication the step size for the sprung mass error was set to 0 0001 and the step size for the unsprung mass was set to 0 00001 Figure 6 22 and Figure 6 23 show the converging error overlaid on the desire response for both masses 104 Desired Unsprung Response Controller Error ITU T A TAT ar Acceleration G Wil bit tunel A P LI 20 40 60 80 100 Time s Figure 6 22 15 Hz Filtered Unsprung Mass Desired Response Controller Error 0 8 Desired Sprung Response Controller Error 0 6 MAT TI 0 4 0 2 Acceleration G Oo 0 2 call 0 6 0 8 0 50 100 150 200 Time s Figure 6 23 15 Hz Filtered Sprung Mass Desired Response Controller Error It is noted that the error convergence of the unsprung mass error does not appear to be very good particularly at the time scale of the plot Further examination of the error plot in Figure
95. nother recommendation is to develop a roll degree of freedom for the sprung mass which could actively replicate the roll dynamics of the body of a vehicle with a variable roll center 116 In terms of the control algorithm and testing performed in this study there are several recommendations which arise First it would be ideal to perform several more tests with the quarter car rig to learn more about tuning the adaptive algorithms There were certain tests performed along the way where the control filter weights had a totally different appearance which included some higher frequency response To the authors knowledge these test could not be repeated on demand It seems that there are some unknown subtleties that affect the results and convergence of the adaptive controller In light of some of the more surprising results noted in this study further tests may also add insight into how to make the test more repeatable Also more tests would be useful to better understand how the frequency content of the desired response and also the shaping of the system ID excitation affect the performance of the inverse controller Further alterations of the adaptive linear combiner might be necessary to help capture some of the non linear dynamics of the hardware This may help the adaptive controller do a better job of replicating the true dynamics of the system Furthermore a similar set of tests should be performed on the quarter car while feeding the sprung
96. nsprung Accelerometer and Error Signal Powers Finally the converged weights of the FIR models were studied The weights of the FIR filter actually represent an impulse response of the adaptive model when plotted versus time In this study the weights of the adaptive filters actually match the impulse response of the unknown system they are modeling very well further showing how well the filter adapts to look like the identified plant This is demonstrated in Figure 5 10 It was expected that the adaptive filters would do a good job of identifying the quarter car model extremely well since the quarter car model was a linear system 64 e Unsprung FIR weights 1 Sprung FIR weights si Discretized SS impulse response Magnitude 0 20 40 60 80 100 120 140 Weight or Sample Figure 5 10 Impulse Response Compared to Converged ID Weights A frequency response of the adaptive FIR model was computed and compared to the frequency response of the original linear state space model The results are plotted in Figure 5 11 The figure shows that the frequency response of the adaptive filter 1s extremely accurate in replicating the magnitude and phase response of the quarter car plant One place that the model shows to have a slight amount of trouble is in the extremely low frequency region of the unsprung mass model 65 Frequency Response Comparison
97. nvert the sprung mass dynamics However the filter appears to just not invert the higher frequency dynamics of the unsprung mass The fact that the error stated is still in the mid 30 range considering how poorly the convolved transfer function looks shows the robustness of these inverse adaptive filters 114 180 90 90 180 10 Phase deg O 10 20 30 Mag dB 40 50 60 Transfer Function 10 10 Frequency Figure 6 36 Frequency Response of FIR Controller Convolved with Plant for 30 Hz Unsprung Mass Response Data 115 7 CONCLUSIONS AND RECOMMENDATIONS The concept of this new quarter car test bed proved to be a very flexible and robust design for the purposes of this and future experiments Future plans set forth for the rig also prove that its design will lend its use for many studies to come with varying purposes The rig s stability provided a great deal of confidence in the results obtained during the tests in this study The design goals for the rig in the scope of this study were achieved in their entirety and future phase developments of the rig look to be performed in a very seamless manner The control algorithm implemented proved to be a different adaptation from current practices Though the RMS errors quoted in this study appear to be slightly higher in some tests the pro
98. nvolved with the inverse transfer function The resulting drive file correction 1s again scaled and added to the first iterated drive file This constitutes the second iteration This process 1s repeated until the error between the response of the specimen and the response during the road test is acceptable It can be deduced that one drawback of this current method 1s that the iteration 1s an off line batch process that can take a large amount of time It is likely that this large convergence time is measured in hours as it is indicated that many days can be spent testing on a 7 post during one session 5 6 7 8 9 15 2 2 2 On line Adaptive Algorithm Another algorithm is a form of on line adaptive filter 16 This algorithm appears in a patent along with another algorithm listed as prior art The block diagram for the prior art Is show in Figure 2 6 Fig 2 PRIOR ART Figure 2 6 Prior Art Algorithm from U S Patent No 5 394 071 Though this algorithm 1s much closer to the one used in this study it still has some very distinct differences In this figure the plant designated by T is the unknown specimen whose response is being controlled The desired signal x 1s first filtered by 14 an inverse model W of the unknown plant This model is the adaptive filter that is continuously changing as dictated by the LMS gradient descent algorithm In this case the desired signal 1s sent through the inverse
99. ny of the functional requirements listed and yet flexible enough to allow for implementation of hardware that 18 will allow for fulfillment of the remaining and added requirements Figure 3 2 is picture of the solid model of the new design This model was created in Solidworks 2006 Linear guides Suspension Adapter plate fixturing Vehicle Sprung mass plate suspension Wheel and tire Force loader M ni s A it oo us a ne pl Wheel pan Reaction load frame Actuator Base plate Figure 3 2 Solid Model of Quarter car Rig in Design Phase From the figure the base plate and reaction frame bolted together are the support structure for the entire rig The linear guides are actually six parts There are two guide rails each with two bearing carriers that move in one degree of freedom The linear guide rails are bolted to the load frame vertically The sprung mass is constrained to the rail 19 using the four carriers There are two force loaders which are known as aeroloaders in the 7 post testing vernacular There is one loader on each side of the sprung mass One loader can be seen in the figure The force loaders which will be implemented in a later phase of construction are two piece electro magnetic linear motors One piece 1s bolted to the load frame and one is bolted the sprung mass The suspension is bolted to the sprung mass via the adapter plate and suspension fixturing With the
100. of of concept of applying these control methods for replication of data has been completed successfully A careful explanation of the concepts of system identification and adaptive inverse control performed with the use of an adaptive linear combiner and least mean squares algorithm was presented These concepts were successfully demonstrated using a purely software simulation applied to a linear quarter car model Once the process of tuning the adaptive filters was practiced in simulation and the concept proved in software the algorithms were then implemented on the new developed quarter car hardware using a real time prototyping control system The concept of on line adaptive inverse control presented in this study was successfully demonstrated on hardware in the loop The system ID technique introduced works extremely well considering the linear model is modeling a non linear system The controller does appear to have some room for improvement There are some recommendations that extend from this study which might be considered before taking future steps For the quarter car platform these recommendations are simply to continue the development of the rig set forth in this thesis The first step 1s to add the electromagnetic force loaders to the sprung mass to simulate body and aerodynamic loads Another step 1s to demonstrate the flexibility of the test rig to mount a different design of suspension such as a Nextel Cup Stock Car or HMMWV suspension A
101. of the plant The magnitude is 0 dB or feed through between 2 5 Hz and starts to roll off after 15 Hz and the phase is basically zero in this range as well Over this range the controller does a great job of inverting the dynamics of the quarter car rig Finally Figure 6 29 shows a 1 s sample of the actual response of both the sprung and unsprung mass accelerations overlaid on their respective desired responses This plot shows the accuracy of the inverse controller on a detailed response scale 109 0 8 Unsprung Desired Unsprung Actual Sprung Desired Sprung Actual Acceleration G 0 6 8 332 332 2 332 4 332 6 332 8 333 Time s Figure 6 29 Detail of Actual Response Over Desired Response 6 4 4 Experimental Results 30 Hz Data The same tests were performed to replicate acceleration data that was filtered with a 30 Hz roll off filter Ideally the extra frequency content would allow the controller to do a much better job at replicating the unsprung mass response which again was the input to the filter The number of filter weights and sample delay size was set to be the same as the 15 Hz replication However because of the higher signal power levels due to the higher frequency content the step sizes needed to be lowered to 0 00001 for the sprung mass error and 0 000001 for the unsprung mass error Figure 6 30 a
102. on the algorithm introduced in Chapter 4 Next an excitation signal was defined as an input for the model and the simulation is run 56 5 2 1 Simulink Model Since there are actually one input and two outputs there are really two transfer functions to be identified in this quarter car model Thus each of the transfer functions must be identified simultaneously Therefore two system ID blocks must be used to identify these two distinct transfer functions As mentioned all of the software development was performed in discrete time This was to control how Simulink discretizes the model and also to make the transition into real time control much more seamless A model of the system ID algorithm 1s found in Figure 5 3 O i Clock Sprung mass adaptive filter PLANT Q car model _ lof den z lpf num vplant k Discrete Filter Excitation iS GH Monit DIE ne Unpsrung Acaptive filter Figure 5 3 Simulink Block Diagram of Basic ID Scheme In this diagram two adaptive filter blocks are introduced to empirically identify the dynamics of the quarter car state space system This 1s the same process described by Figure 4 3 Because each of these adaptive filters function the same way only the operation of one loop will be discussed in detail In this example the focus is on the adaptation of the unsprung mass numerical model The loop for this algorithm 1s loc
103. or in MTS documentation Inspect rubber hydraulic lines twice per year for rubs or cracks Fix protect as necessary The clean the bare steel parts of the load frame and the black oxide coated parts apply a light coating of WD 40 or equivalent with a paper towel or clean cloth This will help prevent rust from forming If disassembly of sprung mass and bearings is required please refer to NSK documentation first Improper disassembly or reassembly misalignment can cause bearing failure 121 Appendix B Rig Specifications The following section 1s a short list of physical specification for the quarter car rig e Overall mass of grounding fixtures base plate and reaction fixture 1s approximately 4500 lbs e Sprung mass has a rail spacing of 22 in and currently has a max travel of 13 in this travel allows for 1 5 in of rail at either end to ensure there 1s no dislodging of the bearing carriers e There is currently a 33x36 in window on which to mount a suspension to the sprung mass plate e The bare aluminum sprung mass plate and carriers weigh approximately 170 lbs This 1s the absolute minimum sprung mass weight allows by this rig e The maximum sprung mass weight is limited by the hydraulic actuator e The servo hydraulic actuator has an amplitude of 3 in and a maximum static load of 5 5 kip e Each bearing carrier has a basic dynamic carrier moving load rating of 13 800 lbf in the direction normal to the
104. pes of software run in conjunction with the simulator 5 6 This section discusses the current state of the art in vehicle testing rigs Particularly a survey of quarter car test rig technology 1s presented which details the need for increased functionality of the new quarter car test rig Finally the section closes with the proposed new functional requirements of said test rig 2 1 1 Complex Shakers Among the most complex test equipment are the 4 post 7 post and 8 post shakers and kinematic and compliance rigs A typical 4 post rig is comprised of 4 servo actuators If the test rig is tire coupled each actuator post supports the vehicle under each tire If spindle coupled each spindle on the vehicle is mounted directly to the actuator Thus the test rig can input various signals into the vehicle and responses may be measured The 7 post works in a similar fashion with the addition of three extra actuators 4 extra actuators if it is an 8 post attached between ground and the sprung mass of the vehicle These offer increased capability in the form of simulating vehicle response from inputs such as braking acceleration and cornering as well as aerodynamic loading Figure 2 1 Image of ServoTest 7 post Test Rig reproduced with permission Figure 2 1 represents a ServoTest tire coupled 7 post rig with a Formula 1 racecar These complex test rigs offer an immense amount of capability however they are very expensive to build
105. pozg 104 TART ed qarun Tepou Iep LNV Id tT3onpozd zrs d as bunids TAPeTSA p dder ADOTI lation ID Algorithm 1mu Model of S lagram k Block Di 4 Simulin 5 Figure 59 The error created from subtracting the output signals is then fed back with a gain or step size multiplying it This step size 1s then multiplied by the same tap delayed input signal X k and then added to the previous set of weights Wu k This addition provides the next corrected set of weights Wu k 1 at the following time step Using the appropriate math for a block diagram and referring to Figure 5 4 the following equation may be written Wu k 1 Wu k MU e_u k X k 21 This equation 1s basically the same as 8 in section 4 2 The identical process takes place for the sprung mass loop as well The simulation 1s allowed to run until both of the error signals are minimized All of the yellow To Workspace blocks such as xk or tk were used to store the data to the workspace in MATLAB for post processing 5 2 2 Excitation Signal Shaping Care must be taken when choosing the filter for shaping the input excitation The idea 1s to use a band limited white noise excitation However this signal should be limited such that it is allowed to excite all of the dynamics of the system that are of interest in modeling The frequency response study of the linear quarter car mode
106. r spring denoted by k The road input to the tire is modeled as a velocity input called x E in Figure 5 1 Two Degree of freedom Quarter car Model The schematic defined above was modeled using Lagrangian dynamics In modeling energy functions are defined for kinetic T and potential energies V as well as a pseudo energy damping function D These functions are defined for this model as r m m 12 V 2k 2y k 9 x 13 2 2 D e 14 52 With these functions defined the equations of motion can be computed for each coordinate based on an expanded form of the Lagrange s equation of motion This equation is defined for each coordinate q as follows Oq e en 15 dt Oq Oq 09 The equation is set to zero because of a lack of forces or other loads from external sources Because there are two degrees of freedom there will are two coordinates and hence two equations of motions The model is a linear time invariant system and can be put into a state space form for ease of computation In MATLAB To put the equations in state form a vector of states must be defined The state vector defined is 16 Ne N a These states include the positions and velocities of the two masses and the displacement of the input The input u ES l for this system Is the velocity of the road The standard continuous time state space 1s then x Ax Bu 17 y Cx Du The state matrices A B C
107. rce for the four carriers used in this design should total less than 10 lbf in the velocity range of interest The design of these bearings also gives them a low variation between static and dynamic friction This is useful because it makes controlling a force loader a much easier task 1f force feedback were used 21 3 5 Moving Mass The moving mass is the part of the rig that replicates the vehicle s sprung mass which includes the body and chassis The most difficult functional requirement of this new rig was addressed with a sprung mass modular design One design goal was to be able to attach various suspension designs to the same test rig without major modifications To this end the moving mass was made into a modular two piece design A sprung mass plate was designed to be the permanently installed moving plate The sprung mass 1s bolted to the linear bearing carriers which are constrained by the rails An adapter plate along with the appropriate fixtures 1s designed to be the interface between the sprung mass and the vehicle suspension 3 5 1 Sprung Mass Plate The primary goals of the sprung mass plate were to be lightweight rigid and functionally flexible Aluminum 6061 T6 was chosen for the material The plate 1s 2 in thick and has dimensions of 33 in x 36 in The long dimension is in the direction of travel The area defined by these dimensions allow for a large working area for various suspension designs To reduce weight the
108. rd to work on this research project under the Virginia Institute for Performance Engineering and Research VIPER project based at the Institute for Advanced Learning and Research IALR in Danville VA Justin finally finished the project in late 2006 and received the Master s degree in 2007 At this point the pursuit of a racing career finally came to fruition After a short stint as a mechanic in the Nextel Cup series with Front Row Motorsports he finally scored a full time gig as an engineer at Hall of Fame Racing in Charlotte NC Justin decided to take a chance and go race Perhaps he ll make it back to VT one day to continue on in pursuit of a PhD This would make Steve John Jimmie and Wilbur very happy probably Justin too 124
109. rican Cup GS Class racecar similar to that seen in Figure 3 8 The car has a minimum weight of 3000 lb 25 Using scale pads the left front corner weight was found to be 630 lb The suspension and mass was setup on the quarter car rig to have the same corner weight springs damper and suspension geometry as that of the actual racecar 26 Figure 3 8 Porsche 996 Grand Am Cup GS Racecar 3 6 1 996 Suspension The Porsche 996 suspension shown in Figure 3 9 is a typical variation of the MacPherson strut type independent suspension The primary components are the upright two piece lower control arm and strut comprised of a coil over spring and damper The suspension requires two mounts for the lower control arm A bracket 1s necessary for 30 connecting the strut mount and a fully adjustable inner tie rod mount is needed to constrain the steering motion of the wheel Strut mount Strut Upright Tie rod Lower control arm Figure 3 9 LF Porsche 996 MacPherson Strut Type Suspension First a solid model of each suspension component was created such that the mounting points were located as accurately as possible Detailed blue prints for these components and chassis mounting points were not found in the public domain making this process somewhat difficult The lower control arm tie rod strut and strut mount were measured directly with a scale and calipers due to their relatively simple geometry The upright was taken to a
110. rithm in simulation only one of the desired responses were fed into the inverse controller The other desired response was used to help adapt the filter weights only 99 lemod joue 1 u02 Z Poe ulua tF13npolg uep joue 6 unics Jamod jous juoo A Zpnpola lqeu3 uleb lous Bunicsun ul goua WOUJ Wy ob y SWT 1e99e A WOU Z Jojeuluua Z JO IJ X ODDS E A ay IX 1J0 n 9 v Ct 9 14 SAUp Mau Jemod uous ndu g1anpalg grojeuiuus Joue yndul m ON O Aejep andui Jamod sep ndul clojeu ua pos spnpald jase A asyo kel Sse LW Gunidsun palisag Ae ap Bunids un Jamod sep A zioe uwa 19npold Jolla Z 89JE Z E Aejap Gunics 833e z Jemod sap z 1038 U Uta Elanpolq esuocse sseu Gunic6 palsag Figure 6 18 Real time Control Simulink Block Diagram 100 OUI AMA MA DOUS AMA DO Ew P SAUP A 0005 AWA 0006 oaz JUblem o1 u03 13594 siyblem u03 O1 UOJ MAA MST L H AA OS Lo npolg 109 4 Sap A 00 G Aejag padde LaplalQ 0005 0005 Ay trz L XE AU IA apIAq LAB eq padde 0005 Sg mC Joo Jamod A 1191 14 91810610 E Ms 9992 A JOO J Jamod Z XBJAUIA 19114 8181 q Z Mr 900872 zAejag padde 24 Z AY 0005 Figure 6 19 Detail
111. rtial and aerodynamic loading on the sprung mass The sprung mass has been designed to accommodate Aerotech electro magnetic motors one on each side These will be somewhat innovative as most loaders in 7 post systems are electro hydraulic with force feedback The design 1s such that the magnets of these motors will bolt directly to the load frame Flanges on the sprung mass have already 39 been designed such that the armatures will bolt directly to the mass This combination will apply the desired inertial and aerodynamic load required Another future project is to demonstrate the flexibility of the test bed by implementing the suspension of a completely different vehicle type Plans are in place to replicate the suspension of an AM General HMMWV This vehicle is substantially different in that it has a corner weight that is nearly 2000 Ibs more than the Porsche and experiences much larger amplitude vibrations in the sprung mass Concurrently there is also discussion of installing a NASCAR Nextel Cup suspension on the rig These racecars have a short long arm suspension which is a completely different design compared to both the Porsche and HMMWV At any given time the quarter car rig can be reconfigured from testing one type of suspension to another in a matter of a few hours Another possible function of the rig is to lock out the motion of the sprung mass and perform compliance or durability tests Additional functionality is to install a dyn
112. s of the Real time Filtered X LMS Algorithm 101 The LMS Algorithm block in Figure 6 18 is further expanded in Figure 6 19 This code has virtually the same functionality as that used in simulation The only alteration is the addition of a switch at the output of the summing junction for the weight vector This switch is included to be able to reset the weights to zeros should the system become unstable or run several test using the same identified plant models Control Desk panels were developed to command the control software Screenshots of the two layouts are shown in Figure 6 20 and Figure 6 21 This software was used to enable and disable the control algorithm and tune the step size for each error path This software could also reset the control filter to zero coefficients change the leak in the algorithm and graphically monitor the convergence of the error A second layout was used to watch the weights move and help determine when they have converged E q_car_to_box_2 power ControlDesk Developer Version control layout power Na File Edit View Tools Experiment Instrumentation Platform Parameter Editor Window Help x Mta E K ban UE amu FEB 49 gt o fi amp 2 power floor y power floor Control Weights Reset Corto Sep Ste prg x Control enabled m Control Sep SE msprag ced Actuator Actuator Limits 0 20 0 20 0 0
113. sed in this study could be applied to a direct comparative test to rate the performance against the existing art for 7 or 8 post test rigs 2 2 1 Industry Standard The current industry standard control method is a batch processing algorithm 7 14 15 The various software packages using this method do so in distinct iterations as follows To start data 1s collected during the road test of a vehicle Next the vehicle or equivalent specimen is installed on the shaker rig The specimen 1s then excited by independent shaped white noise signals running to each actuator simultaneously The response from vehicle mounted sensors is collected and a linear model is estimated to match the multi input multi output relationship of the inputs to the response This model 1s usually based on a frequency response function This model must be of high quality because it is used in each subsequent step An inverse MIMO transfer function of this model is then calculated and convolved with the data recorded from the road test to create a road or drive file The resulting drive file is a collection of signals one for each actuator that are the same length as the original recorded data This is the first iteration The resulting drive file 1s then scaled to protect the equipment and vehicle and then played through the 7 post 13 actuators The response of the vehicle is recorded once again and compared to the desired response The error between these is then co
114. signals 79 6 EXERIMENTAL PROCEDURES AND RESULTS With proof of concept in simulation the final step is implementation to the quarter car test rig This chapter follows much of the same structure as Chapter 5 However this 1s where everything comes together with hardware in the loop The chapter begins with a brief description of the test setup including sensors and data acquisition Next the system identification setup and tests are discussed along with the results of the study Finally the control algorithm 1s implemented on the hardware The chapter closes with a discussion of the results 6 1 Test Setup This section details the equipment used for the physical testing The instrumentation and sensors will be covered along with the basic methods of performing a test 6 1 1 Sensors The sensors used to measure the mass accelerations are PCB model number 333B40 accelerometers These sensors use a powered piezoelectric shear crystal and have a frequency range of 0 5 30000 Hz These accelerometers are rated at 10 G and output approximately 500mV G The sensors were positioned so that they were exposed to as little transverse vibration as possible These vibrations could cause a small non linearity error in the measurement Installation was a fairly easy task for installation on the sprung mass The top of the mass was drilled and tapped to use a threaded stud to hold the accelerometer down This face was perpendicular to the motion o
115. sportation Research Institute Ann Arbor MI p 309 315 1995 MTS Systems Corporation Eden Prairie MN 2007 image provided Servotest Systems Ltd Slough Berkshire England 2007 120 APPENDIX Appendix A Rig Maintenance There are few simple maintenance procedures to ensure good operation of the quarter car test bed The following 1s a short bulleted list of items that require periodic attention NSK Linear guides require Alvania AS2 grease approximately once a year Keep the guide rails lightly coated with grease or other rust inhibitor during long periods of down time to prevent rust from developing Periodically check the torque of the T bolt clamps They can become loose during some vibration tests Monitor the status lights on the hydraulic power unit The unit has over temperature and filter clogged lights If the unit requires filter replacement one can be ordered from the phone number and part number listed directly on the filter housings inside the pump enclosure MTS documentation contains the changing intervals otherwise The service manifold also has a filter with a mechanical indicator Periodically check the indicator while a test is running to ensure that the pressure drop across the filter is not too high If it is replace the filter Inspect service manifold and pump accumulator pressures semiannually or as system performance dictates Proper accumulator pressure for each may be found on the accumulators
116. t have the same linear characteristics over the range in which the test is operating These shortcomings along with eliminated or simplified suspension geometry can lead to a gross error in the representation of the actual vehicle Figure 2 2 is an example of one such quarter car test rig In this system the suspension compliance of a vehicle is wholly represented by a set of air springs The tire 1s represented by elastomeric mounts The sprung mass 1s represented by a sliding carriage carrying lead weights The bearings are roller wheels and Teflon bushings running in grooves on extruded aluminum uprights 11 The rigidity of the load frame is also a potential issue due to the vast amount of bolted joints and aluminum extrusion construction Figure 2 2 Simplified Quarter car Test Rig VT AVDL Other limitations of conventional quarter car rigs include the inability to introduce dynamics such as lateral forces and weight transfer of the vehicle in events such as cornering braking acceleration and aerodynamic loading It was asserted that in a cornering event the outside front wheel may be carrying as much as the entire load of the front half of the vehicle while the inner wheel may be carrying a negligible load 12 Thus the vertical loads that a particular vehicle must carry will change dramatically during such events Also during such cornering events the vehicle may roll causing geometry orientation of the suspension to change This wi
117. t was required Though the plant 1s completely known for this simulation study it 1s treated as an unknown system by the software for the purposes of identification and control Itis also useful to know the plant because this allows a direct measure of how well the FIR filters identify and control the system For this study a simple linear two mass quarter car model was chosen This was an obvious choice because it has the same types of input and outputs that the real quarter car test rig has In this case one velocity input and two acceleration outputs The use of a quarter car model as the plant was not required to demonstrate the concept The quarter car model was chosen simply to allow for a chance at being able to compare data from the test rig later in the study Its use also aids in making physical sense of the results given 5 1 1 Mathematical Model The quarter car model is the usual two degree of freedom vibration model of a single corner of a vehicle Figure 5 1 is a diagram of the quarter car model This model 1s a two mass model which only concentrates on the vertical motion of the vehicle on one corner The model contains a sprung mass and unsprung mass denoted by m and m 51 respectively The coordinate associated with the motion of the sprung mass 1s called z and the coordinate associated with the unsprung mass is y The suspension is modeled with a simple linear spring k and damper c The tire is modeled as a linea
118. ta from the rig could not be reproduced then the problem would be even more difficult to bring track data in for replication using this algorithm To collect data a filtered white noise excitation was input to the rig This noise was filtered with a discrete filter convolved from two low pass filters The two filters were a single pole 4 Hz filter and a four pole 50 Hz filter The filtered noise was played into the rig and the accelerometer signals were recorded directly with the EZ Analyst software running the IOtech system at 1000 Hz The signals were anti aliased by the data acquisition system The same signals were filtered and recorded two different times One data set was 103 created by filtering the data with a 15 Hz low pass filter The second data set was created by low pass filtering the accelerometer data with a 30 Hz filter Two control experiments were performed to replicate each set of data to see how the excitation bandwidth would affect the quality of convergence on a solution The desired response data size was recorded for 60 s 6 4 3 Experimental Results 15 Hz Data Reproduction of each data set was attempted several times to learn the best settings for the adaptive filter coefficients and step sizes Each time the number of filter weights or delay size was changed the software had to be recompiled and uploaded to dSPACE The controller step sizes could be changed during the test via Control Desk For all tests the unspru
119. ter car model detailed later The corner weight chosen was 900 lbs The offset distance or the distance at which the actuator applies a force to the tire relative to the bearing was chosen to be 20 in These somewhat extreme values were chosen to ensure a safety factor in the design and to ensure a high load capacity for future use of the rig 26 3 4 2 Design and Functionality The design of LH35 bearings 1s a two groove gothic arch guide rail made from hardened and ground steel The carrier which runs along the rail has a recirculating ball bearing design Figure 3 6 shows a cross section of the rail and cutout of the carrier The ball bearings are of angular contact design which yields the high load capacity and low friction design These bearings are an interchangeable design between rail and carrier making them a cost effective solution LH LS Series Figure 3 6 Section of LH Series Bearing The guide rails are 1500 mm long This was chosen to allow the sprung mass to have a high range of motion allowing for various applications For this application the specification for the rail to carrier clearance was given such that there 1s a slight amount of preload in the bearings This was done to eliminate rattle space between the carrier and rail which could cause parasitic vibrations during a test The preload can not be too great however as friction is a function of the preload Based on NSK documentation the dynamic friction fo
120. ters converged on their minimum very quickly just as they did in the simulation As expected they do not do as good of a job identifying the quarter car plant as in simulation The last 10 000 points of each signal were used to calculate an RMS value of each signal after convergence These RMS values were used to calculate an error based on how small the model error was compared to the acceleration signals The results are compared to the simulation results shown in Table 3 below Table 3 ID Error Comparison Model Metric Unsprung TF Sprung TF 2 30 xperimental Error 16 90 9 90 B Reduction Sim 30 dB 60 dB B Reduction Exp 15 dB 20 dB The values in the table indicate that the FIR filters are much better at modeling the dynamics of the simulated model than they are at modeling the real physical system This is not surprising because the simulated model was an ideal linear system The 94 quarter car rig has a lot of non linearity associated with the suspension geometry bearings bushing and the like as well as additive measurement noise Figure 6 14 and Figure 6 15 are plots of the power levels of the mass accelerations and the modeling error Much like in the simulation analysis examining these power plots further show the quality of the model The power levels of the signals were computed by squaring the respective signals and then low filtering the squared signal with a fourth order 0 1 Hz filter These product and filter
121. to the identified numerical model the frequency response of the quarter car model was examined Figure 5 2 is a plot of the frequency response of the continuous time state space model The frequency response shows the two expected resonance frequencies The sprung mass appears to have a resonance near 5 3 Hz and the 55 unsprung mass has a resonance near 26 Hz The phase remains relatively unchanged at low frequencies approaching DC This would be expected as such low frequency excitation does not tend to excite the dynamics of the system This low frequency phase 1s at 90 degrees because the transfer function 1s between a velocity input and acceleration outputs Cont time SS frequency response 180 90 0 90 apra 180 Phase deg 50 Sprung 40 Unsprung 30 20 10 Mag dB 0 10 20 30 10 10 10 10 Frequency i 10 Figure 5 2 Frequency Response of the Analytical Quarter car State space Model 5 2 System Identification Study With a quarter car model created the next step was to test system ID In an analytical simulation First a Simulink model was created to implement the system ID technique based
122. turning the actuator on and off If the ID subsystem were disabled the actuator output was programmed to reset to zero and the FIR weights were programmed to hold their current values at the time Thus once the identification routine was completed output to the actuator form the ID subsystem would not interfere with that from the adaptive controller Also the converged weights when held could then be used in the adaptive inverse control subsystem 91 6 3 2 Excitation Signal Shaping Considerations similar to that in the simulation had to be made for the shaping of the excitation of the input signal for system identification In addition to the desire to excite the system in the frequency range of interest care also must be taken not to exceed the limits of the actuator For this test a band limited white noise excitation was filtered with two cascaded low pass filters A single resulting filter was constructed as the convolution of two Butterworth filters One was a one pole filter with a 4 Hz break frequency and the other was a four pole with an 85 Hz break frequency The frequency response of this shaping filter is shown in Figure 6 11 Clearly the filter does not pass much signal past 100 Hz The magnitude crosses 20 dB at 40 Hz Transfer Function Phase deg O 20 40 Mag dB 60 80
123. tware 83 allowed control of the experiment and collection of data with a series of windowed layouts With this interface the hydraulics could be controlled and the system ID and control algorithms could be run and monitored Figure 6 5 is a general layout of the experiment Quarter car Rig IOtech DAQ Accelerometer Signals Ethernet E 5 O a E A gt Feedback Displacement Command MTS PID Controller dSPACE AutoBox Figure 6 5 Instrumentation Layout Generally In an experlment the MTS controller was set to accept and follow an external displacement command This PID controller s purpose was to insure that displacement command signals were followed by the actuator The external command comes directly from dSPACE based on the software running at the time If system ID is enabled the excitation comes from an attenuated filtered white noise signal generator If adaptive inverse control is enabled then the command signal for the actuator comes from the output of the adaptive control filter The IOtech system anti aliases and low pass filters the accelerometer signals before sending them to dSPACE The IOtech is configured for the accelerometers with PC based software called EZ Analyst The digitized filtered signals may also be viewed on 84 the PC with this software The oscilloscope was used to monitor the analog signals moving into dSPACE It was found that the signals picked up a lot o
124. uction from the source signal to the error signal The error signal power of the unsprung mass 1s approximately 22 dB lower than that of the desired signal Likewise the error signal of the sprung mass is about 23 dB down from the desired sprung mass signal 76 35 m 40 2 Desired unsprung mass response A Unsprung mass error s Y 50 55 1 2 3 4 5 6 Simulation Step No x 10 Figure 5 20 Signal and Error Power for Unsprung Mass 35 40 m 2 5 45 2 Desired sprung mass response a Sprung mass error 5 50 Y 55 l 60 i 1 2 3 4 5 6 Simulation Step No x 10 Figure 5 21 Signal and Error Power for Sprung Mass The control weighs are plotted in Figure 5 22 The weights represent the impulse response of the inverse of the quarter car transfer function This response can be moved TI forwards and backwards by adjusting the amount of delay in the desired signal before comparing it to the actual signal A goal is to move the response such there are near zero weights on both the leading and trailing tails of the larger response x 10 Magnitude 0 50 100 150 200 250 300 350 Weights Figure 5 22 Converged Control Weights Another way to gauge the quality of the inverse model is
125. utterworth filter was utilized to create this low pass filter The 2 pole filter had a break frequency of 0 3 Hz The use of a low pass filter removes most of the dynamics from the signal leaving only a relatively clean DC power signal The plots in Figure 5 8 and Figure 5 9 show the power levels of the signals as the error signal 1s close to converging on 1ts minimum The 62 power levels are displayed on a decibel scale In general a 10 dB difference between the desired signal and the error signal is considered acceptable and 20 dB or more of a difference 1s considered excellent These plots show that the power level of the sprung mass error signal decreases to nearly 60 dB lower than the accelerometer signal Likewise the error of the unsprung mass error decreases to nearly 30 dB lower than the unsprung accelerometer signal Both of these converged power level drops are considered fantastic which is to be expected for a simulation without external noise added 10 _ 0 m D 2 10 O a T 5 D 20 30 Sprung accel power 40 error power 3 3 5 4 4 5 5 Sample No x 10 Figure 5 8 Sprung Accelerometer and Error Signal Powers 63 25 20 Signal power dB Unsprung accel power error power 2 5 3 3 5 4 4 5 Sample No x 10 Figure 5 9 U
126. wer supply The power unit shown in Figure 3 13 runs on 480 VAC 3 phase power and 1s water cooled It operates at 3000 psi and can supply up to 30 gpm 35 Figure 3 13 MTS SilentFlo Hydraulic Power Supply Hydraulic power is regulated to the actuator by an MTS 293 11 Hydraulic Service Manifold It also supplies the oil pressure for the hydrostatic bearings in the actuator The manifold seen in Figure 3 14 was specified to have an over sized accumulator on the pressure side to aid in bandwidth requirements of the system 36 L Figure 3 14 MTS Hydraulic Service Manifold Finally the controller shown in Figure 3 15 provides the real time closed loop control for the hydraulic system The controller is an MTS Model 493 02 FlexTest SE Controller This stand alone controller can close the loop with force or position feedback It accepts one analog input for external command signal generation and it also has an internal function generator The controller also has provisions for four digital inputs for triggers and interlocks four digital outputs and three analog outputs for monitoring signals or closing an outer loop Figure 3 15 MTS FlexTest SE Controller a 3 8 Maintenance For the purpose of maintaining the quarter car test rig and supporting apparatus a bulleted list of maintenance items 1s found in Appendix A 3 9 Summary and Future Developments The following section provides a brief summary of the functionality of t

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