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DSP Based Electric Drives Laboratory - HCMUT

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1. Van C Von t Von t Flies Pee Pay ents a CRA PES N _ Veont a t l 7 S Ai Y Veont bt 1 pi id Veont c t 1 A Ad 7 1 2 Fig 1 a Switch mode inverter for ac drives b Average representation of the three phase converter 2 3 Sinusoidal Pulse Width Modulation A traditional approach is sinusoidal pulse width modulation where sinusoidal control voltages are compared with a triangular carrier signal to generate the switching functions qa in Fig 1a The resulting duty factors transformer turn ratios in Fig 1b are based on the following expression etc 4 d 545 2 tri lt a Since Vy d V Vy 4 V V y d V expressions for Viy Vy V y can be similarly written using 4 B DAN tri Vin Ya T G a etc 5 76 Experiment 6 Frequency Control of AC Motor Drives DSP based Electric Drives Laboratory The inverter terminal voltages with respect to the negative dc bus N contain a dc offset V 2 which is of zero sequence This zero sequence cancels out in the motor voltages Van Vpn gt V ch 2 2 Simulink implementation To implement the algorithm in Simulink we shall first assume that the three phase voltages at the stator terminals must have the following expressions v t V cos 2z f t an Vn t Vy cos 2z f 1 22 6 Va t V cos 2a f1 E The freque
2. Fig 3 Voltage and duty cycle calculation using eq 4 and 6 gt After masking the blocks in Fig 3 the Simulink model can be completed with the command value of the frequency the K V f constant and the DS 104SL_DSP_PWMs3 block A Rate Limiter block is inserted in the reference frequency path to set the acceleration and deceleration times Limitation of these two transients is necessary to limit the stator currents during start up or breaking The Sinusoidal PWM block contains the masked model from Fig 3 Of course in our experiment we would like to monitor the speed and at least one stator current Complete your model as follows A duty cycle limiter must also be added the bounds should be set to 0 1 and 0 9 to ensure that the motor drive board works properly Copy and paste the speed measurement blocks from a previous experiment Copy and paste the A D current measurements from the dc motor experiment The model should be similar to the one in Fig 4 DS1104SL_DSP_PW M3 PWM Stop oka i a Enc dela positon DS1104ADC_C5 DS1104ENC_POS Cl b lt ADC MASTER SETUP DS1104ADC_C6 2 pi Ts 2000 b DS1104ENC_SETUP Fig 4 Complete Simulink model of experiment 6 78 Experiment 6 Frequency Control of AC Motor Drives DSP based Electric Drives Laboratory Make sure you define at Matlab prompt all the necessary parameters Va Ts K gt Set the simulation parameters as in previous experimen
3. x 54 Run the curve fitting algorithm using FITRAZ lambda and FMINSEARCH FITRAZ and FMINSEARCH returns the error between the data and the values computed by an exponential function of lambda FITRAZ assumes a function of the form y yO c 1 exp lambda 1 t c n exp lambda n t with n linear parameters and n nonlinear parameters lamO 100 Define one initial root n 1 lambda fminsearch fitraz lam0 Start iteration using initial root hold off 54 Computing the motor parameters 5 The algorithm returns the best lambda Ra La 4 With the steady state current i0 y0 calculate the armature resistance V 3 i0 y0 Ra V i0 La Ra lambda 63 inerdet m Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh 4 inerdet m h h Calculation of dc motor inertia using a curve fitting algorithm for the speed response on shutdown from steady state operation vA h h Author Razvan Cristian Panaitescu 4 Date Feb 06 2002 h University of Minnesota Department of Electrical and Computer Engineering Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh global Plothandle t y y0 Variable declarations Load the speed mat file saved from the dSPACE Experiment The file contains the speed response at shutdown load speed t speed X Data Define time variable y speed Y 3 Data Define the y variable speed Calculat
4. ext 120 40 wa ext 25 47 5 TL exe 25 108 a p Examples of drawing commands p Examples of drawing commands Command port_iabei labe specific ports gt Command Jocet_aanes labei specific ports Symtax port_labei output 1 xy Syntax port_labelfoutput 1 y Unmask OK Cancel Help Apply Unmask OK Cancel Help Apply a DC Motor Icon b DC Motor Parameters Figure 5 2 Masked Model of DC Motor and Drawing commands for Graphical Representation 68 e Now enter the values of DC motor parameters which we have evalued in earlier experiment 5 3 Controller Design Once the dc motor model is built the controllers can be added and tuned Start with the current loop for which a PI controller is required e The model for a PI controller is first created see Fig 5 3 Double click the integrator block and enable limit output Then set the Upper and Lower saturation limits to lim lim The lim value should be set to 1 as the control voltage maximum value will be 1 which is the input to Kpum block The resultant maximum value of voltage applied to the DC motor will be 42 which is the rating of the DC motor e The armature current is fed back to the controller input gt gt Ve Saturation Ki_i Integrator Figure 5 3 PI controller Model e The parameters of the PI controller namely Kp_i and Kii are computed using the motor paramet
5. 37 Duty cycle a Duty cycle b Duty cycle Constant PUMA Stop D5 11045L_DSP_PWM3 PWM Control Figure 3 4 Two Pole Switch Mode Comverter Model in Simulink and another one negative 3 3 Real time DC Switchmode Converter Implementation The lower side of the model is grouped in a block so called Duty Factor Calculator Since in the real time implementation the upper part is physically present outside the PC the only computation required is the duty ratios for each converter pole DSPACE provides a block called DS1104SL_DSP_PWM3 which embeds the triangular wave form generator and the comparator for all converter poles Thus when building a real time system all the upper portion of the model is replaced with this ASPACE block to generate the PWM signal as shown in Fig 3 4 The inputs in the DS1104SL_DSP_PWM3 are the duty ratios needed for converter control 3 3 1 Simulink model for real time implementation e Create a new simulink model and save it as Step4_03 mdl Drag and Drop the DS1104SL_DSP_PWM3 block from the dSPACE library Set the switching frequency to 10000 Hz and dead band to 0 by double clicking the block Cut and Paste the Duty ratio calculator portion from Step3_03 mdl e Connect a constant block to the remaining inputs as shown in Fig 3 4 Set the value of constant blocks to 0 38 3 3 2 Creating the user interface in Control Desk e Connect the Lab Oscilloscope to the PHASE A1
6. Te effect equal to zero in the mechanical dynamics eqn 4 7 it requires a complete shutdown of the motor supply The motor is brought to a no load speed w such that the armature current is zero and the friction losses are compensated by controlling the active load At t 0 the whole system is shutdown This implies that the electromagnetic torques in both the MOTOR Te and the LOAD Tz becomes zero The dynamic equation will become dw 0 T friction Bw S 4 11 The speed decreases exponentially in time w t wo EEE en e im 4 12 55 Our friction model is approximate The constant friction torque is in fact dependent on speed It should cancel once the speed reaches zero otherwise it would become an active torque and drive the motor into the fourth quadrant Rearranging equation 4 12 w t gee ERE nition wo Bae nition e Tt Q t Ape 7 4 13 from the above eqn 4 13 it is clear that by up shift the exponential curve with a constant interia is just dependent on the slope of the curve at t 0 dQ dt dw 0 0 4 14 mwas 4 14 Bee 6 ae t 0 J Knowing wg and B and graphically determining the slope of the curve one can calculate the motor equivalent inertia J Note Inertia is a scalar The value obtained is the algebraic sum of each motor s inertia 4 4 2 Simulink model for dynamic parameter determination The model presented in section 4 3 will be used for this secti
7. block provided by Simulink Create a new directory for the experiment Expt03 Start Matlab and set the path to this directory e Open a new Simulink model Drag and drop the Repeating Sequence block from the Sources library 33 e Double click the block and enter the following set of data Time values 0 0 5 fsw 1 fsw Output values 1 1 1 Where the fsw variable will be our switching frequency set as a global variable in Matlab e Add a Scope to the Repeating Sequence block output Type the value of fsw at the Matlab prompt say fsw 10000 which means 10kHz e Set the Simulation parameters to the following values Stop time 0 002 Fixed step size 0 000001 Solver Options fixed step odel Euler e Run the experiment The result should look similar to the one shown in Fig 3 1 stepi_04 10 xj EE Iol x File Edit View Simulation Format Tools Help la o P fp dh ej e Tg D B amp n p m fNo Repeating s Sequence PA F 100 LEGE Figure 3 1 Triangular Waveform generator with 10kHz frequency 3 2 2 Duty Ratio and Switching Function To obtain the duty ratio for one pole PWM generation we can use the equation 4 7 in Chapter 4 Electric Drives by Ned Mohan i e 1 lv trol A d z 3 1 34 Using the relation 4 10 the duty factor can be obtained with VAN dy z EEE 3 2 3 2 Solving the Eqn 3 1 and Eqn 3 2 and considering the a
8. Creating a Model in Simulink Using SIMULINK we will develop a simple continuous time system to understand the mechanical interactions rotating system consisting of motor and load Follow the steps below e Create a folder exptl e Start MATLAB 6 5 from the Start menu e At the top of the screen you will see a box that lists the Current Directory This is your Path Browser and needs to be changed to the folder that you have just created i e expt0 e Type Simulink at the prompt line A new window will pop up that contain the various Libraries provided by Simulink and dSPACE We are trying to develop a simple rotating mechanical system model for which following equations apply 1 1 Jeg Jm JL 1 2 Ej 1 a RE 1 3 is jed 1 4 mat 1 5 For our example we will use Jeg 0 058kg m e To create the above model in Simulink first create a New Model from the File menu e To add blocks to your Simulink model you simply click on the block you want in the Library window and drag it to your model and drop it For our model we will need the following blocks One sum block from the Math library One gain block from the Math library Two slider gains from the Math library Two integrators from the Continuous library Two constants from the Source library One mux from the Signals and Systems library One scope from the Sinks library e In many cases the Simulink blocks have properties
9. Figure 3 6 Averaging model in Simulink e Drag a Gain block and connect it at the output of Sum block Set the value to 1 11 for 11 point averaging e Select the output port Out1 from Sink library and drag it into your model e Connect all the blocks as shown in Fig 3 6 e Select the unit delay s input port output port gain and sum block together and create a subsystem For creating a subsystem go to Edit menu of your model and then Create Subsystem e The system obtained is nothing but 11 point avaraging system Change the subsystem name to Averaging e Connect a Terminator at the output of this 11 point averaging of speed measurement and label the signal wm The model obtained should look like the one shown in Fig 3 7 Before building the real time model don t forget to define Ts and Vz as global variables at Matlab prompt 3 4 3 Creating Control Desk Layout e Build the DSP code for the simulink model saved as Step5_03 e Start the control desk and create the new experiment in the same working directory as that of simulink file e Create a layout and drag a slider gain control and two plotters e Drag and drop V_motor into slider gain control 42 Duty cycle a Duty cycle b Duty cycle Constant Pind Stop DS11045L_DSP_PWM3 PM Control la ep BS1104ADC_C5 Enc position ENCODER Enc detta position MASTER SETUP DS1104ENC_POS_C1 DS1104ENC_SETUP Figure 3 7 Real time model for no loa
10. PushButton RadioButton E SelectionBox Fig Slider Br Static T ext FE TableE dior LED s Automotive BE leyout Ef example Lee finalTime 1x1 Floatleee6 Simulation sto EE Model Root Q Transfer Fen currentTime 1x1 Floatleee6 Current simul E OutGan modelstepSize 1x1 Floatleee64 Fixed step siz E In Gain simState 1x1 Int32 Simulation sta E D 1104ADC_C5 errorNumber Ulnt32 Error number R DST104DAC_CI Eh ATI Data S E Slider nGain M4 TPN Loo Viewer A Interpreter File Selector c manojiexpt3 example1 sat For Help press F1 Eor om 04 02 2003 15 50 sRstart 4 E ABExperiment 3 control Sex fabmp Paint Gm asom Figure 2 10 New Layout Window for Instrumentation and Control 24 The controls displayed in the Virtual Instruments toolbar let us handle only the variables that can be modified on line i e the P type variables Our example has 5 such variables Four of them were listed in Table 2 2 and there is one more under the Slider Gain hierarchical level which controls the amplitude of the Gain block e Select the SLIDER button from the right toolbar e The cursor changes into a square target Click and hold the mouse while dragging a rectan gular shape in the Layoutl window see Fig 2 11 aeG Bessa 222 x 7 6 az lex e Figure 2 11 Selecting Slider Bar from Visual Instruments and
11. The system of two first order differential equations shows that the dc motor is a second order system The two state variables armature current ia and angular speed w are not independent 54 Therefore the inductance La and the moment of inertia J would both contribute to the variation of each of the two state variables It is convenient to isolate the variations described in 4 6 and 4 7 thus only a first order differential equation has to be solved for each variable Two sets of experiments are then required to determine La and J while keeping the speed and respectively the current to a zero value Inductance Determination To estimate the armature inductance the motor must be held standstill w 0 Block the rotor with a mechanical brakes and then apply a step voltage at the armature terminals The current increases exponentially in time and equation 4 6 becomes di Via ad 4 8 dt Solve the above Eqn 4 8 for the current we get Va Sza ia t zr 1 0 c 4 9 where La NE a Ra The current increases exponentially to the final value equal to ta The slope of this exponential curve measured at 0 is depenedent on the value of inductance La as given below dia Va Ra Ra 0 Va ZE ep a ot to hg ee 4 10 ZA GRE i 4 10 A graphical determination of the slope at a given voltage would lead to the determination of the motor inductance La Determination of inertia To make electrical torque
12. and PHASE B1 terminals of the motor drives board e Open the simulation parameters and change the fixed step size to 0 0001 e Build CTRL B the Simulink model e Open ControlDesk and create a new experiment in the same directory e In a new Layout drag and drop a slider gain and assign the V_AB variable to it e Add some Plotters to visualise the duty factors Your layout should look similar to the one shown in Fig 3 5 e Run the experiment and after turning on the power supply check the output waveforms on the Lab Oscilloscope 3 3 3 Real time Results of Switch mode DC Converter Once the setup is ready collect the following data e Record the output voltage waveform of oscilloscope for the values of V4p set in Sec 3 2 4 e Record the corresponding duty ratio waveforms for the above values e Measure the output voltage frequency and comment on the result obtained 3 4 Controlling of DC Motor under No Load Condition in Open Loop Before we start the implementation of the model for control of DC Motor in open loop make sure that you have connect the armature of the dc motor under test to the output of two converter poles A and B The IA1 current measurement port on the drives board has to be connected to Channel 5 A D converter of the dSPACE controller box Also the encoder output is connected to the INC1 9 pins DSUB connector on the dSPACE controller The speed of a dc motor can be modified by varying its supply voltage The
13. delta position and position of the first encoder interface input channel The delta position represents the scaled difference of two successive position values of a channel To receive the radian angle from the encoder the result has to be multiplied with 20 20 es 3 8 encoder_lines 1000 SB where encoder_lines is 1000 for the encoders used in the laboratory setup Since we need to determine the speed the delta position scaled to a radian angle has to be divided by the sampling time as in d A0 A90 w T digital tai t i T 3 9 Drag and drop the DS1104ENC_POS_C1 block from the dSPACE library In addition the en coder block the DS1104ENC_SETUP block is to be added to the model Connect a Terminator block to the Enc position Connect a Gain block at Channel 1 output i e Enc delta position and set its value as TET where Ts is the sampling time set in the simulation parameters under the fixed step box Now if you try to measure the low speeds you will see oscillations between the two speed values Hence we will add an averaging to get more accurate readings For preparing the averaging block e Select the Unit Delay block from Discrete library and drag the required number into your model say 10 for 11 point averaging e Select the input port In1 from Source library and drag it into your model e Drag a sum block and double click on the sum block and add the required number of signs in list of signs 41
14. drawing When the mouse is released you will obtain a slider control which let you continuously change any P variable between the limits selected As long as we decided to use amplifications between 0 and 5 double click the Slider control select the Slider Tab and set the Range Min and Range Max as shown in Fig 2 12 Now the limits where the cursor can be adjusted are 0 to 5 But the slider is still bordered with a red line This means that it hasn t been assigned a variable to control yet In the Variable Manager window at the bottom of the screen select the Slider Gain Click the P Slider Gain Gain variable and drag it to the rectangle drawn in the Layout window The new Slider control will display the handled variable and will no longer be bordered with a red line as shown in Fig 2 13 Now we can add some visualization equipment In our example only two signals are worth monitoring the system input coming from the real signal generator connected to ADC 1 and the output of the second order system Both should be displayed on the same scope The output signal will also be monitored with the Lab Oscilloscope connected to the DAC 1 channel on the dSPACE Interface Box Remember that the real values 25 p F 4 bi p b bi bi 3 fi 6 Figure 2 12 Slider Control Setting Window layouti 77777777777777777777777979777772077777777277777770277977279797770 cum SOS Sos Figure 2 13 Slide
15. i i i i i i i i 0 0 02 0 04 0 06 0 08 0 1 0 12 0 14 0 16 0 18 0 2 Figure 4 6 Current Waveform prompt See the program listing in Appendix 1 Inertia determination e In the Capture Settings Window two modifications must be made Increase the display length to 2 seconds and change the Trigger Signal to SD e Check the SD control and increase the voltage on the MOTOR to 42 V Decrease the LOAD voltage reference to negative values such that the MOTOR current becomes zero The digital 59 100 l l l l 1 I L I l Figure 4 7 Current Waveform displays let you monitor the operations e Record the speed value at this operating point e Uncheck the Shutdown button This will initiate the display process and after two seconds the speed plot will stop and a decreasing exponential curve will be obtained see Fig 4 7 e Press again the SAVE button in the Capture Settings Window and store the data in another mat file Run Inerdet m at the Matlab prompt and record the result for the moment of inertia The program listing is shown in Appendix 2 4 5 Lab Report The lab report should be brief and should contain the details asked below e Complete all the tables e Provide all the machine parameters which you obtain using the above procedure e Provide all the graphs you obtain while finding the machine parameters 60 fitraz m function err fitcur lambda global Plothandle t y y0 A zer
16. mask editor as seen in Fig 5 2 After modifying the mask double clicking on the subsystem should bring up a window to enter the DC motor parameters kon Parameters Inilializason Documentation l kon Pararmoters Initializason l Documentation leon options Orawing commands leon options Drawing commands Frame lor 30 30 140 140 Frame lor 30 30 140 140 seie gaff Iproeits 75 50 80 05 5 o o 51 190 so 60 100 110 110 100 40 903 smie gap preeits 75 0 80 25 5 o o speso so 40 100 110 110 100 40 SOJ lot 10 10 70 70 30 110 110 30 1ot 10 10 70 70 30 110 110 30 Transparency lot 15 15 5 75 75 6S 65 90 25 25 20 20 2 25 30 Transparency lotl 15 1S 75 75 GS 65 90 25 25 20 20 25 25 30 lot 00 105 105 96 96 60 65 65 7 75 75 96 105 75 751 lotl 00 105 105 96 90 60 65 65 77 77 75 75 96 105 75 751 opaque zj loe 10 30 30 10 10 110 110 120 120 110 opaque gt lor 10 30 30 10 10 116 110 120 120 1103 Rotation lot 15 65 100 100 15 65 90 903 Rotation plot 15 65 100 100 15 65 90 90 lot 15 65 80 80 15 65 70 70 lot 15 65 80 80 15 65 70 70 Frea z lotl 15 657 60 603 15 65 50 0 Frea z LOC L1S 65 60 60 15 653 050 50 Units 1ot 15 657 40 40 unite 1otl 15 65 140 40 pex 0 127 5 DC Motor model exe 0 127 8 DC Motor model fautoscate gt mxt 120 120 Ta fautoscate text 120 120 Ta ext 110 80 Tea text 110 80 Teu
17. that can be modified by double clicking on them Make the following modifications Change the sum block so that is has instead of Change the bounds on the slider gains to 10 and 10 Set the current values for one block to 5 and the other one to 0 Change the mux to 3 inputs i a O Change the value of the gain to Jej TORR e To connect the blocks click on an input or output arrow and drag it to the other input or output you would like it to go to Make the connections as stated in the equations for the rotating mechanical system e To rename blocks click on their current names and change them To name connections double click on them and a text block will come up e After the connections are made the model should look like Fig 1 1 ox File Edit View Simulation Format Tools Help Tm input Integrator ki Integrator1 TL input TL 100 Figure 1 1 Simple Mechanical System Model e The next step is to run the simulation Before running the simulation do the simulation parameters settings To do this go to the Simulation menu and select simulation parameters Set the parameters as shown in Fig 1 2 e Once simulation parameter setting is done model is ready for simulation e Click the triangular button to start the simulation Simulation Parameters step1 Ej xi Solver Workspace vo Diagnostics Advanced Real Time Workshop Simulation time Start
18. time 0 0 Stop time 1 Solver options Type Fixed step x ode1 Euler gt Fixed step size 0 001 Mode Auto x Output options Refine factor 1 Refine output OK Cancel Help Apply Figure 1 2 Simulation Parameters Settings e Once the simulation is completed double click on the scope box To auto scaling the axes click the binoculars on the scope screen Your scope results should look like Fig 1 3 100 90 4 70r gt 60 50 5 40 20 Figure 1 3 Step 1 Simulation Results e Now by changing either of the slider gains and running the simulation using triangular button you will obtain different results in your scope 10 1 3 Changing the Simulation Model Now that we have created a simple mechanical rotating model let s add friction to our rotating system T tric Bw 1 6 For our example we will use B 0 025 e First make sure you have saved your previous model as Stepl Then make another copy of it and name it Step2 e In addition to making the change for the above equation it would also be nice if theta would become a repeating type sequence instead of continuously rising or falling To do this add either a sine or cosine block from the math library e Also remove the mux block and add another input port to the scope by double clicking on the scope Find the parameters icon in the upper right and change number of axes to two and time
19. will appear on the screen 30 Important note Remember that the object file compiled has to be in the DSP memory It is not implicitly loaded with the experiment 2 7 Lab Report The lab report should contain a brief along with the details what have been done in the lab and details asked below e Simulation results of the 274 order system obtained in sec 3 2 4 e Results obtained on oscilloscope and in control desk in sec 2 6 e Compare the simulation and real time results and comment on the that e Change the value of slide gain in real time simulation and see its effect 31 32 Experiment 3 Switch mode DC Converter and No Load DC Motor Test 3 1 Introduction In this experiment the operation of a DC switch mode power converter will be studied First the building block approach will be used for simulation of converter operation Then a PWM algorithm will be implemented for a DC power converter The purpose of the real time implementation is obtaining variable voltage at the output of the power converter while controlling its amplitude with a dSPACE based user interface 3 2 Simulation of DC Switchmode Converter 3 2 1 Triangular Waveform To modulate the width of the voltage pulses in a power converter a control voltage has to be compared with a triangular waveform signal Before we build the model for the converter a triangular waveform generator will be built in Simulink using the Sources Repeating Sequence
20. 104ADC_CS DS1104ADC_C Constanti ENCODER MASTER SETUP DS1104ENC_POS_C2 DS1104ENC_SETUP Averaging Block Figure 4 1 Real time Simulink Model for Motor and Load Control 4 2 1 Adding a dc load to the dc drive To determine the dc motor steady state characteristics a second dc motor will be axially coupled to the motor under test MUT The second motor will be voltage controlled in an open loop similarly to the MUT e The armature voltage of the load should be connected to PHASE A2 and PHASE B2 terminals on the power board Set the Bus Voltage Va to 42V 48 e Ensure a firm mechanical coupling between the motors e Add asecond voltage control set of blocks in the Simulink model and connect the duty cycles to the 2 and 3 inputs of DS1104SL_DSP_PWM e Set the switching frequency in Unit as 10000H z e Double click the D 1104SL_DSP_PWM block go to PWM Stop and Termination uncheck Set all Ch and then click on Set all e Connect the IA2 channel to ADCH6 on the controller box e Make the load current available in the Simulink model by copying the first current measure ment and then double clicking on DS1104ADC_C5 and changing it to channel 6 e Save the model as Step1_04 mdl Your model should like the one shown in Fig 4 1 4 2 2 Creating the Control Desk Interface e First build the DSP code out of the original Simulink model saved in Step1_04 mdl e Open Control Desk and create a new exper
21. 47 84 G s e Set the parameters of the Transfer Fen block as shown in Fig 2 1 e Next drag a Signal Generator block from Sources library a Slider Gain from Math library and a Scope from Sinks library Connect all blocks as in Fig 2 2 e Now set the simulation parameters by pressing Ctrl E as 16 Block Parameters Transfer Fen x Transfer Fen Matrix expression for numerator vector expression for denominator Output width equals the number of rows in the numerator Coefficients are for descending powers of s Parameters Numerator 3347 84 Denominator ri 87 32 3947 84 Absolute tolerance to Cancel Help Apply Figure 2 1 Parameters for Second Order System o xi File Edit View Simulation Format Tools Help 3947 84 ER 52 87 92s 3047 84 Signal Slider Generator TianeferFon Gain noe Tet A Figure 2 2 Simulink Model of 274 Order System Set the solver options to fixed step and odel You need to specify a fixed step size Let it be 0 001 i e 1ms Stop time as 2 seconds Set the Signal Generator output to Square wave and frequency as 2Hz Keeping other parameters unchanged e Run the simulation by pushing the triangular play button and adjust the display of the Scope with the autoscale option You will obtain a plot similar to the one shown in Fig 2 3 17 loj x lsBlIOPPABE BER Figure 2 3 Simulati
22. DSP Based Electric Drives Laboratory User Manual Department of Electrical and Computer Engineering University of Minnesota ii Drives Board Familiarization 1 Introduction The drives board which we use in the Electric Drives Laboratory has been designed to enable us to perform a variety of experiments on AC DC machines The main features of the board are e Two completely inependent 3 phase PWM inverters for complete simultaneous control of two machines e 42 V dc bus voltage to reduce electrical hazards e Digital PWM input channles for real time digital control e Complete digital analog iterface with dSPACE board 2 Board Familiarization The basic block diagram of drives board is shown in Fig 1 and the actual drives board is shown in Fig 2 Please note that various components on the board are indicated in Table 1 2 1 Inverters Each 3 phase inverter uses MOSFETs as switching devices The 3 phase outputs of the first inverter are marked Al D 6 in Fig 2 Bl E 6 in Fig 2 Cl F 6 in Fig 2 and those of the second inverter are marked A2 I 6 in Fig 2 B2 K 6 in Fig 2 C2 L 6 in Fig 2 2 2 Signal Supply 12 volts signal supply is required for the isolated analog signals output form the dirves board This is obtained from a wall mounted isolated power supply which plugs into the DIN connector J90 B 2 in Fig 2 Switch S90 C 2 in Fig 2 controls the signal power to the board The green LED D70 C 2
23. ble Description File examplel trc Optional User Variable Description File examplel usr trc not available Generating template User Code File examplel usr c Generating template User Makefile examplel_usr mk Creating project marker file rtw proj tuw Creating examplel mk from c dspace matlab rtill04 m rtill04 tmf Building examplel dsmake f examplel mk WORKINGBOARD ds1104 BUILDING APPLICATION Single Timer Task Mode WORK DIRECTORY c manojijexpt3 BUILD DIRECTORY c manojiexpt3iexamplel_rtil104 TARGET COMPILER C PPCTools20 COMPILING examplel c COMPILING C d5PACE MATLAB RTI1104 C rti_sim_engine c C d5PACE MATLAB RTI1104 C rti_external_sim c C MATLAB6pl rtw c src odel c C MATLAB6pl rtw c sre rt_sim c examplel_lib o03 library sources BUILDING LIBRARY examplel_lib o03 BUILDING LIBRARY FINISHED LINKING APPLICATION LINKING FINISHED LOADING APPLICATION examplel sdf 1 dsll04 RTI Initializing 720 2 dsll04 RTI Initialization completed 721 3 dsll04 RTI Simulation state RUN 700 LOADING FINISHED MAKE PROCESS SUCCEEDED Successful completion of Real Time Workshop build procedure for model examplel gt Finished RTI build procedure for model examplel gt gt Figure 2 6 Compilations details developed by dSPACE and SIMULINK in Matlab Screen Thus for handling the variables of a simulation we must load the sdf file before starting the graphical design e F
24. d motor test Averaging Block e Assign one of the plotter for Ia and another one for wm e In order to record the numerical values of current and speed add two DISPLAY into the layout Drag and drop Ia in one of the display and wm in another one Now your experiment should look similar to the one shown in Fig 3 8 3 4 4 Results of No Load condition of DC Motor e Record the values of current and spend for different set of readings for the corresponding voltage values specified in Table 3 1 e Plot the voltage vs speed curve e Find the slope of the above graph Note Please keep the readings obtained in Sec 3 4 4 It will be required in future experiment 43 E EF SE ZZM SAMI motor Motor Current H Speed rad sec MMM EL SH lelea goog 11 40 30 20 10 0 10 20 30 4 RS p Motor Current Mb A Ay be 000 0 002 0 004 0 006 0 008 0 010 0 012 0 014 0 016 0 018 0020 000 0 002 0004 0 006 0 008 0010 0012 0014 0016 0018 0020 RZ expt_3_step2 Figure 3 8 Control Desk Layout Table 3 1 No Load Measurement ho O rad sec w D 3 5 Lab Report The lab report should be short with all the details asked below e Switching function result along with the simulation results of the 2 pole converter e Results of 2 pole converter obtained in real time for some positive value of V4p and for some negative value of VAB e Measure the
25. del in Simulink Our first example introduces the analog channels input output communication with external de vices For this example a Signal Generator is used to generate different waveforms as inputs to our signal processing algorithm The result of this process will be directed to an analog output channel in order to be monitored with the lab oscilloscope Suppose that we need to analyze the response of a second order system at different types of input signals with variable amplitudes The second order system is defined by the following parameters e Damping 0 7 Natural frequency wn 20Hz e We need its response at different types of input signals such as Sine wave Square wave Saw tooth wave e The input has a variable gain in the range of 0 5 Firstly simulation model will be developed using a model for signal generator and model for Oscil loscope e Create a folder expt03 e Start MATLAB and set the Path Browser to your working folder expt03 e Type Simulink at the prompt line and create a new model from File menu e Choose from the Simulink Continuous library the Transfer Fen block and drag it into a new simulation model The second order system with the parameters specified can be described in transfer function with the following relation 2 a 2 1 CE s 2fws w where w 2nf 27 20 62 63 and 0 7 The numerical model becomes 3947 84 ee ci m 2 2 s2 87 9625 39
26. e Start the Animation by pressing the animation icon in the Edit Mode toolbar 29 e You will see both the signal generator and the system output signals on the plotter Every two seconds the scope will clear and a new set of data are displayed e Change any of the parameters and watch the modifications in the signals displayed on the scope Also observe the waveforms in the plotter window and they should like shown in Fig 2 18 for the slider gain value displayed in Fig 2 18 Now the experiment is running and our ARAR s 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 18 2 0 1 0 2 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 Time design job is done SlidernGain Gain UU OOo RUC OOO EP erp un OOS tae 5 4 45 5 Input and Output Signals o Figure 2 18 Real Time Simulation Waveforms e For saving an experiment you must follow these steps otherwise you might loose some precious design in the layout or some simulation settings 1 Click File Add All Opened Files This implies that the experiment will remember the sdf file containing the variables to handle will know the path for all other files and will open the connections between the layout and the variables 2 Save the Layout in a file with the lay extension 3 Save experiment in a cdx type file e For loading an experiment simply click File Open Experiment and if saved as previously instructed the layout and the variables
27. e interaction with the system We need to visualize modify and analyze the variables For this dSPACE comes with its own Graphical User Interface called CONTROL DESK So let s learn how to use the Control Desk to interact with the real time simulation 2 4 Creating a new experiment file with Control Desk ControlDesk is a software that allows the user to look at the variables display their behavior and modify the simulation parameters by interacting directly with the DSP board e Start ControlDesk and select only the toolbars checked as shown in Fig 2 7 The Tool Window is displayed at the bottom of Control Desk screen as shown in Fig 2 7 The Tabs display the tool currently used In the figure only three of the working tools are available Log Viewer Interpreter and File Selector As we shall further describe there is one tool very important to which we shall give a special attention This tool is called Variable Browser and the Parameter Editor It provides access to the variables of an application These variables are stored in a file called example1 sdf 20 Comman Starting RTI build procedure with RTI 4 3 RTI1104 06 May 2002 Optional User System Description File examplel_usr sdf not available Initializing code generation Starting Real Time Workshop build procedure for model examplel Generating code into build directory examplel_ rtill04 Invoking Target Language Compiler on examplel rtw Generating Varia
28. e signals are displayed on the same y axis the graph settings will be identical for both Otherwise you will be able to select different y axis limits for each of the signals independently Set Y limits Width Scaling Mode as shown in Fig 2 15 At the X label you can write Time and at Y label write Input and output signals One more step before you actually can start the simulation setting the visualization pa rameters The process parameters can be set in the Capture Settings Window under View Controlbars menu 27 dSPACE Plotter Control Properties Inner Border Grid Background Border Extended Properties sam me Aris 00 IN lt lt zj sam cm JE mmm eO Srl ox cancel Av He 3 j 4 E 4 3 E 3 4 Figure 2 15 Plotter Setting Window e Open the Capture Settings Window and set the Length of the simulation as 2 while leaving unchanged the Downsampling number Your capture settings should look like as shown in Fig 2 16 For more complex systems this number has to be increased when the Length is larger than 20 times the sampling time Now we are ready to start the simulation 2 6 Running the Experiment There are two operations that have to be done to run stop the experiment First the DSP execution has to be started Second the animation and data acquisition printing needs to be initiated When stopping an experiment the operations have to be done in the
29. e the steady state final value B 0 000252 These parameters were determined Tf 0 0979 in the previous experiment steps y0 Tf B Plot the initial saved data cla reset axis 0 2 0 450 axis limits depend on the actual data hold on plot t y r EraseMode none title Speed response hold on Plothandle plot t y EraseMode x Run the curve fitting algorithm using FITRAZ lambda and FMINSEARCH 64 FITRAZ and FMINSEARCH returns the error between the data and the values computed by an exponential function of lambda FITRAZ assumes a function of the form y yO c 1 exp lambda 1 t c n exp lambda n t with n linear parameters and n nonlinear parameters lamO 1 Define one initial root n 1 lambda fminsearch fitraz lamO Start iteration using initial root hold off 54 Computing the motor parameters The algorithm returns the best lambda B J wfin y0 J B lambda 65 66 Experiment 5 DC Motor Control 5 1 Introduction The purpose of this experiment is to design and implement a cascade control of a dc motor drive We shall use the Lab Kit dc motor for which the parameters were calculated in the previous experiment The controllers will be designed and will be tested on a simulation model of the dc motor Once the parameters are tuned the model of the dc motor will be replaced with the real motor and the control algorithm w
30. ector Thus two Gain blocks from the Math Library will be required to correctly read and write the values from and to the analog channels 18 e Drag the DS1104ADC_C5 and DS1104DAC_C1 blocks into the Simulink model and replace the Signal generator and Scope blocks Place the two gains of 10 and 0 1 on the input and output signals respectively The model should become similar to the one depicted in Fig 2 4 You might need to save the model with another name to preserve the simulation model laj xd File Edit View Simulation Format Tools Help OwW Ge Bt gt Noma EER OG gt 3947 94 a 2487 925 3947 84 DS1104ADC_C5 Gai Transfer Fen Slider OutGain DS1104DAC_C1 Gain 100 Figure 2 4 Real Time model for dSPACE in Simulink Remember that we performed the simulation for only 2 seconds In real time however the system needs to run continuously Therefore press CTRL E for simulation parameters and e Set the Stop Time as inf The simulation parameters should look like shown in Fig 2 5 e In Simulation Parameters go to Advanced and make Block Reduction OFF e Next choose the Real Time Workshop Build Model from the Tools menu Once the above command is given you will observe a list of messages displayed in Matlab Command window These messages correspond to the different steps that the RTI Software perform in order to transform the Simulink code of the example1 mdl file i
31. eference such that the active torque will decrease the MOTOR current until it becomes zero e Record the values for speed at Iyoror 0 and calculate k as per Eqn 4 5 Drawing the torque speed characteristics e Maintain the MOTOR voltage at constant levels 42 21 10 3 V Adjust the LOAD voltage reference such that the MOTOR current takes the following values at each voltage 0 1 0 2 0 3 0 4 0 5 0 A e Record the speed wm the LOAD current Iroap and LOAD voltage Vzoap required to obtain the specified MOTOR currents All current measurements will be multiplied with ke to obtain the corresponding torque values refer Eqn 4 2 e Fill in the TABLE 4 1 with the measured data e Draw the MOTOR and LOAD characteristics using the data acquired during the measurement process 51 Table 4 1 Steady state Experimental Data i a my e apo tm e o e e so E E oo M ow a E Paw o nn 20 JE 80 es ee ee lt a js JES 1 06 4 p rec ae ee eo eee M ee WE ee E NEK ee ae AGE o ee a WECGE Goh po e ee a Ee JE SE JE d a e Find the slope m and intercept n using MATLAB The slope and the intercept of the linearized characteristic could be determined with the following instructions p polyfit ia_data w_data 1 m p 1 n p 2 w _data is the array of speed data while ia_data is the corresponding current data for the speed Two set of parameter
32. ers which were evalued in the earlier experiment and the algorithm described in section 8 7 1 of Electric Drives book for 500Hz bandwidth e The Saturation block sets the maximum and minimum limits for the control voltage in our case 1 e Set the value of Kp_i and ki i in Matlab prompt Also set the values of lim 1 Kpwm 42 Ta_ref 1 in Matlab prompt Instead of setting the values of various variables in Matlab prompt create a m file which contains the values of all the variables Run the m file before running the simulation which will load the values of all the variables e Running the Simulink model for the current controller with reference current as 1A results similar to the Fig 5 4 b and Fig 5 4 c will be obtained 69 BEEN GO lol x File Edit View Simulation Format Tools Help Ole S EE O lt C gt m Normal Hee BET e Current Controller Load Torque DC Machine Ready 100 ode45 Ui a Simulink Model for Current Control Loop DEMotor2 oxi EL 101 x salope ABB 88 68 oep ABBAR b Current Waveform for 1A Reference Current c Speed Waveform for 1A Reference Current Figure 5 4 Simulink Model and Results for Current Control Loop e Once the response in current is considered optimal low overshoot fast rise time zero steady state error the speed controller can be designed e A similar PI controller for the speed loop will be added
33. es The dynamics can be divided into electrical and mechanical dynamics Independently studying both transients two motor parameters can be determined armature inductance La and moment of inertia J 53 Table a Steady state poon m characteristic Spora Torque Nz 1 Table 4 4 Calculation of the mechanical steady state parameters BINm rad s Thriction Nm ee u sa ee For this section we shall use the same Simulink model and dSPACE layout as in earlier section To analyze the dynamics of a dc motor drive some theoretical background will be presented then using the already determined steady state data the experiment steps will be described The setup consists of two dc motors axially coupled and supplied from two converters in four quadrant configuration One motor is controlled in current such that it will act as either a passive or an active load This motor will be named here LOAD The second motor is controlled in open loop with variable voltage This motor will be named here MOTOR In this experiment two parameters need to be determined L armature inductance H and J moment of inertia kg m 4 4 1 Dynamic Model Characteristic There are several ways to determine the inductance and the inertia All methods involve the dynamic analysis of the machines in transient operation The dynamic equations of a dc motor are dig Vi Raia kew Lg 4 6 and dw Te Tr T friction Bu JT 4 7
34. ill be downloaded into the dSPACE board 5 2 Simulink model of the dc motor The equations written in Laplace transform for a dc motor were derived in Chapter 8 If the voltage and the current are assumed not to contain switching frequency components the motor model can be written Vals Fa s Ra sLa Teml m Tem s krl s kr ke 5 2 la s E s kz wm s 5 1 wns Eqn 5 1 and eqn 5 2 can be easily be implemented in Simulink using standard blocks as presented in Fig 5 1 e Create a new Simulink model and drag all blocks as shown in Fig 5 1 e Make the connections and define the parameters as shown in Fig 5 1 67 Tem PL s wm Kt Mech Eqn Jeq Integrator B Voltage Eqn Integrator Figure 5 1 Simulink model of DC Motor The representation in Fig 5 1 uses integrators instead of transfer functions This allows to set initial conditions for the current and speed state variables The model also includes the friction coefficient B However during simulations B can be considered zero and the model will be similar to the one described by eqn 5 1 and eqn 5 2 Note that the torque constant is already replaced with the voltage constant in the Gain block at the top of the figure e The model can further be grouped and masked in Simulink such that all parameters can be inserted in a dialog box by selecting the system and creating a sub system Modify the
35. ime system 5 4 Real time implementation of feedback control For dSPACE implementation the dc motor model will be replaced with the real motor and Kpwm block will be replaced by power converter with 42V dc supply The control voltage to duty cycle conversion was already discussed and implemented in earlier experiments e Add the reset block used in the earlier experiment e Modify the Speed Control block as shown in Fig 5 6 Change the integrator block parameters by double clicking on it and changing its external reset to either Open the Current Controller and change its integrator s reset as was done in the Speed Control Connect the reset inputs of speed controller and current controller as shown in Fig 5 7 These changes allow the integrators to start up correctly in the real time environment la_ref Saturation Integrator Figure 5 6 Simulink model for real time speed control of DC Motor Control e Remove the DC motor mask model and gain Kpwm block e Copy and paste the duty cycle calculator from the Simulink model used in earlier experiments see figure below e The current and the speed are to be measured For measurements use the blocks already designed in earlier experiments e Replace the speed ref wm_ref_step and sum block with a constant block for setting the speed reference 72 Constant Vic D511045L_DSP_PWM3 PWM Control Speed Controller wm_ret Current Contro
36. iment in the same working root as the simulink file e Create a new layout and drag two Slider Gain controls and two Plotters e Drag and drop the V_motor and V_load variables to the Slider gains e Assign one plotter to display Ja and JZ currents and one plotter for the speed wm e In order to record the numerical values of currents and speed add to your layout three Display type controls and assign them the speend and current label variables Your experiment should look like the one shown in Fig 4 2 4 3 Steady state characteristics of dc motor drives In this experiment you will derive the characteristics of a dc motor using the second motor as load For a constant V_motor voltage the load is modified using V_load The MOTOR current and the speed are recorded in a table A set of measurements are obtained for different supply voltages The characteristics will be drawn using Matlab 49 Figure 4 2 Control Desk Layout 4 3 1 Theoretical background The steady state mechanical characteristics of each dc machine are the dependency between the electromagnetic torque Nm and the electrical radian speed rad s Since the dependency is linear the characteristics will be straight lines with a constant slope for the whole voltage range 0 V ateqd and independent on the load The motor equations reflect this linearity Vmotor Rala Kew 4 1 Ts Kila 4 2 From Eqn 4 1 one can obtain the steady state motor characteris
37. in Fig 2 indicates if the signal supply is available to the board Fuses F90 C 2 in Fig 2 and F95 B 2 in Fig 2 provide protection for the 12 V and 12 V supplies respectively Please note that the green LED indicates the presence of only the 12 V supply Please note that turning off S90 will not stop the PWM signals from being gated to the inverters The power supply for the 3 phase bridge drivers for the inverters is derived from the DC Bus through a flyback converter A 2 in Fig 2 Table 1 Locations of components on drives board emi PAS 7 emina PAS u orom Pau bo 29 Phase A2 current sensor LEM CS5 z z D z PWM PWM INV 1 INV 2 Figure 1 Block Diagram of Electric Drives Board 2 3 Voltage Measurement Test points are provided to observe the inverter output voltages BNC connector VOLT DC B 4 in Fig 2 has been provided to sense the DC bus voltage To measure the DC bus voltage e Connect a BNC cable to VOLT DC BNC connector e The scaling factor of input voltage is 1 10 2 4 Current Measurement LEM sensors are used to measure the output current of the inverters Only A and B phase currents are sensed The C phase current can then be calculated using the current relationship 1 0 assuming that there is no neutral connection for the machines The calibration of the current sensor is such tha
38. irst we start a new experiment Click File New Experiment In the pop up window write the name of the experiment and very important set the path where the simulation files are stored see Fig 2 8 Note When creating a new experiment don t forget to set correct working directory e Next load the file containing the variables of the simulation Click File Open Variable File and select examplel sdf The Variable Manager Tab appears at the bottom of the screen see Fig 2 9 The window contains the structure of the simulation model At the highest level we see the simulation control variables Their function is described in Tablel 21 ControlDesk Developer Yersion lj xl File Edit View Tools Experiment Platform Instrumentation Window Help REI eee eo Se es SE ee jzc EszajEae xE lege e 42 5 e m Framework Initializing ReferenceData Component Framework Initializing SCOUT Component Platform Establishing the connection Platform Connecting to the bus completed Framework Initializing TreP arser Component Real Time Processor 1 ds1104 ATI Initializing 720 Real Time Processor 2 ds1104 RTI Initialization completed 721 Real Time Processor 3 ds1104 RTI Simulation state RUN 700 Figure 2 7 Control Desk Screen For the purpose of our simulation the variables of interest are contained under the Model Root group This g
39. ller Speed Ref Enc position Enc delta position DS1104ENC_POS_C1 ENCODER MASTER SETUP DS1104ENC_SETUP 2 pii Ts 1000 Aweraging Block SLAVE BIT OUT Reset Data Type Conversion 544045L_DSP_BIT_OUT_C10 Figure 5 7 Simulink model for real time implementation of DC Motor Control At the Matlab prompt set the sampling time Ts 0 0001 and the dc bus voltage at Vd 42V Also set the values of various variables you have defined in the model Change the switching frequency in the DS11045L_DSP_PWM3 to be 50000Hz Set the simulation parameters with Ts as sampling time and inf as total simulation time Now the model looks like in Fig 5 7 Build CTRL B the model and start Control Desk Create a new Experiment and set the working root the same as the path for the Simulink model Create a new Layout and add some controls as shown in Fig 5 8 73 e Run the experiment and compare the real time results with the simulations A dc_motor Figure 5 8 Control Desk interface for DC Motor control Step change from 200 450 rad s 74 Experiment 6 Frequency Control Of AC Motor Drives 1 Introduction The experiment intends to design and implement a V f control algorithm for an induction motor First a switch mode sinusoidal PWM algorithm is implemented for a three pole switch mode converter Then the V f strategy is designed and the experiment is downloaded in the dSPACE control board to run a 42V ind
40. model of output voltage control of the switch mode dc converter was discussed in the previous section and we shall use the same 39 A layout1 0 010 0 012 0 014 0 016 Figure 3 5 Control Desk layout for Switchmode DC COnverter e Go back to SIMULINK e Open a new Simulink model e Set the simulation parameters as described in the section 3 2 1 e Copy the Step4_03 mdl model and save it with a new name Step5_04 mdl e Change the name of the Constant block from V_AB to V_motor since this will be the input in our dc motor drive system Now we have an open loop control of the dc motor under test However we are not able to monitor the current and the speed while controlling the motor Hence we will have to add the current and speed measurement blocks to our existing model 40 3 4 1 Current measurement For measuring the current we will be using Channel 5 of the A D converter Remember from the first experiment that the data have to be scaled with 10 In addition on the motor drives current sensor 1V equals 2 amps so it actually needs to be scaled by 20 e Drag and drop the DS1104ADC_C5 block from the dSPACE library e Connect a Gain block at Channel 1 output and set its value at 20 e Connect a Terminator at the output of the Gain block and label the signal as Ja 3 4 2 Speed measurement To measure speed we shall use the DS1104ENC_POS_C1 block from the dSPACE library This block provides read access to the
41. mplitude of the triangular voltage equal to unity i e V 1 we obtain the relationship for control voltage of pole A as 20AN Va lt i 3 3 Ucontrol A The above relationship in Eqn 3 3 is implemented in Simulink The control voltage is compared with the triangular signal The Relay block output is set to 1 when the difference is positive and 0 when the difference is negative The desired voltage Uan with respect to the negative dc bus ground is set by a Constant block with the value of one and can be varied with a Slider gain from 0 to the maximum dc bus voltage Vg Va 42V in the model The simulink model is shown in Fig 3 2 3 2 3 Two Pole Converter Model To obtain the model for a DC converter we need to add in our model two building blocks for a converter pole The building block is the Switch block from Nonlinear library which allow the upper signal to pass when the middle input is greater than the specified threshold and the lower signal in the opposite case The converter output voltage will be the difference between the two pole output voltages measured with respect to the dc bus ground Now the reference value for our model will be vag We know that VAB VAN UBN 3 4 At any given instant of time the control voltages for the two poles are complementary i e Ucontrol A Vcontrol B 3 5 Thus by solving the Eqn 3 1 through Eqn 3 5 we can write VAB Vcontrol A 7 Vc
42. ncy f and the amplitude V are variables However the V f control algorithm implies that there is a relationship between the amplitude of the voltage and the frequency i e the ratio between the two quantities is constant y Kam 7 i Now setting the frequency and knowing the constant K it is easy to derive the amplitude of the voltage using 7 The expressions for stator voltages are written in continuous domain where the time is a continuous variable For a digital system time is a discrete variable depending on the sampling time Since a new value of the voltage is calculated every T seconds the time will have to be updated by adding the sampling time to the precedent time value t T t 8 This is easily done using a Memory block in Simulink shown in Fig 2 In the model the time is already multiplied by 27 f to give the t variable 2 pi u 1 u 2 O 0 Memory Fig 2 Simulink model for the voltage argument calculation Mask this model and don t forget to set the parameter in the Memory block to 7 This ensures that the delay performed in time calculation will be exactly of one sampling time 77 Experiment 6 Frequency Control of AC Motor Drives DSP based Electric Drives Laboratory Use three Function blocks to implement the relations in 6 and 4 The model becomes u 1 cos u 2 0 5 da u 1 cos u 2 2 pi 3 0 5 db duty_a b c u 1 cos u 2 4 pi 3 0 5
43. nto DSP code First there is a compilation stage in which the Simulink file is transformed into a C file then comes the link stage where all the variables and subroutines are correlated with the DSP environment and finally the code is transformed into an object file and downloaded into the DSP memory The MATLAB window screen will look like shown in Fig 2 6 You can see that the file was successfully built The result is examplel obj which was already loaded in the DSP memory and its execution started Please note that the directory in which the model was built is the same you choose for creating the Simulink model If you look now in this directory you will find several files generated during the 19 Simulation Parameters examplel zj xj Workspace 1 0 Diagnostic Advanced Real Time Workshop Solver Simulation time Start time 0 0 Stop time inf Solver options Type Fied step ode1 Euler Fixed step size 0 001 Mode SingleT asking Dutput options Refine output Refine factor 1 Figure 2 5 Simulation Parameter setting for real time model build command Due to the large number of files generated it is advisable that each project to be located in a separate sub directory Now our simulation is running in the DSP board in a digital real time format We can predict that this is much faster than what we saw on the Scope screen in Simulink More important now seems to be th
44. on However one additional block has to be inserted such that a step command in voltage is possible Both electrical and mechanical dynamic parameters require either a positive from 0 to V or a negative from V to 0 step change in supply voltage The V 0 condition implies also that the motors have no armature current i e they do not enter the regenerative braking mode with negative torque To achieve open circuit of the motors armatures the converters need to be shutdown and all the switches opened when the V 0 command occurs This operation is possible by using the SHUTDOWN signal on the drives board The SHUTDOWN signals are controlled by the digital I O channels 11 and 12 When IO11 12 is 0 OFF state the switching signals are inhibited and the switches are opened Setting IO11 12 to 1 ON state and resetting O10 resumes the regular operation of the converters The 010 11 12 digital channels will be added as slave bit out blocks for our model from the slave library In addition two constant blocks and two Boolean conversion blocks should be added with SD1 and SD2 using the same signal The model should like the one shown in Fig 4 3 4 4 3 dSPACE Experiment Layout for dynamic model determination e A new experiment will be created in the same directory containing the Step1_04 mdl file e Copy the Layout from the previous experiment and rename it e Add 2 CheckButtons controls to the Layout 56 Duty cycle a V_mot
45. on Results of 274 Order System for Square Wave Input This simulation was really fast The generator waveform can be changed by double clicking the signal generator block Now since we have the idea how the system work we will implement the system in real time and observe the results 2 3 Build the real time simulation model The model developed for simulation is now to be connected to the external devices Signal generator and Oscilloscope Since these devices are physically generating accepting signals going to or coming from the DSP board we need to stream these signals via the analog Input Output channels located on the controller box Firstly make sure that the Signal Generator and the Oscilloscope are connected via shielded BNC cables to ADC 5 and DAC 1 respectively The Signal Generator output is set such that its signal amplitude is approximately 1V Communication with the input output channels is performed via two dSPACE blocks found in the dSPACE RTI1104 library under the sub library DS1104 MASTER PPC named DS1104ADC_C5 and DS1104DAC_C1 They will replace our Signal Generator block and Scope block respec tively The analog input channel is down scaled by the hardware with a ratio of 1 10 This means that 10 V at the input will be read as 1V in our model The analog output channel is also down scaled in the hardware with the same ratio Thus a 1 V signal generated within the model will have an amplitude of 10V at the conn
46. ontrol B vV 3 6 d and z r da Ucontrol A 1 37 73 3 7 dp 2 Veontrol A 1 The above relations can be implemented in a Simulink model together with the two pole switches as in Fig 3 3 The input is the desired average output voltage v4p The instantaneous output 35 Istep2_04 loj xj File Edit View Simulation Format Tools Help DW sae Repeating Sequence Constant1 Figure 3 2 Switching Function generation for single pole converter voltage will be a square wave signal and the average value will be equal to the value set by slider gain By varying the value of slider gain i e vary the desired average output voltage value the output voltage value changes Now set the simulation time to inf and start the simulation Vary the slider gain value and observe the output voltage waveform Set the axes values of the scope as shown in Fig 3 3 36 IMESERYE Fi II x File Edit View Simulation Format Tools Help Repeating Sequence Slider_a Scope dA dB Scope V_AB japs Lr ABBE lsa OSPABB BER Figure 3 3 Two Pole Switch Mode Comverter Model in Simulink 3 2 4 Simulation Results Once the above system is ready collect the following results for the two pole switch mode dc converter e Switching function q t for single pole converter e Simulation results of two pole converter model for two different values of Vag one positive
47. or Duty cycle b Constant DS1104SL_DSP_PwM3 PWM Control PWM Channel 1 PWM Channel 2 dAl dB1 PvM Channel 3 Py Channel 4 Enc position Enc delta position DS1104ENC_POS_C2 IL Averaging Block IE lt A ADC ENCODER MASTER SETUP DS1104ADC_C6 DS1104ADC_C5 DS1104ENC_SETUP boolean SLAVE BIT OUT Reset Data Type Conversion DS1104SL_DSP_BIT_OUT_C10 02 si SLAVE BIT OUT 1 SE SLAVE BIT OUT SD Data Type Conversion DS1104SL_DSP_BIT_OUT_C11 DS1104SL_DSP_BIT_OUT_C12 Figure 4 3 Simulink Model for Dynamic Parameter Characterisation e Link all variables from the model with the controls in the Layout as in earlier section e Link the Reset and SD to the CheckButton control The layout of the experiment is shown in Fig 4 4 4 4 4 Dynamical parameters determination Inductance determination e Using the blocking device block the rotors firmly e Uncheck and then recheck the SD control 57 This button works as a switch to connect and layout2 Figure 4 4 Control Desk Layout for Dynamic Parameter Characterisation disconnect the machines from the power supply Set the V_MOTOR to a low value around 3 V and uncheck Reset to give a step in voltage and then recheck Reset The current should increase exponentially as shown in Fig 4 6 and reach a constant steady state value To save the current response open View Controlbars Capture Settings Window Drag the P Reset signal from
48. or Inverter 1 7 CC wa BB sm 20 21 N N or Q Q DSJ a zlajajaja r zizizia jziziz iaja lt Q Q Q aja N oO 29 30 31 32 33 w R 3 36 37 o u 2 NEJ i ad s Ea 29 20 2 24 25 26 sza 2 29 30 EES 32 33 NEJ 35 Ea E gala i N Figure 2 Electric Drives Board Experiment 1 Building A simple model in SIMULINK 1 1 Introduction Mathematical modeling of electric machines and drives involves solving a set of differential equa tions Mathematical tools like Matlab helps in solving these differential equations in a fast and easy way Matlab also contains a modeling tool SIMULINK which helps to pose the problem in a graphical way using interconnected blocks and capability to visualize the solution to the set of dif ferential equations using graphs and plots In fact many real time systems like dsp now comes with an interface to SIMULINK by which they can convert the SIMULINK block set to a machine code that can be run on a DSP based system This greatly reduces the development and prototyping time for a variety of drive systems In this experiment we will try to learn to use SIMULINK so that we can e Build a simple model using SIMULINK blocks e Simulate the model to see the performance of system in different scenarios 1 2
49. os length t length lambda for j 1 length lambda A j exp lambda j t end c A y y0 z A C set Plothandle ydata z y0 drawnow err norm z y y0 61 inddet m Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh inddet m Calculation of dc motor inductance and resistance using vA a curve fitting algorithm for the current response at a step in voltage and blocked rotor h h Author Razvan Cristian Panaitescu 4 Date Feb 06 2002 h University of Minnesota vA Department of Electrical and Computer Engineering k Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh global Plothandle t y y0 Variable declarations Load the current mat file saved from the dSPACE Experiment 4 The file contains the current response at a step in voltage load current t current X Data Define time variable y current Y 2 Data Define the y variable current 2 is sometimes a 1 depending on ControlDesk setup Calculate the steady state final value by averaging 4 the current data during the last half of the time interval nmax length y yO mean y nmax 1 2 nmax Plot the initial saved data cla reset axis 0 2 0 3 5 axis limits depend on the actual data hold on plot t y r EraseMode none 62 title Armature current response hold on Plothandle plot t y EraseMode
50. r Control with Variable handled and its control limits of the input signals will be obtained after the In Gain block while the real values of the output signals will be obtained before the Out Gain block e Click on the Data Acquisition tab in the Instrument toolbar at the right e Select the Plotter icon and draw a larger rectangle in the Layout window 26 Figure 2 14 Drawing a Plotter for Signal Monitoring Drag the signals which you need to monitor in the new plotter Model Root In Gain gt Out1 and Model Root Slider Gain gt Out1 When dragging the second signal make sure that you release the mouse button above the first one on the vertical axis Otherwise a new vertical axis will be drawn and you will have less available space for visualize the waveforms Now both signals are assigned to the plotter and will be displayed with different colors The label on the vertical axis will show only the last signal dragged to the scope You should have your layout as shown in Fig 2 14 Any time you wish to make a correction or see what signal was added to the plot right click in the scope area and select Edit Data Connections command You can delete any signal by selecting it and press Delete key You can even delete or modify your signals or changing the colour of the signals by double clicking Y axis and going in to the Signals To format the scope double click in the rectangle and select Y axis tab When th
51. range to one second as in Fig 1 4 Scope parameters lol x General Data history Tip try right clicking on axes Axes Number of axes 2 I floating scope Time range 1 Tick labels bottom axis only Sampling Decimation x E OK Cancel Help Apply Figure 1 4 Scope Parameter Setting e We would also like the system to run continuously To do this go to the simulation parameters as was done in Step 1 and make sure all the parameters are the same as in Step 1 but change the Stop Time to inf e When you are finished changing the model it should look like Fig 1 5 e Run the simulation again and change Tm and Ty as the simulation is running to see how the system responds 11 Integrator1 MET R g loj xj File Edit View Simulation Format Tools Help DS Se eB S 1 m Noma JS RETE Scope E O2P ABGE 0OGR Running 4 Figure 1 6 Simulation Results for Model Including Friction 12 1 4 Lab Report The lab report should contain a brief along with the details what have been done in the lab and details asked below e Simulation results of mechanical system obtained in section 1 2 Comment on the results obtained e Simulation results of the mechanical system along with friction included in the model i e sec 1 3 Comment on the results obtained What s the effect of friction on the system performance e Change the value of Tm and Tz What is the effec
52. reverse order e To start and stop the DSP you can use the icons in the Platform Management toolbar see Fig 2 17 e Edit mode toolbar contains edit test or animation icons Refer Fig 2 17 for edit test and 28 Capture Settings Window ds1104 examplet a PPC examplel HostService z Re 0 lengh 4 IV Auto Repeat Downsampling 14 Trigger Signal awo kA Level 0 Delay 0 lt lt Drop trigger variable here gt gt Reference Capture Capture Variables Take Save B 002 of 002 4412 Tei PPC example1 HostService f Figure 2 16 Capture Setting Window animation tool icons Edit mode is used to edit or modify your layout start and stop your real time simulation Once you start the real time simulation click the animation icon this will let you modify parameters in real time and observe the waveform Unless real time simulation starts you cannot go into this mode Clicking on Test icon lets you go into the Test mode In this mode you can observe the snap shot of your real time simulation Parameter Editor Window Help o is a y Se STOP EDIT TEST ANIMA MODE MODE MODE Figure 2 17 Execution and Animation Control Toolbar e Start the DSP by pressing the green triangle button If the examplel obj is loaded in the DSP memory then it will start running and the Stop red rectangle shaped button will become active
53. roup contains the variables belonging to the top level of the Simulink model Variables from subsystems go into further groups in deeper hierarchical levels The variables available have a prefix to distinguish the different variable types and are generated in the following order as detailed in Table 2 1 Prefix Example Variable Type L Output labeled signals B Integrator block outputs P Signal Generator Amplitude block parameters Table 2 1 Variable Types and Signal Correlation The name following the prefix is the block name except for labeled signals where the label itself is used Here are all the variables corresponding to the Model Root for our example are detailed in Table 2 2 22 xl Experiment Name Experiment 3 Working Root C Amanojtexpt31 Ll R Mo Create Subdirectories Author s Manoj R Rathi Description Text This is an Example for using dSPACE board and Control Desk for Real Time Simulation Dept of ECE University of Minnesota April 2004 Experiment Graphic Bd Figure 2 8 Experiment Settings Lb ay variable Size type Orign Description Gif Model Root FinalTime Floatleee Simulation 1 a Transfer Fen currentTime Floatleee Current si Out Gain na modelStepSize Floatleee64 Fixed step J In Gain E simState Int32 Simulation a AAA errorNumber Ulnt32 Error num S E ATI Data H E Slider nGain SER Task Info Eh Timer Task 1 File Selec
54. s m n are determined for each dc machine MOTOR and LOAD 52 e Determine R k Using the corresponding m and n the machine parameters can be de termined using the following equations where i 1 4 the number of voltage levels considered previously ke avg ke_i since ke is a machine constant the best estimation is achieved by averaging the previous determinations Ra kem A table for Ra ke final values is obtained see Table 4 2 Table 4 2 Calculation of the electrical steady state parameters Voltage V n intercept R Q ae CZ EZ GS mie ee pom Ea ae zz es e Determine the friction model parameters For determining the friction parameters you will have to run the motor under no load con dition which you had done in the earlier experiment Since the MOTOR has to overcome only the friction Ty 0 the electromagnetic torque Te kela will follow the linear friction model see Eqn 4 4 in steady state Fill in the Table 4 3 provided using the values obtained in the earlier experiment Linearize the dependency of Te w by determining the m n coefficients depicted in Eqn 4 4 by using the same procedure as for drawing the torque speed characteristics e Determine B and Tfiction Using Eqn 4 4 the friction parameters will be B m Tfriction n Fill in the Table 4 4 provided 4 4 Dynamics of DC Machine In this section we will try to derive the dynamic characteristic of DC driv
55. switching frequency of the output voltage of the converter Explain why you get that value e The output voltage result of real time implementation of two pole switch mode converter along with its corresponding duty ratio waveforms e Plot of voltage vs speed curve for the no load condition of DC machine 44 e Specify the slope of the curve obtained 45 46 Experiment 4 Characterization of DC Machine 4 1 Introduction In the earlier experiment you designed and implemented the switchmode control and no load measurement of DC machine along with the current and speed measurement In this experiment you will try to derived dc machine characteristic which will be helpful in designing the closed loop control of DC motor We will be using the model prepared in the earlier experiment and modify the same one to derive the dc machine characteristic 4 2 Open loop control of DC Drive with load We will use the same model used in earlier experiment to do the no load testing of DC machine e Create a new folder Expt 4 e Start Matlab and change the directory path to Expt 4 e Open the Simulink model Step5_03 mdl Once we have the model for controlling the motor we will have to add appropiate blocks for controlling the load 47 Duty cycle a Duty cycle b Duty cycle Constant PUKA Stop DS 11045L_DSP_PWM3 PWM Control PM Channel 1 Pit Channel 2 Pind Channel 3 Pid Channel 4 D511045L_DSP_PWM D 1
56. t for 1 A current flowing through the current sensor output is 0 5 V To measure the output current of phase A of inverter 1 e Connect BNC connector to CURR A1 B 3 in Fig 2 To measure the output current of phase B of inverter 1 e Connect BNC connector to CURR B1 C 3 in Fig 2 To measure the output current of phase A of inverter 2 e Connect BNC connector to CURR A2 H 3 in Fig 2 To measure the output current of phase B of inverter 2 e Connect BNC connector to CURR B2 1 3 in Fig 2 2 5 Inverter Drive Circuit The inverters are driven by 3 phase bridge drivers IR2133 The PWM inputs are isolated before being fed to the drivers 2 6 PWM Digital Signals PWM and other digital signals for the board are to be given to the 37 pin DSUB connector H 1 in Fig 2 For pinout of the connector see Table 2 2 7 Fault Protection The Drives Board consist of overcurrent protection for each inverter An overcurrent fault occuring on inverter 1 is indicated by red LED MOTOR FAULT 1 D 2 in Fig 2 while that of inverter 2 is indicated by red LED MOTOR FAULT 2 L 2 in Fig 2 Each time a fault occurs reset the fault using the RESET switch L 1 in Fig 2 on the board All the faults are reset by this switch Table 2 37 pin DSUB Connector Inverter 1 Fault output Fault Signal high o awnem biegowa e Pwmp po PWM signal oferte o war G pio PWM signal of imie i i z 7 Shutdown signal f
57. t of each and explain why e Change the load torque Tr What is the effect of sudden change Observe the dynamics obtained after the load change and comment about its effect on speed acceleration and theta 13 14 Experiment 2 Building A simple REAL TIME model in SIMULINK 2 1 Introduction One of the best features of the SPACE package is the ease of building real time applications The time between converting the design into digital instructions for the DSP and effectively running the application depends only on how fast your computer can compile the initial code Basically a real time application can be created by means of two methods e Using MATLAB Simulink for building the model and automatically generate the C code and download it into the DSP memory e Hand coding in C and compile the model into DSP code The fastest way of developing a real time code is developing the model in Simulink and preparing a real time model from that Basically once you have completed the Simulink model which you want to run in real time the only command required is RTW Build under Tools menu in SIMULINK Once the command is executed dSPACE software creates the object obj file downloads it on DS1104 board and automatically starts the hardware execution However there are some important settings you have to make before transporting your model into the real time world Let s start with a simple example 15 2 2 Creating a mo
58. tate operation of an induction motor and the transient characteristics for different acceleration and deceleration slopes 80
59. the Tool Window into the gray box situated below the Level Delay set boxes Check the box called On Off check the edge direction and set the Level value to 0 5 Now you will observe that every time you uncheck the Reset control in your layout the plot area will display the current and it will stop when it reaches the maximum measurement time Set the Length to 0 2 see Fig 4 5 This will set the data capture time as 0 2s which is large enough to observe the whole transient process in current Check and uncheck SD and Reset to make some measurements You current waveform will look some what similar to the one shown in Fig 4 6 After you are satisfied with the data displayed go to the Capture Settings Window and press the SAVE button The dialog box will ask you to name the mat file that will contain the graphic data in all plot areas To extract the inductance information as in 4 9 this equation will be used in a Matlab program to determine the slope of the current transient Run Inddet m at the Matlab 58 Capture Settings Window ds1104 step2_ 04 x PPC step2_04 HostService z H 0 Length 0 2 v Auto Repeat Downsampling 15 Trigger Signal On Off fe Level 0 5 Delay 0 Model Fioot Fieset Y alue Reference Capture Capture Variables Take Saye i 003 of 003 JaJa TIPI PPC step2_04 HostServicef Figure 4 5 Current Waveform 4 5 o
60. tic w Ia sai Vmotor _ mI n 4 3 k k where m _ fa and n Vnotor ke k The steady state model for the load can be approximated with a friction type model where the torque is proportional to the speed and a constant friction torque is always present Te Tr Bw T friction 4 4 50 where all terms in the right member are load related For our setup where the load is a voltage controlled dc machine the load torque Ty is in fact the electromagnetic torque developed by the second dc motor The parameter determination process for the steady state model uses the current voltage and speed measurements to obtain a linear approximation for both equation 4 3 and 4 4 Once the slope and the interception point are found the parameters can be easily derived 4 3 2 Steady state parameters determination According to the theoretical description from section 4 3 1 the motors will be driven in several steady state operating points as follows Estimation of ke k e At the rated armature voltage supplying the MOTOR control the LOAD in the active re gion such that the MOTOR current would become zero 0 and measure the speed Substituting value of Ia Eqn 4 1 becomes Va rate ke Vo_rated 42V 4 5 e Increase V_MOTOR and decrease V_LOAD slider gains until V_MOTOR reaches 42 V Notice the speed increasing to about 565 rad s Once the maximum voltage is obtained decrease the V_LOAD voltage r
61. to the Simulink model e Follow the algorithm described in paragraph 8 7 2 to design the speed control loop for 1Hz bandwidth using the motor parameters determined in earlier experiment 70 The Simulink model for the cascade control and the waveforms for speed and current are shown in Fig 5 5 El step2_05 5 loj x File Edit View Simulation Format Tools Help DSHS BBS m Normal J heula e Speed Controller Current Controller DC Machine Ready 100 ode45 Z a Simulink Model for Cascade Control J DCMotor2 x pcmotors een ACE SB OSP ABB BG 5 b Current waveform for step change in speed c Speed waveform for step change in Speed Figure 5 5 Simulink Model and Results for Cascade Control The Speed PI controller has a current limit output of 5A necessary to limit the current during transients both in simulation and real time systems To check the controller design we will give a step change in the speed reference In the example of Fig 5 5 the speed is commanded to a step change to 200rad s at t 0s then at t 5s its is changed to 450 rad s The above reference speed 71 command is implemented using a constant and step source blocks The results of cascade control are shown in Fig 5 5 b and Fig 5 5 b If the controller parameters were correctly tuned then it s time to go on for the next step and implement the control algorithm in a real t
62. tor c manojiexpt3iexample1 sdf Figure 2 9 Variable Tab Manager 2 5 Display Controls and Scopes with Instrumentation Manage ment Tools In order to see the behavior of each variable and modify the parameters in real time while the system is running we need a series of buttons knobs slider gains plotter etc that can handle these variables Therefore we need to start a new LAYOUT screen in which all those instruments can be added e Click File New Layout from the menu Two new windows appear in the ControlDesk workspace as shown in Fig 2 10 The one called Layoutl will contain the instruments used for managing the experiment The second window is 23 Model Root B Transfer Fen Display the output of the Second order Transfer Func tion Handle the transfer function parameters numerator and denominator Table 2 2 Variables handled by dSPACE in the eramplel experiment actually a toolbar which let us drag and drop the necessary controls for the experiment Experiment 3 ControlDesk Developer Version layout1 File Edit View Tools Experiment Platform Instrumentation Parameter Editor Window Help mMtai melozcs e jaan e juas RE las jeG issa sae xE EGefe 42 erse layout J Selector Bi AnimatedNeedle lea Ej CheckButton fs Display fF Frame B Gauge nvisibleSwitch JEJ Knob at Message z MultiStateLED E Numericinput 4 On0lfButton FT
63. ts gt Set the switching frequency in the DS 04SL_DSP_PWM3 block to 20000Hz gt Build CTRL B the model and obtain an obj file 3 dSPACE Implementation gt Start the ControlDesk and a new experiment in the same working root as where your model was saved gt Create a new Layout and drag some controls and plotters e One slider gain for the frequency command e Two Numeric Inputs for your acceleration and deceleration times e One Numeric Input for the boost voltage e Three plotters one for phase currents one for speed and one for the duty cycles 5 Your layout should look like in Fig 5 d lsl x freq 103 O IL 0 20 40 60 80 100 120 0 6 0 4 0 2 4 SE S 0 0 0 EB 0 010 0 015 duty cycles 00 0 005 0 010 0 015 0 020 Fig 5 Layout of the Experiment 6 79 Experiment 6 Frequency Control of AC Motor Drives DSP based Electric Drives Laboratory Note The boost voltage is a constant that can be added to your Simulink model to match the requirements specified in the V f control method The boost voltage compensates for resistance drops at low speeds and improves the startup process of the motor In Fig 5 the frequency has been increased to about 70Hz The duty cycles are sinusoidally generated and phase shifted with 120 The currents in phase a and b are also sinusoidal in steady state The experiment can be used to determine the characteristics of the steady s
64. uction motor 2 Simulink model To run an induction motor we need to supply it with a sinusoidal voltage variable in amplitude and frequency In electric drives and other power electronic applications such as in switch mode rectifiers the intent is to supply three phase sinusoidal currents In the system of Fig 1a the neutral n is the star connection node of the induction motor stator windings At switching frequencies relatively high compared to the fundamental frequency of synthesis it is possible to represent the switching circuit of Fig la by means of ideal transformers in terms of switching average quantities as shown in Fig lb Average variables with a bar on top do not contain switching frequency ripple The intent to supply balanced sinusoidal currents into a balanced ac motor implies that the line to line voltages across the motor terminals be sinusoidal in steady state In a balanced ac motor it can be shown that the motor phase voltages Van Ven and ven are also sinusoidal and similarly to the motor currents the three phase voltages sum to zero on an instantaneous basis Experiment 6 Frequency Control of AC Motor Drives DSP based Electric Drives Laboratory v 6 v t v t 0 1 Of course the above equation is also valid on an average basis Van t t t 0 2 when i t i i t 0 3 ita aA pa M a Va 12 t K gt d 0 K gt de M

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