Lab5 – Quanser Coupled Tanks Modeling and
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1. kv a The maximum voltage that the motor can tolerate is 12 V However since the DAQ can only handle up to 10 V the voltage supplied to the motor will be limited by a saturation block Instrumentation Pressure transducer The pressure transducers are located at the bottom of tanks 1 and 2 Note that in this lab we will only be reading pressure from tank 2 The pressure transducers give a voltage proportional to the height of the liquid in the tank h k iV or b Signal Conditioning Board The output of the pressure transducers are filtered and amplified in the signal conditioning board before they are sent to the DAQ This processed signal ranges from 0 to 5 V NOTE The pump should not run without water Theory The governing equations of motion can be derived as below Applying conservation of mass for tanks 1 and 2 oh aa a a 1 dh ae ae aera 2 where q is the volume inflow rate from the pump to the tank 1 qnis the flow rate from tank 1 to tank 2 q is the flow rate of fluid coming out from tank2 A and A are the cross sectional areas of tanks and 2 respectively h and h represent the height of liquid in the tanks at any given time Applying Bernoulli s equation between points a and b gives MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Micak 2005 Last Update 3 September 2012 by A G Parlos 2 2 P P V as a_ V of b 3 2 p 2 p between points c and d2. s series of expansion we have Jr o oh Jo y Ayy 1 2h oh 2h 20 MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Mlcak 2005 Last Update 3 September 2012 by A G Parlos Using 19 and 20 in 12 13 and 14 we arrive at dih c h 0 q 21 dt 2 ho coh c 6h A d h 22 2h n t dt q ko v 23 Let ci Cy Gv Gv 24 2 hio 24h Hence we arrive at the following set of linearized equations d h A Gv 6 h 6 q 25 d h Gv 6 h Gv 6 h A 26 q ko v 27 Lab procedure 1 Create a Simulink model capable of sending a constant voltage to the DC motor driving the pump and reading a voltage from the pressure transducer a b c d e f g Use Simulation Interface Toolkit and LabVIEW to interface with the hardware Use a simulation step size of 0 01 seconds a 100 Hz sampling rate Use Analog Output channel 1 on the DAQ to output a voltage to the motor Use Analog Input channel 2 on the DAQ to input the transducer voltage Note that the white plug corresponds to the pressure transducer in tank 2 Use a numeric indicator to view the transducer voltage While taking data be sure the simulation is running to verify steady state and read the transducer voltage Add a saturation block immediately before the Out block for the pump motor Set the saturation block range as 0 4 V Also create a nu
3. 2012 by A G Parlos System Description The experimental setup consists of 1 2 3 4 Tanks Two hold up tanks with orifice 1 draining tank 1 into tank 2 and orifice 2 draining tank 2 into the fluid reservoir for the pump A pump driven by a DC motor to fill tank 1 A pressure transducer to measure the pressure in the second tank Power supply The coupled tank apparatus consists of two transparent Plexiglas tubes 32 5 cm long each with an inside diameter of 4 5 cm Deionized water from a reservoir is pumped into the top of tank 1 which drains through orifice 1 into tank 2 below it Tank 2 then drains via orifice 2 into the fluid reservoir The entire assembly is mounted on a Plexiglas frame Tank 1 h2 O a Dz e gt d Water Basin Figure 3 Quanser coupled tank system modified from Quanser User Manual Pump Unit MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Mlcak 2005 Last Update 3 September 2012 by A G Parlos Water is pumped from the reservoir to the first tank by means of a variable speed gear pump driven by an electric motor The motor changes speed rapidly in response to changes in input voltage compared to the time required for the tank levels to change Therefore motor dynamics will be neglected In effect this means that the motor speed is always proportional to the supply voltage The flow rate for the pumping unit is proportional to the input voltage q
4. MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Mlcak 2005 Last Update 3 September 2012 by A G Parlos Lab5 Quanser Coupled Tanks Modeling and Parameter Identification Introduction A common control problem in petrochemical process industries is the control of liquid levels in storage tanks chemical blending and reaction vessels A typical situation is the one that requires supplying fluid at a constant rate qi A reservoir can be used with the dual aim of filtering out any variations in the upstream flow and ensuring a temporary supply of reactant in case of process failure upstream of the hold up tank This may be achieved by a feedback control loop which maintains a constant level h of fluid in the tank by controlling the input flow rate qi or the position of a valve in the outlet Like the modeling of DC motor this lab is also a setup of the liquid level system for further experiments Objective e To derive the mathematical model which governs the fluid levels in the two tank system e To determine the numerical parameters in the model This is called parameter identification e To calibrate the transducers used in the setup Prelab The system shown above consists of a tank with a liquid of density p Find out the mass flow rate of the liquid leaving the system MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Mlcak 2005 Last Update 3 September
5. gives 2 2 P P V c V d 4 2 p 2 p P p8h P 0 P pg P 0 6 V 0 V 0 The following notation has been used above V s represent the velocities and P s represent the pressures p represents the density of the liquid being used Volumetric flow rates can be determined as qn V A 6 qe E V A 7 inserting 6 into 3 and simplifying we get q A 28h 8 inserting 7 into 4 and simplifying we get q A 28h 9 The actual flow rates are lesser than the theoretical flow rates by some factor So we have Gin C 2 gh Jh 10 qe Cah 28h C fh 11 Using 10 and 11 in 1 and 2 we get h qi iai aTi o 12 MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Micak 2005 Last Update 3 September 2012 by A G Parlos dh ciy ca h A 0 13 q ky 14 The above equation assumes that for our operating conditions the input output relation of the pump is linear At steady state we have 0 t So we have from 12 and 13 dio c4 o 15 Bio ig es gt dio GN fap 16 Rewriting 15 and 16 we get 2 hx 2 17 Cy 2 h 18 ci Given h parameters qi294e0s o and q can be established Now let us linearize the non linear equations that we obtained in 12 13 14 Assuming h h 6 h h ha 6 h 19 qi qo t q where J refers to the equilibrium value Using Taylor
6. meric control in LabVIEW to control the upper limit of the saturation block Set this value to 4 when running the VI and to 0 just before stopping the VI DO NOT STOP THE VI WITHOUT SETTING THIS TO 0 MEEN 364 Vijay Alladi 2001 Aninda Bhattacharya 2002 Andrew Rynn 2002 Justin Mlcak 2005 Last Update 3 September 2012 by A G Parlos 2 Determination of C and C2 a Select five voltages to send to the pump motor as follows i If the coupled tanks system does not settle with the maximum motor voltage determine maximum pump motor voltage at which the coupled tanks system reaches steady state i e does not overflow ii Minimum motor voltage that yields a flow into tank 1 Stop the pump if there is air in the suction line iii Three additional voltages equally spaced between maximum and minimum voltages b Send voltages to pump motor in descending order c Allow coupled tanks system to reach steady state this will likely take 10 15 minutes d Record heights of tanks 1 and 2 as well as motor voltage e Estimate the pump flow constant for the Quanser tanks Use this information to plot flow rate vs h gt C is slope of linear fit with a 0 intercept f Plot flow rate vs h2 gt Co is slope of linear fit with a 0 intercept 3 Calibration of Pressure Transducer a Set height of tank 2 to values from 0 20 cm in 1 cm increments b Record voltage from pressure transducer c Plot height of tank 2 vs pressure transduce
7. r voltage determine linear calibration equation with a non zero intercept 4 Estimation of Steady State Gain plot h Vs v to find an estimate of the steady state A gain of the system k Issues to be addressed in the report 1 Description of the set up 2 Calibration of the pressure transducer 3 Parameter identification All the parameters of the system that you had to find experimentally 4 Include all calibration plots Things you have learned in this lab 1 Modeling of nonlinear systems 2 Taylor series and linearization 3 Calibration of sensors
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