Brian MalkowskiFigure 1- Motor control servo amplifierEGR 345Dynamics System Modeling and ControlLab 10a – Proportional Control Brian MalkowskiAndrew EdlerBrian BialkNovember 16, 1999KIT ObjectiveTo study the properties of various motor control systems.TheoryA motor is made up of wires and a magnetic field, the current will oppose the magnetic field creating a torque. The torque generated will be proportional to the current.(1)Where T is torque, K is a constant and I is current.The power of the motor is given in equation 2(2)Where P is power, Vm is the voltage across the motor and w is the rotational velocity.By summing the moment the torque can be defined as the polar moment multiplied by theangular acceleration.(3)By using KCL we can solve for the current. (4)Substituting eq. 1 into 4(5)Then substituting eq. 3 into 5 yields: (6)Then putting it into first order differential form.(7)Where Tf is the torque caused by dynamic friction.KITIVPmdtdJTMRVVImsRVVKTmsRVVKdtdJmsJTJRKVJRKwwdtdfs2Solving for Vs we get,(8)By setting the angular acceleration equal to zero and knowing the input voltage we can find the coefficients from the following equations.(9)(10)We now can obtain values for K, Tf, and J.EquipmentLab 10a:(1) cadet trainer #197530(1) computer -PSE Dell #123 w/ LabVIEW and DAQ board(1) digital multimeter - #23116(1) Interface cable(1) LM675 Op-Amp(2) 1K resistors(1) 2.2K resistor (1) 12VDC motor (Buehler 4392)(!) Potentiometer(2) +/- 12V supply (Power Mate 19086, 19097)ProcedureLab 10a:The motor control servo amplifier was wired as shown in figure 1. After the wiring was done properly, the 12Vdc motor was connected to the circiut. The angular velocity of the motor shaft should rotate proportionally to the input voltage. The potentiometer was then connected to the motor shaft with tape. This allowed the potentiometer voltage to beproportional to the angle of the motor shaft. After the potentiometer is connected LabView can be used to take readings from the poteniometer. KRTwKwdtdKJRVfsKRTKwVfs1KRTKwVfs2Figure 1- Motor control servo amplifierResultsThe measured resistance of the motor was found to be 3 ohms. We supplied the motor with two different voltages. We used these voltages and the corresponding angular velocities to solve for the coefficients K and TfR/K in equations 9 and 10. The voltages used were -3 and 2 while the angular velocities were –2.7 and 5.03 respectively. This resulted in K= .647 , Tf = -.270, and J = 4.25*10-5. K was substituted into the coefficients of the differential equation to calculate Tf and J. Voltage verses angular velocity was plotted and shown in Figure 2. Figure - 2Velocity vs Time (2 volt input)-11.630176-5.81508800205.81508800211.63017617.445264010 0.5 1 1.5 2 2.5 3Time (s)Angular VelocityBest fit curveFigure - 3Angular acceleration was calculated from measured points along the angular velocity plots. The angular acceleration was calculated from figure 2 and figure 3 as follows:2V input:57.1235.4.4t-3V input:86.17.3.1tConclusionThis lab found properties of a motor control system including the torsional resistance (Tf)in the motor. Tf was found to be a very small value, which hardly affected the motor. Also the polar moment of the motor was found to be very small and could probably be neglected in the differential equation. Velocity vs Time(-3 volt input)-3-2.5-2-1.5-1-0.500 5 10 15 20 25Time (s)Angular
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