November 24, 1998EGR 345 Lab 9a Servomotor Proportional Control SystemsLee C. Groeneweg, Tim JousmaNovember 24, 1998Purpose: To determine the time constants for the feedback signal of a controller in a proportional servo motor control system. Theory:DC servomotors typically have a first order (velocity) response as found in a previous lab.(1)We can develop a simple control technique for a control of the velocity using the equationbelow. For this form of control, we need to specify a desired velocity by setting a value ‘Vd’. The difference between the desired speed and actual speed is calculated (Vd-Vi). This will give a voltage difference between the two values. This difference is multiplied by a constant ‘K’. The value of ‘K’ will determine how the system responds.Vo = K(Vd-Vi) (2)where,Vo = Voltage to motor amplifier to control speedVi = Voltage from tachometer to measure speedVd = Desired motor speed voltage (user input)K = Controller gainBy substituting Vo of equation 2 in for Vs in equation 1, we can get a first order response for Vi. The development of this eqaution is found in Appendix A.The basic controller is set up as shown in Figure 1. We used a LabVIEW program to implement the basic control equation described above (equation 2)Figure 1. Setup for controller.JRKVJRKdtds2Equipment:- Computer running LabVIEW (PSE Dell 120)- Computer running Mathcad (PSE Dell 123)- Feedback Controller Kit (Drive Amp, Motor, Tachometer, Power Supply)- Circuit design Trainer breadboard- Various leads and connectors - Inertial Mass- Collar on motor to connect motor and tachometerProcedure:1. Set up the amplifier, motor, tachometer assembly as follows:- The D/A output port of LabView controlled the voltage to the amplifier which powered the motor,- The voltage output of the tachometer was used as the feedback signal to the A/D inputport of LabVIEW.2. Developed a VI using LabVIEW that recorded the data from the tachometer to a file. The VI is shown in Figure 2.3. Developed a Mathcad document to compare the theoretical values for the accelerationof the motor, with a given emf, against the values obtained using LabVIEW. 4. Solved the differential equation to determine the theoretical response, the voltage of the feedback signal, to the system .5. Determine the theoretical time constant for the motor to reach steady state operation.6. Ran the control system with output voltages from LabVIEW with chosen values for the desired voltage output and controller gain 7. Ran the control system without an inertial mass and with an inertial mass to see the effects for different load conditions.Figure 2. VI developed in LabVIEW to collect data.Results: The results for this experiment are shown in Table 1.Desired Voltage (Vd) &Controller Gain (Kc)Time Constantin milliseconds(Theoretical)Time Constant inmilliseconds(Experimental)(No inertial load )Vd=5 Kc=1 29.531 27Vd=5 Kc=10 5.268 4.5(Inertial Disk added)Vd=5 Kc=1 70.875 72Vd=1 Kc=10 12.644 IndeterminateTable 1. Results of Theoretical and Experimental time constantsThe calculations for the theoretical time constants are attached as Appendix A, with the graphs in Appendix B. The graphs used to determine the experimental time constants are attached as Appendix C. Discussion:The theory agrees well with the experimental values of the time constants, with one exception: When the inertial disk was added Vd was set to 1, and Kc was set to 10, thetachometer voltage exceeded the maximum allowable input to the controller. Therefore, the graph is truncated at 5 volts, preventing us from determining a time constant from it.Also, when the motor and tachometer were connected, they rotated about slightly different axes (the rotor shaft of the motor was warped), resulting in graphs that appear tobe second order. However, the motor and tachometer yielded a first order response, and the vibration was external to the system, so we averaged the external oscillation when finding time constants. This can be seen in Appendix C.Conclusion:The model of this controller feedback system approximates the mechanism’s behavior within 8%
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