Assignment
6-1. Create a model of the motor shown in Fig. 5-25. Use the following parameter values: Jm = 0.0004 kg-m2: B = 0.001 Nm/rad/sec, Ra= 2 Ω, La= 0.008 H, Km = 0.1 Nm/A, and Kb= 0.1 V/rad/sec. Assume that the load torque TL is zero. Apply a 5-V step input to the motor, and record the motor speed and the current drawn by the motor (requires modification of SIMLab blocks by making current the output) for 10 sec following the step input.
(a) What is the steady-state speed?
(b) How long does it take the motor to reach 63% of its steady-state speed?
(c) How long does it take the motor to reach 75% of its steady-state speed?
(d) What is the maximum current drawn by the motor?
6-2. Set the viscous friction B to zero in Problem 6-1. Apply a 5-V step input to the motor, and record the motor speed and current for 10 sec following the step input. What is the steady-state speed?
(a) How long does it take the motor to reach 63% of its steady-state speed?
(b) How long does it take the motor to reach 75% of its steady-state speed?
(c) What is the maximum current drawn by the motor?
(d) What is the steady-state speed when the applied voltage is 10 V?
6-3. Set the armature inductance L„ to zero in Problem 6-2. Apply a 5-V step input to the motor, and record the motor speed and current drawn by the motor for 10 sec following the step input.
(a) What is the steady-state speed?
(b) How long does it take the motor to reach 63% of its steady-state speed?
(c) How long does it take the motor to reach 75% of its steady-state speed?
(d) What is the maximum current drawn by the motor?
(e) If Jm is increased by a factor of 2, how long does it take the motor to reach 63% of its steady-state speed following a 5-V step voltage input?
(f) If Jm is increased by a factor of 2, how long does it take the motor to reach 75% of its steady-state speed following a 5-V step voltage input?
6-4. Repeat Problems 6-1 through 6-3, and assume the load torque TL = -0.1 N-m (don't forget the minus sign) starting after 0.5 sec (requires change of the disturbance block parameters in SIMLab).
(a) How does the steady-state speed change once TL is added?
(b) How long does it take the motor to reach 63% of its new steady-state speed?
(c) How long does it take the motor to reach 75% of its new steady-state speed?
(d) What is the maximum current drawn by the motor?
(e) Increase TL and further discuss its effect on the speed response.
6-5. Repeat Problems 6-1 through 6-3, and assume the load torque TL = -0.2 N-in (don't forget the minus sign) starting after 1 sec (requires change of the disturbance block parameters in SIMLab).
(a) How does the steady-state speed change once TL is added?
(b) How long does it take the motor to reach 63% of its new steady-state speed?
(c) How long does it take the motor to reach 75% of its new steady-state speed?
(d) What is the maximum current drawn by the motor?
(e) Increase TL and further discuss its effect on the speed response.
6-6. For the system in Fig. 6-1, use the parameters for Problem 6-1 (but set La= 0) and an amplifier gain of 2 to drive the motor (ignore the amplifier voltage and current limitations for the time being). What is the steady-state speed when the amplifier input voltage is 5 V?
6-7. Modify the model in Problem 6-6 by adding a proportional controller with a gain of KJ, = 0.1, apply a 10 rad/sec step input, and record the motor speed and current for 2 sec following the step input.
(a) What is the steady-state speed?
(b) How long does it take the motor to reach 63% of its steady-state speed?
(c) How long does it take the motor to reach 75% of its steady-state speed?
(d) What is the maximum current drawn by the motor?
6-8. Change Kp to 1.0 in Problem 6-7, apply a 10 rad/sec step input, and record the motor speed and current for 2 sec following the step input.
(a) What is the steady-state speed?
(b) How long does it take for the motor to reach 63% of its steady-state speed?
(c) How long does it take for the motor to reach 75% of its steady-state speed?
(d) What is the maximum current drawn by the motor?
(e) How does increasing Kp affect the response (with and without saturation effect in the SIMLab model)?
6-9. Repeat Problem 6-7, and assume the load torque TL = -0.1 N-m starting after 0.5 sec (requires change of the disturbance block parameters in SIMLab).
(a) How does the steady-state speed change once 71 is added?
(b) How long does it take the motor to reach 63% of its new steady-state speed?
(c) How long does it take the motor to reach 75% of its new steady-state speed?
6-10. Repeat Problem 6-7, and assume the load torque TL = -0.2 N-in starting after 1 sec (requires change of the disturbance block parameters in SIMLab).
(a) How does the steady-state speed change once TL is added?
(b) How long does it take the motor to reach 63% of its new steady-state speed?
(c) How long does it take the motor to reach 75% of its new steady-state speed?
6-11. Insert a velocity sensor transfer function Ks in the feedback loop, where Ks= 0.2 V/rad/sec (requires adjustment of the SIMLab model). Apply a 2 rad/sec step input, and record the motor speed and current for 0.5 sec following the step input. Find the value of Kp that gives the same result as in Problem 6-7.
6-12. For the system in Fig. 6-3, select Kp = 1.0, apply a 1 rad step input, and record the motor position for 1 sec. Use the same motor parameters as in Problem 6-1.
(a) What is the steady-state position?
(b) What is the maximum rotation?
(c) At what time after the step does the maximum occur?
6-13. Change Kp to 2.0 in Problem 6-12, apply a 1 rad step input, and record the motor position for I sec.
(a) At what time after the step does the maximum occur?
(b) What is the maximum rotation?
6-14. Using the SINILab investigate the closed-loop position response, using a proportional controller. For a position-control case, use proportional controller gains of 0.1, 0.2, 0.5. 1.0. and 2.0: record the step response for a 1 rad change at the output shaft; and estimate what you consider to be the best value for the proportional gain. Use the same motor parameters as in Problem 6-1.
6-15. Using the SIMLab, investigate] the closed-loop position response using a PD controller. Modify the controller used in Problem 6714 by adding derivative action to the proportional controller. Using the best value you obtained for Kp, try various values for KD, and record the step response in each case.
6-16. Repeat Problem 6-15 and assume a disturbance torque TD = -0.1 N-m in addition to the step input of 1 rad (requires change of the disturbance block parameters in SIMLab).
6-17. Repeat Problem 6-15 and assume a disturbance torque TD = -0.2 N-m in addition to the step input of 1 rad (requires change of the disturbance block parameters in SIMLab).
6-18. Use the SIMLab and parameter values of Problem 6-1 to design a PID controller that eliminates the effect of the disturbance torque, with a percent overshoot of 4.3.
6-19. Use the SIMLab and parameter values of Problem 6-1 to design a PID controller that eliminates the effect of the disturbance torque, with a percent overshoot of 2.8.
6-20. Investigate the frequency response of the motor using the Virtual Lab Tool. Apply a sine wave with a frequency of 0.1 Hz (don't forget: 1 Hz = 2 π rad/sec) and amplitude of 1 V the amplifier input. and record both the motor velocity and sine wave input signals. Repeat this experiment for frequencies of 0.2, 0.5, 1.0, 2.0, 5.0, 10.0, and 50.0 Hz (keeping the sine wave amplitude at 1 V).
6-21. Using the Virtual Lab Tool, investigate the closed-loop motor speed response using a proportional controller. Record the closed-loop response of the motor velocity to a step input of 2 rad/sec for proportional gains of 0. I , 0.2, 0.4, and 0.8. What is the effect of the gain on the steady-state velocity?
6-22. Using the Virtual Lab Tool, investigate the closed-loop position response using a proportional controller. For a position-control case use proportional controller gains of 0.1, 0.2, 0.5, 1.0, and 2.0; record the step response for a 1 rad change at the output shaft; and estimate what you consider to be the best value for the proportional gain!
6-23. Using the Virtual Lab Tool, investigate the closed-loop position response using a PD controller. Modify the controller used in Problem 6-15 by adding derivative action to the proportional controller. Using the best value you obtained for Kp, try various values for KD, and record the step response in each case.
6-24. In Design Project 2 in Section 6-7, use the CarSim tool to investigate the effects of controlling acceleration 2 on relative motion (or bounce) Z and vice versa.
(a) Use a PD controller in your investigation.
(b) Use a PI controller in your investigation.
(c) Use a PID controller in your investigation.
6-25. Using the Quarter Car Modeling Tool controlling,
(a) Set the simulation mode to "Passive Suspension" and set up the top axes to display 57(t). Select a step input with amplitude 0.02 m/s2 and step time 0 seconds. Plot the response. Repeat this procedure for 0.2 and 0.5 m/s2 input. Compare the results.
(b) Change the stiffness, k, to 15 N/m. With a step input of 0.02 m/s2 and the lower axes configured to display what is the frequency of the oscillatory response? This is the damped frequency of the system using default parameters (cod). How does the period of oscillation compare to the value that was observed in part (a)? Repeat the simulation several more times, gradually reducing the damping (variable c in the Model Parameters control window) to find the natural frequency of the system (w„).
(c) Obtain the effect of washboard buMps with amplitude of 0.02 m/s2 on the response of the system. Vary the frequency from 10 rad/s to 0.1 rad/s. What happens to the amplitude of relative displacement at the damped natural frequency, cod, measured in part (b)?
Attachment:- LAB-Assignment.pdf