We consider the same DC motor as of Lab 1 and 2 for Speed Control with parameters K = 0.1, R = 1,L = 1 mH, B = 0.001 N. m. sec/rad; J = 0.001 N.m. s^2/rad Note that the rated current for the motor is 5A input current with a pic of 50A. The maximum speed that the motor can reach is 100 rad/ sec (~ 1000 rpm) 1. Write the transfer function G(s) = (@(s))/(V(s)) of the DC motor. 2. Get the reduced representation of the transfer function PART I: We consider in this part a P-type controller G,(s) = K, 3. Show that with such a controller, the steady state error can never reach zero. 4. Show that the stability of the system is not altered with such a controller. 5. What is the maximum allowed value of the gain Kp by the hardware?

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We consider the same DC motor as of Lab 1 and 2 for Speed Control with parameters
K = 0.1, R = 1, L = 1 mH,B = 0.001 N. m.sec/rad; ] = 0.001 N.m. s^2/rad
Note that the rated current for the motor is 5A input current with a pic of 50A.
The maximum speed that the motor can reach is 100 rad/sec (~ 1000 rpm)
1. Write the transfer function G(s) = (w(s))/(V(s)) of the DC motor.
2. Get the reduced representation of the transfer function
PART I: We consider in this part a P-type controller G.(s) = Kp
3.
Show that with such a controller, the steady state error can never reach zero.
4.
Show that the stability of the system is not altered with such a controller.
5.
What is the maximum allowed value of the gain Kp by the hardware?
6.
Demonstrate the results in c-e) by simulation
7.
What would be the effect of a torque disturbance of 0.2 N.m on the steady state
performance of the system. Would you maintain the same value of K,? If not
fine-tune the design.
8.
Conclude about this part
PART II: We consider in this part a PI type controller G.(s) = Kp +
9. Show that with such a controller, the steady state error reaches zero.
10. Are there any constraint on the values of Kp and Kị for i) to be valid
11. Show that the maximum allowed value of the gain Kp by the hardware is the
same as in e).
12. If we use the reduced model, would the result in j) be altered? Explain.
13. Use the reduced model to set the gains of the PI controller in a way that the
system response never overshoots with the minimum settling time. (Hint: think
about cancelling the system pole with the controller zero)
14. Check the effectiveness of your design by simulation on both the reduced model
and the original one. Is there any difference?
15. Analyze the effect of a loading torque of 0.2 N.m. on the system performances.
16. Conclude about part II and about the full work.
1/1
Transcribed Image Text:We consider the same DC motor as of Lab 1 and 2 for Speed Control with parameters K = 0.1, R = 1, L = 1 mH,B = 0.001 N. m.sec/rad; ] = 0.001 N.m. s^2/rad Note that the rated current for the motor is 5A input current with a pic of 50A. The maximum speed that the motor can reach is 100 rad/sec (~ 1000 rpm) 1. Write the transfer function G(s) = (w(s))/(V(s)) of the DC motor. 2. Get the reduced representation of the transfer function PART I: We consider in this part a P-type controller G.(s) = Kp 3. Show that with such a controller, the steady state error can never reach zero. 4. Show that the stability of the system is not altered with such a controller. 5. What is the maximum allowed value of the gain Kp by the hardware? 6. Demonstrate the results in c-e) by simulation 7. What would be the effect of a torque disturbance of 0.2 N.m on the steady state performance of the system. Would you maintain the same value of K,? If not fine-tune the design. 8. Conclude about this part PART II: We consider in this part a PI type controller G.(s) = Kp + 9. Show that with such a controller, the steady state error reaches zero. 10. Are there any constraint on the values of Kp and Kị for i) to be valid 11. Show that the maximum allowed value of the gain Kp by the hardware is the same as in e). 12. If we use the reduced model, would the result in j) be altered? Explain. 13. Use the reduced model to set the gains of the PI controller in a way that the system response never overshoots with the minimum settling time. (Hint: think about cancelling the system pole with the controller zero) 14. Check the effectiveness of your design by simulation on both the reduced model and the original one. Is there any difference? 15. Analyze the effect of a loading torque of 0.2 N.m. on the system performances. 16. Conclude about part II and about the full work. 1/1
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