Question

Q4. (10 points) Consider the DC motor that you have used in running your experiments. Application of a proportional-velocity (PV) compensator with a proportional control gain kp and a velocity control gain ky to the motor produces the transfer function for position control to be 01(s) Kk a) Assuming nominal plant values of K-1.7 and 0.03, find the controller gain values kp and ky necessary to obtain a desired peak time and peak overshoot of tp 0.3 s and PO-: 10%. (6pts) b) If the error transfer function for position control for the above plant is given by: E(S S(Ts + 1) Using the gain values of the PV controller obtained from part (a), find the steady state erro ess for a ramp input, R(s)(4 pts)

Answer 1

(AN5) (au) 9u(5) (5) 7 kp Od (5) 56.61 kp Odcs) 533.33 CI+1.7xo)5 + 56.67 kp tp 0.35 , PO: 10% ㅠ-0.3 Cod = 10.yz2l : - 0.59 12. 10472 1 1-O-59)产 G8n = aon 12.984 |

fom o 56.6ikp 12.9BY冫1156.67 kP 2Co.5912 ) ( 12-984): 33.33() +14h9) 2

b) ECS) RC5) E (5) secs) steady słake ero SEC5) TS+I It kKP(I.7)(2.975) 0.5932
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