Ex. 834. Use the plant transfer function in Ex830 and unity feedback. Replace the controller with a PID controller (K*(s+z1)*(s+0.5)/s) that will have CL poles that were dominant in Ex832. The other PID zero will be close to the fast zero that you found in Ex832. Find K, the error constant (Kv), the steady state error for a ramp input, the other PID-zero location, the steady state error for step input, and the expected time to achieve that step-response steady-state error based only on the slowest closed-loop pole. ans:6

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Ex. 830. Design a proportional controller (Kp) cascaded with the plant: (s+12)/( (s+ 4) (s+ 8) (s+14) ) within a unity feedback system so that the dominant poles result in a 28% overshoot step response. Find Kp, zeta, wn, wd, Ts, Tp, the error constant (Kp_error) and corresponding SS error. Note: Kp_error is different from Kp in the PID-TF. ans:8

kp=305.826, zeta=0.376, wn=18.345, wd=16.99, Ts=0.57982, Tp=0.1849, kp_error=8.19, SS_error=0.1087

Ex. 832. Replace the proportional controller in Ex830 with a PD controller (K*(s+z)) and use the same plant transfer function so that the closed loop system has a peak time that is 2/3 of that in Ex830 and still has the the same PO. Find all the answers as in Ex830 plus the PD zero location. Note: The controller zero is located at s=-z (s is negative and z is positive.) Final answers are sensitive to intermediate values. Do not round intermediate values including Tp from Ex830. Possible to make all calculations in MATLAB. ans:9