Question

Consider the plant sDs2) 1) What is the plant's type? 2) Let C(s) - K (a proportional controller). Find the closed-loop transfer function from reference to output using unity feedback. ) Choose different gains for K within the range 1 to 100. Plot the unit step response for the different gains. What happens with the transient response of the closed-loop as K increases? 4) For K 20 find the maximum value attained by the output y(t) and the settling time T, for a unit step input (the time it takes the output to settle within a band of 2% around its final value) (The zoom tool in the Figure window may be useful here; also, you may try the command find). 5) Design a controller that will increase the system's type by 1 and that will yield the smallest settling time you can obtain for a step input. What is the settling time? 6) Generate a triangular input (ramp input) with amplitude 2 and period 120 seconds. Plot the response of the closed-loop system using the controller you designed in part (5) for two periods. The sawtooth command will be useful here. (Use the command lsim to obtain the time response of the system.) Record your observations. Is there a steady-state error? If so, what is its magnitude? What would happen with the steady-state error if the input were, instead, a train of steps? You do not need to give a plot for this question, just answer based on the type number of the plant together with your controller design. 7) Comment on the performance limitations you found in part (5)

Answer 1