Question

If anyone has Matlab, help me with problem e and f. Thank you.

Design by Synthesis: It is possible to design the PID so that the overshoot of the feedback system would be zero, furthermore, the feedback system would behave as a first order system. This is done by noting the PID transfer function: 3. PID Controller Plant Gp (s) R(s) C(s) s2+s+1 Note in the above KPK and Ki/Kp may be chosen so that the numerator of the PID would cancel the plant denominator, in that case PID Controller Plant Gp (s) R(S)+ C(s) Single loop feedback system C(s) R(s) Forward Gain KD L.e. the feedback system behaves as a 1t order system of time constant 1/K and a DC gain of 1 Now, do the following a. Choose K so that feedback system acts like a 1st order system of t 0.5 seconds. b. Then, calculate Kp and K, so that the denominator of the plant cancels with the numerator of the PID C. Plot the resulting feedback system unit step response d. There is a control cost for demanding such a fast response from the plant, to see this, find the controller t transfer function R M(s) R(s) symbolically by t he single loop Mason's gain fo Use "Eplot" or "ezplot" command to plot the unit step response of the controller output m(t) by finding the inverse Laplace transform of M (s) with R (s) = 1/s. To make the system causal, add a low pass filter pole to the derivative action with a time constant of 0.05 seconds as shown below. Explain what you see in this plot and the cost of pushing the plant to have a high speed response fplot (vpa (mt), [O, 5]) axis tight. This plots m(t) from t 0 to 5 seconds Also, find the plant unit step response c(t) by inverse Laplace of C(s) symbolically and plot the response: fplot (vpa (ct),[0,51) Include above plots and your answers in the pdf file you are going to submit. e. f. axis tight g. M(s) PID Controller Plant Gp (s) R(s) C(s) 0.05s+1+s+1) s2s +1

Answer 1

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