EEGR 431: Linear Control Systems Matlab Assignment 2 (Due Monday, November 5, 2014) Review the computer-aided learning examples in the text: (p.57) C1.7-1.9, (p.125) C2.1, C2.3, C2.5 A: For problems D2.8 (a) and (c) from the text, in each case 1. Plot the step response, using matlab. 2. Calculate the damping ratio. 3. On your plots, indicate and determine the values of Mp, Tp, Tr and Ts (as specified by problem D2.8). 4. Using the above variables, discuss any tradeoffs by comparing the speed of response and overshoots, etc. B : Effect of varying gain in a closed-loop system (Proportional control) Consider the feedback system shown, consisting of a plant G(s) in cascade with a gain K (proportional controller). + K G(s) R(s) - Y(s) Controller Plant Let the Plant be G(s) = 1/ (s(s+2)) 1) Is this plant stable? Calculate and plot the step response of this plant (i.e. Open-loop step response, with K=0 in closed-loop characteristic polynomial). 2) Find the transfer function of this closed-loop system. 3) Use matlab to plot the closed loop step responses for the following gains: K= -1, ¼ , 1, 4 , 16. 4) Find the damping ratio, , for each K-value and use this to explain the type of response in each case. 5) For the K-value, which gives an underdamped response, determine the values of Mp, Tp, Tr and Ts.
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