Answer Happy

4 1 P3: Feedback System with Two Inputs (35 points). The Fig. below shows the block diagram of a feedback system having two inputs: 1) the reference input labelled as R(s) and ii) the disturbance input D(s). Let Gp(s) = HS) while Gc(s) = 80 (5+3) (0.5s+1)(25+1) 0.05s+1' S+45 Ideally, we would like the output to follow the reference input and to not be affected by the disturbance input. Although it is possible to construct a 2-input/1-output mode of such a system by using the "connect” command of the control systems toolbox, we will instead construct two 1- input models and use the appropriate one depending on which input is under consideration. For example: when we are interested in the response to the reference input, we can set the disturbance input to zero and obtain the single-input feedback. Likewise, when we are interested in the response to the disturbance input, we set R(s) = 0 and obtain the single-input block diagram. a. Draw the two one-input models, based on the above discussion D(s) Controller Plant R(s) Y(s) Gc(s) Gp(s) Sensor H(S) b. Develop two separate Matlab models, one model having the input R(s), and the other having the input D(s). c. Use the models developed in b) to determine the closed loop zeros and poles for both models. Comment on your results. d. Plot the responses of both models to a unit step function on a single set of axes. Use your plots to find the steady state gain of the reference model and the disturbance model. Comment on your results. e. Replace the gain of 80 in the numerator of Gc(s) with the variable gain K whose value you can specify with the input command, as in K = input(enter controller gain..."). Then plot the responses of the reference and disturbance signals for several values of K (K= 20, 50, 100, 120). f. Comment on the shape of the responses as the gain is increased, how fast is the response with the variation in K, and the steady state gain variation with the variation in K?