A first-order system is given by x = -x + it with the initial condition x(0) = .v0. We
Chapter 0, Problem CP11.9(choose chapter or problem)
A first-order system is given by x = -x + it with the initial condition x(0) = .v0. We want to design a feedback controller u = -kx such that the performance index J = (x2 (t) + \u2 (t)) dt Jo is minimized. (a) Let A = 1. Develop a formula for / in terms of k, valid for any x(), and use an m-file to plot J'fx\ versus k. From the plot, determine the approximate value of k = kmi that minimizes J/XQ, (b) Verify the result in part (a) analytically, (c) Using the procedure developed in part (a), obtain a plot of &min versus A, where kmm is the gain that minimizes the performance index.
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