Figure P8.15 shows a simplified drawing of a feedback

Chapter 8, Problem 56

(choose chapter or problem)

Figure P8.15 shows a simplified drawing of a feedback system that includes the drive system

G(s) = \(\frac{25\left(s^2+1.2 s+12500\right)}{s\left(s^2+5.6 s+62000\right)}\)

presented in Problem 67, Chapter 5 (Thomsen, 2011). Referring to Figures P5.43 and P8.15, \(G_p(s)\) in Figure P8.15 is given by:

\(G_p(s)\) = \(K_M \frac{G(s)}{1+0.1 G(s)}\)

Given that the controller is proportional, that is, \(G_C(s)\) = \(K_P\), use MATLAB and a procedure similar to that developed in Problem 40 in this chapter plot the root locus \({ }^4\) and obtain the output response, c(t) = \(\omega_L(t)\), when a step input, r(t) = \(\omega_r(t)\) = 260 u(t) rad/ sec, is applied at t = 0. Mark on the time response graph, c(t), all relevant characteristics, such as the percent over- shoot (which should not exceed 168 ), peak time, rise time, settling time, and final steady-state value.