Answer Happy

Use MATLAB to find the following:
Consider a control system described by the following Transfer Function: C(s) 0.2 (52 +5+ 1)(+0.2) R(S) To be controlled by a proportion al controller with gain K, and s S PI = (Kp + **) and PID=(Kp + Ki K + Kps (T+1) a) Use MATLAB to plot the root locus with respect to K, of the characteristic equation of the closed loop system. For which values of K, > Oisthe closed loop system asymptotically stable. (10 Pts) b) Assume that the system is controlled by a Pl controller where K, = 1. Plot the root locus of the characteristic equation, with respect to K; , and determine for which values of K, >0 the closed loop system is asymptotically stable. (20 pts) c) Finally, let the system be controlled by a PID controller, where Ko = 1, K; = 1 and 7 = 0.1. Plot a root locus of the closed loop characteristic equation, with respect to K, >0, and (10 Pts) d) Show that the derivative part increases the damping of the closed loop system, loop system, but a too large Ky will give an oscillation with a higher frequency, and finally an unstable closed loop system. (20 pts) =