1. Problem:05-01 x points: -7, -4+3i HW- 05 In the control system as shown in the figure, a) Write the MATLAB program to plot root-locus diagram for the closed loop system. b) Add the commands the program to plot the line when the damping ratio is 0.707. c) Root-locus diagram resulting in a and b is shown. Find the eigenvalues of the open loop system from the diagram. d) Add the commands that give the value of the gain at the point when any point is clicked on the root-locus diagram. e) The gain is K=250 for the point A. Is the closed loop system stable for K=300? f) It can be found as K=40 at the point B. Find the steady-state error of the closed loop system for the step input. g) If the disturbance exists, find the sensitivity for the gain of K=40. h) Find the eigenvalues of the closed loop system for the gain of K=40.

2. Answer 05-01: (c) -4±3i, -7,0 ( e) Unstable (f) 0 (g) % 2.5 (h) 2.7 s (a) ng=[1,6];dg=[1,15,81,175,0];rlocus(ng,dg) (b) hold on;plot([0,-8],[0,8]);hold off (d) rlocfind(ng,dg) (h) kp=40;dh=polyadd(dg,kp*ng);p=roots(dh) (i) sys=tf(kp*ng,dh);[c,t]=step(sys);plot(t,c);overs=max(c)-c(length(c)) (overs=3e-4 )

3. Problem 05-02 Thompson (p. 157) a) Write the MATLAB program to plot root-locus diagram for the closed loop system. b) Add the command to find the critical gain. c) Find the critical gain by Routh criteria. Is the system stable for the gain of K=1. d) Add the commands the program to plot the line when the damping ratio is 0.65. e) Write the MATLAB program to find the values of the eigenvalues, the settling time, the overshoot and to plot the step response of the closed loop system. g) Find the steady-state error of the closed loop system for the step input (K=9). h) If the disturbance exists, find the sensitivity. i) What type of control is added to the system to eliminate the steady-state errors. j) What type of control is added to the system to decrease the level of the overshoot.

4. Problem 05-03 Numerical values: J=0.01; b=0.1;K=0.01;R=1;L=0.5; Design criteria: t s <2, Max. overshoot< %5, e ss < %1 Solve the problem by using root-locus diagram. The block diagram of a DC-motor control system is shown below.