Question

1. Using the MATLAB rltool command (or rlocus and rlocfind), plot the K > 0 root locus for What is the value of the largest damping ra- 2+2s+1 s(s120)7,7 -2,12). 1 + KL(s) = 0, where L(s) = tio associated with the pair of complex poles? At which value of K is it achieved? Turn in a printout of your plot showing the location of the poles on the damping ratio line that you found. 2. Suppose the unity feedback system shown in Figure 1 has an open-loop plant given by G(s) Design a lead compensator, D(s) K-, K > 0, to be added in cascade with the plant so that the dominant poles of the closed-loop system are located at s =-2 ± 2j (Hint: You may have to place the compensator zero to the right of -2). Try 2 different compensators, document the values of the compensator parameters in a brief table, and select the best one. Justify your selection 3. For the unity feedback system shown in Figure 1, the open-loop plant is given by G(s) Design a lag compensator, D(s) K the following specifications are met: (i) Step response settling time is less than 5 seconds (ii) Step response overshoot is less than 17%. (iii) Steady state error to a unit ramp input should not exceed 10% , K > 0, to be added in cascade with the plant so that G(s) Figure 1: Unity feedback control system

Answer 1

Hello,
          Please find the answer to the first question attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

The answers to all questions of 1 has been printed directly on the figure.

**** Matlab Code ***

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% using root locus to study system characteristics

G1 = tf([1,2,1],[1 40 400 0]);          % first transfer function
G2 = tf(1,[1 -2 2]);                    % second transfer function

G = G1*G2;                              % whole transfer function G = L
rlocus(G);
grid;

**** End of Code ****

Output: