CONTROL THEORY II Mock Exam 1 Mock Exam 1

Sketch the root locus for a system with open loop transfer function given by equation (Q1) assuming $K > 0$. $G(s)H(s) = \frac{K}{s(s+4)(s+5)}$

Using Bode plot determine the phase and gain margin for the system with transfer function given by equation (Q3) and comment on the system relative stability. $G(j\omega) = \frac{1}{j\omega(j\omega+1)(0.2j\omega+1)}$

Assuming the resulting system model from identification process and the controller transfer function are given by equations (Q4a) and (Q5b) respectively. Using both methods due to Ziegler-Nichols assuming ultimate gain ($K_c'$) of $26$ and ultimate frequency of oscillation ($\omega_u$) of $15$ rad/s, design PID controller for this system and compare the two results. $G_p(s) = \frac{1.5e^{-0.1s}}{1+2s}$