PYQs Based Test - 04 : Control Systems

The overall closed loop transfer function $\frac{C\left(s\right)}{R\left(s\right)},$ represented in the figure, will be

In a control system with unity gain feedback, the plant has the transfer function P(s) = 3/s. Assuming that a controller of the form C(s) = K/ (s + P) is used, where K is a positive constant, the value of P for which the root-locus of the closed-loop system passes through the points $-3\pm j3\sqrt{3}$ where $j=\sqrt{-1}$, is

Taking N as positive for clockwise encirclement, otherwise negative, the number of encirclements N of (−1, 0) in the Nyquist plot of G(s) = 3/(s -1) is

The dynamics of the state ≤ft[ {*20c x_1\\ x_2 } ] of the system is governed by the differential equation ≤ft[ {*20c x_1\\ x_2 } ] = ≤ft[ {*20c 1&2\\ - 3& - 4 } ]≤ft[ {*20c x_1\\ x_2 } ] + ≤ft[ {*20c 20\\ 10 } ] Given that the initial state is ≤ft[ {*20c 0\\ 0 } ], the steady value of ≤ft[ {*20c x_1\\ x_2 } ] is

Consider a unity feedback configuration with a plant and a PID controller as shown in the figure. $G(s)=\frac{1}{(s+1)(s+3)}$ and $C(s)=K\frac{(s+3-j)(s+3+j)}{s}$ with K being scaler. the closed loop is