PYQs Based Test - 05 : Control Systems

Let Y(s) be the unit-step response of a causal system having a transfer function

$G\left(s\right)=\frac{3-s}{\left(s+1\right)\left(s+3\right)}$

that is, $Y\left(s\right)=\frac{G\left(s\right)}{s}$ . The forced response of the system is

The position control of a DC servo-motor is given in the figure. The values of the parameters are K${}_T$ = 1 N-m/A, Rₐ = 1 Ω, Lₐ = 0.1 H, J = 5 kg-m², B = 1 N-m/(rad/sec) and K${}_b$ = 1 V/(rad/sec).



The steady-state position response (in radians) due to unit impulse disturbance torque T${}_d$ is _______.

Consider a causal second-order system with the transfer function $G\left(s\right)=\frac{1}{1+2s+s^2}$ with a unit-step $R\left(s\right)=\frac{1}{s}$ as an input. Let C(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value $\underset{t\to \infty }{\lim }c\left(t\right)$, rounded off to two decimal places, is

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as

$\mathrm{G}\left(\mathrm{s}\right)=\frac{\mathrm{K}\left(\mathrm{s}+2\right)}{{\mathrm{s}}^2+2\mathrm{s}+2}\mathrm{and}\mathrm{H}\left(\mathrm{s}\right)=1$

respectively. If the variable parameter K is real positive, then the location of the break point on the root locus diagram of the system is __________