PYQs Based Test - 06 : Control Systems

The system shown in Fig. (a) has a time response y(t) to an input r(t) = 10 u(t) as shown in Fig. (b), u(t) being the unit step input. Both K. τ are positive. The gain K of the system is _______

In the control system shown in the figure below, a reference signal r(t) = t² is applied at time t = 0. The control system employs a PID controller C(s) = K${}_P$ + K${}_I$ / s + K${}_D$ s and the plant has a transfer function P(s) = 3/s. If K${}_P$ = 10, K${}_I$ = 1 and K${}_D$ = 2, the steady state value of e is

The block diagram of a closed-loop control system is shown in the figure. The values of k and kₚ are such that the system has a damping ratio of 0.8 and an undamped natural frequency ωₙ of 4 rad/s respectively. The value of kₚ will be __________ .

The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d(t) is given by d (t) 0.1sin(ωt) where ω = 5 rad/s, the steady-state amplitude of the output y(t) is

The unit step response y(t) of a unity feedback system with open loop transfer function $G\left(s\right)H\left(s\right)=\frac{k}{{\left(s+1\right)}^2\left(s+2\right)}$ is shown in the figure. The value of K is _______ (up to 2 decimal places.)