Recent questions in Control Systems

The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undampe...

The loop transfer function of a closed-loop system is given by $G(s)H(s)=\frac{K(s+6)}{s(s+2)}$. The breakaway point of the root-loci will be ___________.

A closed-loop system is shown in the figure. The system parameter $\alpha$ is not known. The condition for asymptotic stability of the closed loop system is $\alpha<-0.5$...

The overall closed loop transfer function $\frac{C(s)}{R(s)}$ ,represented in the figure, will be $\frac{(G_1(S)+G_2(S))G_3(S)}{1+(G_1(S)+G_2(S))(H_1(S)+G_3(S))}$$\frac{(...

The term hysteresis is associated with $\text{ON-OFF control}$$\text{P-I control}$$\text{Feed-forward control}$$\text{Ratio control}$

In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant $\tau$${_1}$. Similarly, the closed loop tr...

The loop-gain function L(s) of a control system with unity feedback is given to be L(s) = $\frac{k}{(s + 1)(s + 2)(s + 3)}$, where k >0. If the gain cross-over frequency...

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 ...

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...

In the control system shown in the figure below, a reference signal $r(t)=t^2$ is applied at time $t=0$. The control system employs a $PID$ controller $C(s)=K_p+K_1/s+K_D...

The transfer function relating the input x(t) to the output y(t) of a system is given by G(s) = 1/(s + 3). A unit-step input is applied to the system at time t = 0. Assum...

In a control system with unity gain feedback, the transfer function of the loop-gain function is L(S) = 9e$^{-0.1s}$/S. The phase margin of the loop-gain function L(S) is...

The number of times the Nyquist plot of $G(s)= \frac{s-1}{s+1}$ will encircle the origin clockwise is _______.

The value of $a_0$ which will ensure that the polynomial $s^3$ + $3s^2$ + $2s$ + $a_0$ has roots on the left half of the $s$-plane is$11$$9$$7$$5$

The relationship between the force $f(t)$ and the displacement $x(t)$ of a spring-mass system (with a mass $M$, viscous damping $D$ and spring constant $K$) is$$M\frac{d^...

The transfer function $G(s)$ of a system which has the asymptotic Bode plot shown below is $10^4 \frac {(s-1)^2}{(s+100)^2}$$10^4 \frac {(s+1)^2}{(s+100)^2}$$10^4 \frac {...

For the feedback system given below, the transfer function $G(s)=\frac{1}{(s+1)^2}$. The system $\text{CANNOT}$ be stabilized with$C(s)=1+\frac{3}{s}$$C(s)=3+\frac{7}{s}$...

Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below.$P(s)-(3), Q(s)-(2), R(s)-(1)$$P(s)-(1), Q(s)-(2), R(s)-(3)$$...

A mass-spring-damper system with force as input and displacement of the mass as output has a transfer function $G(s)=1/(s^2+24s+900)$. A force input $F(t)=10\sin(70t)$ ne...

A system with transfer function $G(S)=\frac{1}{s^2+1} $ has zero initial conditions. The percentage overshoot in its step response is ______________ $\%$.

A transfer function $G(s)$ with the degree of its numerator polynomial zero and the degree of its denominator polynomial two has a Nyquist plot shown in the figure. The t...

The open loop transfer function of a system is $G(s)=\frac{s^2+6s+10}{s^2+2s+2}.$ The angles of arrival of its root loci are$\pm \frac{\pi}{4}$$\pm \frac{\pi}{3}$$\pm \fr...

A system is represented in state-space as $\dot{X}=AX+BU,$ where $A=\begin{bmatrix} 1 & 2 \\ \alpha & 6\end{bmatrix}$ and $B=\begin{bmatrix} 1 \\ 1\end{bmatrix}$. The val...

A loop transfer function is given by:$$G(s)H(s)=\frac{K(s+2)}{s^2(s+10)}$$The point of intersection of the asymptotes of $G(s)H(s)$ on the real axis in the s-plane is at ...

A plant has an open-loop transfer function,$$G_p(s)=\frac{20}{(s+0.1)(s+2)(s+100)}$$The approximate model obtained by retaining only one of the above poles, which is clos...

The transfer function of a system is given by$$G(s)=\frac{e^{-s/500}}{s+500}$$The input to the system is $x(t)=\sin100\pi t$. In periodic steady state the output of the s...

The loop transfer function of a feedback control system is given by$$G(s)H(s)=\frac{1}{s(s+1)(9s+1)}$$Its phase crossover frequency (in rad/s), approximated to two decima...

Consider a transport lag process with a transfer function$$G_p(S)=e^{-s}$$The process is controlled by a purely integral controller with transfer function$$G_c(S)=\frac{K...

Consider the control system shown in figure with feed forward action for rejection of a measurable disturbance $d(t)$. The value of $K$, for which the disturbance respons...

Consider a plant with the transfer function $G(s)=1/(s+1)^3.$ Let $K_u$ and $T_u$ be the ultimate gain and ultimate period corresponding to the frequency response based c...

Consider a plant with the transfer function $G(s)=1/(s+1)^3.$ Let $K_u$ and $T_u$ be the ultimate gain and ultimate period corresponding to the frequency response based c...

The signal flow graph for a system is given below. The transfer function $\frac{Y(s)}{U(s)}$ for this system is given as $\frac{s+1}{5s^2+6s+2}$$\frac{s+1}{s^2+6s+2}$ $\f...

The open-loop transfer function of a dc motor is given as $\frac{\omega(s)}{V_a(s)}=\frac{10}{1+10s}.$ When connected in feedback as shown below, the approximate value of...

The bode plot of a transfer function $G(s)$ is shown in the figure below.The gain $(20\;log|G(s)|)$ is $32$ dB and $-8$ dB at $1$ rad/s and $10$ rad/s respectively. The p...

In the feedback network shown below, if the feedback factor k is increased, then theinput impedance increases and output impedance decreasesinput impedance increases and ...

Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is$u(t)$$t u(t)$$\frac{t^2}{2}u(t)$$e^{-t}u(t)$

If the A-matrix of the state space model of a $SISO$ linear time invariant system is rank deficient, the transfer function of the system must have a pole with a positive ...

The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$The phase of the above lead compensator is maximum at $\sqrt{2}\;\text{rad/s}$$\sqrt{3}\;\tex...

The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$$G_c(s)$ is a lead compensator if $\text{a=1, b=2}$$\text{a=3, b=2}$$\text{a=-3, b=-1}$$\text...

The open loop transfer function of a unity gain negative feedback control system is given by $G(s)=\frac{s^2+4s+8}{s(s+2)(s+8)}.$ The angle $\theta$ , at which the root l...