Recent activity in Control Systems

In the phase-locked-loop circuit shown below, the output of the VCO is a digital square wave.If the input is a square wave at $10$ $\mathrm{kHz}$, the steady state freque...

The system $G(s)=\dfrac{K}{(s+1)^{4}}$ has a gain margin of $20$ dB. The value of $K$ is $\_\_\_\_$. (rounded off to two decimal places)

A linear time invariant (LTI) system has a transfer function$$G(s)=\frac{10(s+1)}{s\left(s^{2}+2 s+5\right)}$$The system is placed in unity negative feedback configuratio...

A linear time invariant (LTI) system is described by:$$\begin{array}{c}{\left[\begin{array}{l}\dot{x}_{1} \\\dot{x}_{2}\end{array}\right]=\left[\begin{array}{cc}0 & 1 \\-...

Among the following, the differential equation(s) not representative of a linear dynamical system is/are $\_\_\_\_\_\_$.$\dfrac{d^{2} x}{d t^{2}}+2 t \dfrac{d x}{d t}+x(t...

Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value ...

​​The transfer function of a system is$$G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}}$$Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} ...

​​​​Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ i...

The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T>0$, is$1-j \omega T$$\dfrac{1-j \omega T}{1+j \omega T}$$1+j \omega T$$\dfrac...

Consider the state-space representation of a system$$ \dot{x}=A x+B u $$where $x$ is the state vector, $u$ is the input, $A$ is the system matrix and $B$ is the input mat...

The pressure drop across a control valve is constant. The control valve with inherent characteristic has decreasing sensitivity. If $x$ represents the fraction of maximum...

A feedback control system is shown in the figure.The maximum allowable value of $n$ such that the output $y(t)$, due to any step disturbance signal $d(t)$, becomes zero a...

The plant in the feedback control system shown in the figure is $P(s)=\frac{a}{s^{2}-b^{2}}$, where $a>0$ and $b>0$. The type(s) of controller $C(s)$ that CANNOT stabiliz...

The figure shows a closed-loop system with a plant $G(s)=\frac{1}{s^{2}}$ and a lead compensator $C(s)$. The compensator is designed to place the dominant closed-loop pol...

Consider the control system block diagram given in Figure (a). The loop transfer function $G(s) \: H(s)$ does not have any pole on the $j \omega$-axis. The counterclockwi...

For the transfer function $G(s)=1+\frac{2 s-1}{s^{3}+5 s^{2}+3 s+22}$, the number of zeros lying in the left half of the $s$-plane is$0$$1$$2$$3$

The signal flow graph of a system is shown. The expression for $Y(s)/X(s)$ is ___________ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s)} {1 + G_{2}(s) + G_{3}(s)}$$2 + G...

A proportional-integral-derivative $\text{(PID)}$ controller is employed to stably control a plant with transfer function$$P(s) = \frac{1}{(s+1)(s+2)}$$Now, the proportio...

Taking $\text{N}$ as positive for clockwise encirclement, otherwise negative, the number of encirclements $\text{N}$ of $(-1,0)$ in the Nyquist plot of $G\left ( s \right...

Consider a unity feedback configuration with a plant a $\text{PID}$ controller as shown in the figure. $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+3 \rig...

Consider a system with transfer-function $G\left ( s \right )=\dfrac{2}{s+1}$. A unit step function $\mu \left ( t \right )$ is applied to the system, which results in an...

A sinusoid $\left ( \sqrt{2} \sin t \right ) \: \mu \left ( t \right )$, where $\mu \left ( t \right )$ is the step input, is applied to a system with transfer-function $...

The closed loop transfer function of a control system is given by $\frac{C(s)}{R(s)}=\frac{1}{s+1}$. for the input $r(t)=\sin\;t$ the steady state response $c(t)$ is ____...

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 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...

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 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 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 ...

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 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...

Consider a standard negative feedback configuration with G(s) = $\frac{1}{(s+1)(s+2)}$ and H(s) = $\frac{s+a}{s}$, For the closed loop system to have poles on the imagina...

Consider the standard negative feedback configuration with G(s) = $\frac{s^2+0.2s+100}{s^2 – 0.2s +100}$ and H(s) = $\frac{1}{2}$. The number of clockwise encirclements o...

An input p(t) = sin(t) is applied to the system G(s) = $\frac{s-1}{s+1}$. The corresponding steady state output is y(t) = sin(t + $\varphi$), where the phase $\varphi$ (i...

The approximate phase response of $\frac{100^2e^-0.01s}{s^2+0.2s+100^2}$ is

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 ___________.

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 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{(...

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