Control Systems

The asymptotic Bode magnitude plot of a system is shown. Which one of the following options best represents the transfer function of the system?

A system is characterized by the following state equation and output equation (U: input, X: state vector, y: output) $\dot{x} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}x + \be...

A system is represented in state-space form as follows: ($u$: input, $\mathbf{x}$: state vector, $y$: output) $\dot{\mathbf{x}}} = \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix} \ma...

Let $G(s) = \frac{1}{(s+1)(s+2)}$. Then the closed-loop system shown in the figure below, is

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system...

The Nyquist plot of a strictly stable G(s) having the numerator polynomial as (s – 3) encircles the critical point –1 once in the anti-clockwise direction. Which one of the followi...

The open-loop transfer function of the system shown in the figure, is $G(s) = \frac{Ks(s + 2)}{(s + 5)(s + 7)}$ For $K \ge 0$, which of the following real axis point(s) is/are on t...

Let $G(s) = \frac{1}{(s+1)(s+2)}$. Then the closed-loop system shown in the figure below, is

Consider the state-space model $\dot{x}(t) = Ax(t) + Br(t)$, $y(t) = Cx(t)$ where $x(t)$, $r(t)$, $y(t)$ are the state, input and output, respectively. The matrices A, B, C are giv...

A controller $D(s)$ of the form $(1+K_D s)$ is to be designed for the plant $G(s) = \frac{1000\sqrt{2}}{s(s+10)^2}$ as shown in the figure. The value of $K_D$ that yields a a phase...

For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is

Consider the standard second-order system of the form $\frac{\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2}$ with the poles $p$ and $p^*$ having negative real parts. The pole locatio...

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approx...

Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?

Consider the closed-loop system shown in the figure with $G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}$ The root locus for the closed-loop system is to be drawn for $0 \le K < \in...

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of -20 dB/decade at least till 100 rad/sec with the ga...

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of G(s) are given in the table. The value of the gain K_I (>0)...

For the block diagram shown in the figure, the transfer function $\frac{Y(s)}{R(s)}$ is

In the Nyquist plot of the open-loop transfer function $G(s)H(s) = \frac{3s + 5}{s - 1}$ corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of t...

Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 a...

Consider a lead compensator of the form $K(s) = \frac{1 + \frac{s}{a}}{1 + \frac{s}{\beta a}}, \beta > 1, a > 0$ The frequency at which this compensator produces maximum phase lead...

A system transfer function is H(s) = $\frac{a_1s^2+b_1s+c_1}{a_2s^2+b_2s+c_2}$. If $a_1 = b_1 = 0$, and all other coefficients are positive, the transfer function represents a

The output response of a system is denoted as y(t), and its Laplace transform is given by $Y(s) = \frac{10}{s(s^2+s+100\sqrt{2})}$. The steady state value of y(t) is

The open loop transfer function of a unity feedback system is given by $G(s) = \frac{\pi e^{-0.25s}}{s}$. In G(s) plane, the Nyquist plot of G(s) passes through the negative real a...

The asymptotic Bode magnitude plot of a minimum phase transfer function G(s) is shown below. Consider the following two statements. Statement I: Transfer function G(s) has three po...

The transfer function of a phase lead compensator is given by D(s) = 3(s+1/(3T))/(s+1/T) The frequency (in rad/sec), at which ∠D(jω) is maximum, is

Consider a state-variable model of a system [ẋ1; ẋ2] = [[0, 1]; [-α, -2β]] * [x1; x2] + [[0]; [α]] * r y = [1, 0] * [x1; x2] where y is the output, and r is the input. The damping...

The transfer function of a system is given by, $V_o(s) / V_i(s) = (1-s) / (1+s)$. Let the output of the system be $v_o(t) = V_m sin(\omega t + \phi)$ for the input, $v_i(t) = V_m s...

When a unit ramp input is applied to the unity feedback system having closed loop transfer function $\frac{C(s)}{R(s)} = \frac{Ks+b}{s^2+as+b}$, $(a>0, b>0, K>0)$, the steady state...

The transfer function C(s) of a compensator is given below. $C(s) = \frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$ The frequency range in which the phase (lead)...

A closed loop system has the characteristic equation given by s³ + Ks² + (K+2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

In the system whose signal flow graph is shown in the figure, $U_1(s)$ and $U_2(s)$ are inputs. The transfer function $\frac{Y(s)}{U_1(s)}$ is

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: $\begin{bmatrix} \dot{x_1}(t) \\ \dot{x_2}(t) \end{bmatrix} = \begin{bmatrix} 1 & 2 \\...

The root locus of the feedback control system having the characteristic equation s² +6Ks +2s+5=0 where K > 0, enters into the real axis at

The range of K for which all the roots of the equation s³ + 3s² + 2s + K = 0 are in the left half of the complex s-plane is

Which of the following systems has maximum peak overshoot due to a unit step input?

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

When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} = {{Ks + b} \over {{s^2} + as...

Loop transfer function of a feedback system is $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3} \right)}}.$$ Take the Nyquist contour in the clockwise dir...

The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr...

The state variable formulation of a system is given as $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matri...

The state variable formulation of a system is given as $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matri...

A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t \right) + 2u\left( t \right)$$...

A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \ri...

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$...

Consider the function $$F\left( s \right) = {5 \over {s\left( {{s^2} + 3s + 2} \right)}}$$ Where $$F(s)$$ is the Laplace transform of the function $$f(t).$$ The initial value of $$...

The following equation defines a separately exited $$dc$$ motor in the form of a differential equation $${{{d^2}\omega } \over {d{t^2}}} + {{B\,d\omega } \over {j\,\,dt}} + {{{K^2}...

A unity feedback system has an open loop transfer function, $$G\left( s \right) = {K \over {{s^2}}}.$$ The root locus plot is

$$D\left( s \right) = {{\left( {0.5s + 1} \right)} \over {\left( {0.05s + 1} \right)}}$$ Maximum phase lead of the compensator is

For a feedback control system of type $$2,$$ the steady state error for a ramp input is

The transfer function for the state variable representation $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = CX + DU,$$ is given by