Control Systems

A control system is shown in the Figure. Which option represents the correct transfer function of the system?

For the control system shown in the Figure, the transfer function of a plant, $G(s) = \frac{1}{(s+1)(s+2)}$ is connected in cascade with a compensator $C(s) = K (s + \alpha)$, wher...

The state and output equations for a control system are: $\dot{x} = \begin{bmatrix} -4 & -1.5 \\ 4 & 0 \end{bmatrix}x + \begin{bmatrix} 2 \\ 0 \end{bmatrix}u$ $y = \begin{bmatrix}...

Consider the unity negative feedback control system shown in the Figure. The value of gain K (>0) at which the given system will remain marginally stable is __. (Answer in integer)

The Nyquist plot of a system is given in the figure below. Let $\omega_P, \omega_Q, \omega_R$, and $\omega_S$ be the positive frequencies at the points P, Q, R, and S, respectively...

Consider the unity-negative-feedback system shown in Figure (i) below, where gain K ≥ 0. The root locus of this system is shown in Figure (ii) below. For what value(s) of K will th...

Let $G(s) = \frac{1}{10s^2}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below. Consider the...

Consider the polynomial p(s) = s^5 + 7s^4 + 3s^3 - 33s^2 + 2s - 40. Let (L, I, R) be defined as follows. L is the number of roots of p(s) with negative real parts. I is the number...

Consider a system where $x_1(t)$, $x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given...

Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).

In the context of Bode magnitude plots, 40 dB/decade is the same as ________.

In the feedback control system shown in the figure below $G(s) = \frac{6}{s(s+1)(s+2)}$. $R(s), Y(s)$, and $E(s)$ are the Laplace transforms of $r(t), y(t)$, and $e(t)$, respective...

Consider a unity negative feedback control system with forward path gain G(s) = K / ((s+1)(s+2)(s+3)) as shown. The impulse response of the closed-loop system decays faster than e⁻...

A satellite attitude control system, as shown below, has a plant with transfer function $G(s) = \frac{1}{s^2}$ cascaded with a compensator $C(s) = \frac{K(s+\alpha)}{s+4}$, where K...

Consider a system $S$ represented in state space as $\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}r, y=[2 \ -5]x$. Which of...

The open loop transfer function of a unity negative feedback system is G(s) = k / (s(1+sT₁)(1+sT₂)), where k, T₁ and T₂ are positive constants. The phase cross-over frequency, in r...

A closed loop system is shown in the figure where k > 0 and α > 0. The steady state error due to a ramp input (R(s) = α/s²) is given by

In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as Y(s) = G₁(s)R(s) + G₂(s)D(s). G₁(s) and G₂(s) are given by

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $G(s) = \frac{k(s+z)^a}{s^b (s+p)^c}$, where k, z, p, a,...

The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function H(s) = \frac{Y(s)}{X(s)} is

Let the state-space representation of an LTI system be $\dot{x}(t) = A x(t) + B u(t)$, $y(t) = C x(t) + d u(t)$ where A, B, C are matrices, d is a scalar, u(t) is the input to the...

Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function $G(s) = \frac{1}{s^2 + 3s + 2}$ where K > 0. Th...

The state equation and the output equation of a control system are given below: $$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matr...

Consider the state space realization $$$\left[ {\matrix{ {\mathop x\limits^ \bullet } & {\left( t \right)} \cr {\mathop x\limits^ \bullet } & {\left( t \right)} \cr } } \right] = \...

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation. X: The sys...

The transfer function of a plant is $$$T\left(s\right)=\frac5{\left(s+5\right)\left(s^2+s+1\right)}$$$ The second-order approximation of T (s) using dominant pole concept is:

The state variable equations of a system are: $$${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u$$$ $$${\mathop x\limits^ \bullet _2} = 2{x_1}$$$ $$$y = {x_1} + u.$$$ The s...

The zero, input response of a system given by the state space equation $$$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \over {\mathop {{x_2}}\limits^ \bullet }}} \right] = \left[ {\...

The system mode described by the state equations $$$X = \left( {\matrix{ 0 & 1 \cr 2 & { - 3} \cr } } \right)x + \left( {\matrix{ 0 \cr 1 \cr } } \right)u,y = \left[ {\matrix{ 1 &...

Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+2s\right)}$$$ The type of the...

The 3-dB bandwidth of a typical second- order system with the transfer function $${{C\left( s \right)} \over {R(s)}} = {{\omega _n^2} \over {{s^2} + 2\xi {\omega _n}s + \omega _n^2...

An electromechanical closed-loop control system has the following characteristic equation $$s^3+6Ks^2+\left(K+2\right)s+8\;=\;0$$, where K is the forward gain of the system.The con...