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GATE EC Control Systems questions

Practise Control Systems questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify the feedback structure before forming the transfer function. Check the characteristic equation and stability conditions before calculating steady-state behaviour.

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Official PYQ2026Control SystemsMCQ · 1 mark
Consider the differential equation w⃗˙=Aw⃗\dot{\vec{w}}=A \vec{w}, with w⃗(t=0)=[11]\vec{w}(t=0)=\left[\begin{array}{l}1 \\ 1\end{array}\right]. If w⃗(t)=etu⃗x+e−2tu⃗y\vec{w}(t)=e^{t} \vec{u}_{x}+e^{-2 t} \vec{u}_{y} be the solution to the equation where u⃗x\vec{u}_{x} and u⃗y\vec{u}_{y} are unit vectors along the positive xx and yy axes respectively, then which of the …
Official PYQ2026Control SystemsMCQ · 1 mark
A control system is shown in the Figure. Which option represents the correct transfer function of the system?
Official PYQ2026Control SystemsMCQ · 2 marks
For the control system shown in the Figure, the transfer function of a plant, G(s)=1(s+1)(s+2)G(s)=\frac{1}{(s+1)(s+2)} is connected in cascade with a compensator C(s)=K(s+α)C(s)=K(s+\alpha), where KK and α\alpha are positive real valued constants. Which of the following pairs (K,α)(K, \alpha) represent the correct values for the closed loop system to have poles at …
Official PYQ2026Control SystemsMCQ · 2 marks
The state and output equations for a control system are: x˙=[−4−1.540]x+[20]uy=[1.50.625]x\begin{array}{c} \dot{x}=\left[\begin{array}{cc} -4 & -1.5 \\ 4 & 0 \end{array}\right] x+\left[\begin{array}{l} 2 \\ 0 \end{array}\right] u \\ y=\left[\begin{array}{ll} 1.5 & 0.625 \end{array}\right] x \end{array} Which of the following expressions correctly represents the transfer …
Official PYQ2026Control SystemsNAT · 2 marks
Consider the unity negative feedback control system shown in the Figure. The value of gain K(>0)K(>0) at which the given system will remain marginally stable is ____\_\_\_\_. (Answer in integer)
Official PYQ2025Control SystemsMCQ · 1 mark
The Nyquist plot of a system is given in the figure below. Let ωP,ωQ,ωR\omega_{P}, \omega_{Q}, \omega_{R}, and ωS\omega_{S} be the positive frequencies at the points P,Q,R\boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{R}, and S\boldsymbol{S}, respectively. Which one of the following statements is TRUE?
Official PYQ2025Control SystemsMSQ · 1 mark
Consider the unity-negative-feedback system shown in Figure (i)(i) below, where gain K≥0K \geq 0. The root locus of this system is shown in Figure (ii)(ii) below. For what value(s) of KK will the system in Figure (i)(i) have a pole at −1+j1-1+j 1 ?
Official PYQ2025Control SystemsMCQ · 2 marks
Let G(s)=110s2G(s)=\frac{1}{10 s^{2}} be the transfer function of a second-order system. A controller M(s)M(s) is connected to the system G(s)G(s) in the configuration shown below. Consider the following statements. There exists no controller of the form M(s)=KIsM(s)=\frac{K_{I}}{s}, where KIK_{I} is a positive real number, such that the closed loop system is …
Official PYQ2025Control SystemsMCQ · 2 marks
Consider the polynomial p(s)=s5+7s4+3s3−33s2+2s−40p(s)=s^{5}+7 s^{4}+3 s^{3}-33 s^{2}+2 s-40. Let (L,I,R)(L, I, R) be defined as follows. LL is the number of roots of p(s)p(s) with negative real parts. II is the number of roots of p(s)p(s) that are purely imaginary. RR is the number of roots of p(s)p(s) with positive real parts. Which one of the following options is …
Official PYQ2025Control SystemsMSQ · 2 marks
Consider a system where x1(t),x2(t)x_{1}(t), x_{2}(t), and x3(t)x_{3}(t) are three internal state signals and u(t)u(t) is the input signal. The differential equations governing the system are given by …
Official PYQ2025Control SystemsMSQ · 2 marks
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).
Official PYQ2024Control SystemsMCQ · 1 mark
​​​In the feedback control system shown in the figure below G(s)=6s(s+1)(s+2)G(s)=\frac{6}{s(s+1)(s+2)}. R(s), Y(s)\text{R(s), Y(s)}, and E(s)\text{E(s)} are the Laplace transforms of r(t),y(t)r(t), y(t), and e(t)e(t), respectively. If the input r(t)r(t) is a unit step function, then
Official PYQ2024Control SystemsMCQ · 2 marks
​​​​​Consider a unity negative feedback control system with forward path gain G(s)=K(s+1)(s+2)(s+3)G(s)=\frac{K}{(s+1)(s+2)(s+3)} as shown. The impulse response of the closed-loop system decays faster than e−te^{-t} if ______\_\_\_\_\_\_.
Official PYQ2024Control SystemsMCQ · 2 marks
​​​​​A satellite attitude control system, as shown below, has a plant with transfer function G(s)=1s2G(s)=\frac{1}{s^{2}} cascaded with a compensator C(s)=K(s+α)s+4C(s)=\frac{K(s+\alpha)}{s+4}, where KK and α\alpha are positive real constants. In order for the closed-loop system to have poles at −1±j3-1 \pm j \sqrt{3}, the value of α\alpha must be …
Official PYQ2024Control SystemsMSQ · 2 marks
Consider a system SS represented in state space as dxdt=[0−21−3]x+[10]r,y=[2−5]x.\frac{d x}{d t}=\left[\begin{array}{ll} 0 & -2 \\ 1 & -3 \end{array}\right] x+\left[\begin{array}{l} 1 \\ 0 \end{array}\right] r, y=\left[\begin{array}{ll} 2 & -5 \end{array}\right] x . Which of the state space representations given below has/have the same transfer function as that of …
Official PYQ2023Control SystemsMCQ · 1 mark
A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when
Official PYQ2023Control SystemsMCQ · 1 mark
The open loop transfer function of a unity negative feedback system is G(s)=ks(1+sT1)(1+sT2)G(s)=\frac{k}{s\left(1+s T_1\right)\left(1+s T_2\right)}, where k,T1k, T_1 and T2T_2 are positive constants. The phase cross-over frequency, in rad/s,\text{rad/s,} is
Official PYQ2023Control SystemsMCQ · 2 marks
A closed loop system is shown in the figure where k>0\mathrm{k}>0 and α>0\alpha>0. The steady state error due to a ramp input (R(s)=α/s2)\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm{s}^2\right) is given by
Official PYQ2023Control SystemsMCQ · 2 marks
In the following block diagram, R(s)\mathrm{R}(\mathrm{s}) and D(s)\mathrm{D}(\mathrm{s}) are two inputs. The output Y(s)\mathrm{Y}(\mathrm{s}) is expressed as Y(s)=G1(s)R(s)+G2(s)D(s)Y(s)=G_1(s) R(s)+G_2(s) D(s). G1( s)\mathrm{G}_1(\mathrm{~s}) and G2( s)\mathrm{G}_2(\mathrm{~s}) are given by
Official PYQ2023Control SystemsMCQ · 2 marks
The state equation of a second order system is x˙(t)=Ax(t),  x(0)\dot{\boldsymbol{x}}(t)=\mathrm{A} \boldsymbol{x}(t), \; \boldsymbol{x}(0) is the initial condition. Suppose λ1\lambda_1 and λ2\lambda_2 are two distinct eigenvalues of A\mathrm{A} and v1v_1 and v2v_2 are the corresponding eigenvectors. For constants α1\alpha_1 and α2\alpha_2, the solution, …