GATE EC || CONTROL SYSTEM|| TIME DOMAIN ANALYSIS & CONTROLLER|| PYQS(2000-2025)

The frequency response of a linear, time-invariant system is given by

[Tex]H(f) = \frac{5}{1 + j 10 \pi f}[/Tex]

The step response of the system is

(GATE 2007 || EC || MCQ||1 MARK)

Consider an even polynomial p(s)p(s) given by
[Tex]p(s) = s^4 + 5s^2 + 4 + K[/Tex],
where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the imaginary axis is 

Two linear time-invariant systems have the following transfer functions:

[Tex]G_1(s) = \frac{10}{s^2 + s + 1}[/Tex]

[Tex]G_2(s) = \frac{10}{s^2 + \sqrt{10}s + 10}[/Tex]

Unit step input is applied to both systems. The corresponding unit step responses are represented as [Tex]y_1(t) \text{ and } y_2(t)[/Tex] , respectively.

Determine which of the following statements is/are true.

( GATE 2022 || EC || MCQ ||2 MARK)

The block diagram of a closed-loop control system is shown in the figure. R(s),Y(s) and D(s) are the Laplace transforms of the time-domain signals r(t),y(t) and d(t)

, respectively. Let the error signal be defined as [Tex]e(t) = r(t) - y(t)[/Tex]. Assuming the reference input [Tex]r(t) = 0[/Tex] for all t, the steady-state error [Tex]e(\infty)[/Tex], due to a unit step disturbance d(t), is _________ (rounded off to two decimal places).

( GATE 2022 || EC || NAT ||2 MARK)

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

( GATE 2023 || EC || MCQ ||2 MARK)

In the feedback control system shown in the figure below [Tex]G(s) = \frac{6}{s(s + 1)(s + 2)}[/Tex].

R(s),Y(s), and E(s) are the Laplace transforms of r(t),y(t) and e(t), respectively. If the input r(t) is a unit step function, then

( GATE 2024 || EC || MCQ ||2 MARK)

A satellite attitude control system, as shown below, has a plant with a transfer function [Tex]G(s) = \frac{1}{s^2}[/Tex] cascaded with a compensator [Tex]C(s) = \frac{K(s + \alpha)}{s + 4}[/Tex]​, where K and α are positive real constants.

In order for the closed-loop system to have poles at [Tex]-1 \pm j3[/Tex], the value of αα must be

( GATE 2024 || EC || MCQ ||2 MARK)

A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has 

( GATE 2003 || EC || MCQ ||1 MARK

A unity negative feedback closed-loop system has a plant with the transfer function [Tex]G(s) = \frac{1}{s^2 + 2s + 2}[/Tex] and a controller G_c(s) in the feedforward path. For a unit step input, the transfer function of the controller that gives the minimum steady-state error is 

( GATE 2010 || EC || MCQ ||2 MARK)

The open-loop transfer function of a dc motor is given as [Tex]\frac{\omega(s)}{V_a(s)} = \frac{10}{1 + 10s}[/Tex] When connected in feedback as shown below, the approximate value of K_a that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

(GATE 2013 || EC || MCQ ||2 MARK)