Control Systems

Q. For a system having transfer function $G\left(s\right)=\frac{-s+1}{s+1}$, a unit step input is applied at time $t=0$. The value of the response of the system of $t=1.5$ sec(rounded off to three decimal places ) is .

Q. The Closed loop transfer function of a control system is given by $\frac{C\left(s\right)}{R\left(s\right)}=\frac{1}{s+1}$. For the input r(t) = sin t, the steady response c(t)______.

1. $\frac{1}{\sqrt{2}}cost$
2. $\frac{1}{\sqrt{2}}sin(t+\frac{\pi }{4})$
3. 1
4. $\frac{1}{\sqrt{2}}sin(t-\frac{\pi }{4})$

Q. A control system with certain excitatioin is governed by the following mathematical equation

$\frac{d^{2}x}{d{t}^2}+\frac{1}{2}\frac{dx}{dt}+\frac{1}{18}x=10+5e^{-4t}+2e^{-5t}$

The natural time constants of the response of the system are

1. 2s and 5s
2. 3s and 6s
3. 4s and 5s
4. 1/3s and 1/6s

Q. The response $h\left(t\right)$ of a linear time invariant system to an impulse $\delta \left(t\right)$, under initially relaxed condition is $h\left(t\right)=e^{-t}+e^{-2t}$. The response of this system for a unit step input u(t) is

1. $u\left(t\right)+e^{-t}+e^{-2t}$
2. ($e^{-t}+e^{-2t}\left)u\right(t)$
3. $(1.5-e^{-t}-0.5e^{-2t})u\left(t\right)$
4. $e^{-1}\delta \left(t\right)+e^{-2t}u\left(t\right)$

Q. Let a causal LTI system be characterized by the following differential equation, with initial rest condition.
$\frac{d^{2}y}{d{t}^2}+7\frac{dy}{dt}+10y\left(t\right)=4x\left(t\right)+5\frac{dx\left(t\right)}{dt}$

Where, x(t) and y(t) are the input and output respectively. The impulse response of the system is [u(t) is the unit step function]

1. $2e^{-2t}u\left(t\right)-7e^{-5t}u\left(t\right)$
2. $-2e^{-2t}u\left(t\right)+7e^{-5t}u\left(t\right)$
3. $7e^{-2t}u\left(t\right)-2e^{-5t}u\left(t\right)$
4. $-7e^{-2t}u\left(t\right)+2e^{-5t}u\left(t\right)$

Q. For the transfer function $G\left(j\omega \right)=5+j\omega$, the corresponding Nyquist plot for positive frequency has the form

1. 
2. 
3. 
4. 

Q. The number and direction of encirclements around the point $-1+j0$ in the complex plane by the Nyquist plot of
$G\left(s\right)=\frac{1-s}{4+2s}is$

1. zero
2. one, anti-clockwise
3. one, clockwise
4. two, clockwise

Q. Which of the following is the transfer function of a system having the Nyquist plot shown in figure below?

1. $\frac{K}{s(s+2{)}^2(s+5)}$
2. $\frac{K}{s^2(s+2)(s+5)}$
3. $\frac{K(s+1)}{s^2(s+2)(s+5)}$
4. $\frac{K(s+1)(s+3)}{s^2(s+2)(s+5)}$

Q.

The number of times the Nyquist plot of
$G\left(s\right)=\frac{s-1}{s+1}$
will encircle the origin clockwise is

1. 1

Q. The Nyquist plot for the open-loop transfer function $G\left(s\right)$ of a unity negative feedback system is shown in the figure, if $G\left(s\right)$ has no pole in the right-half of s-plane, the number of roots of the system characteristic equation in the right-half of s-plane is

1. $0$
2. $1$
3. $2$
4. $3$