Time Response Analysis Practice Questions

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has theses properties ?

Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems ?

Group I lists a set of four transfer functions. Group II gives a list of possible step response y(t). Match the step responses with the corresponding transfer functions.

A linear, time - invariant, causal continuous time system has a rational transfer function with simple poles at s =- 2 and s =- 4 and one simple zero at s =- 1 . A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

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

The unit step response of a system starting from rest is given by $c(t)=1-e^{-2t} \; for \; t\geq 0$ The transfer function of the system is

The unit impulse response of a system is $h(t) = e^{-t},t\geq 0$ . For this system the steady-state value of the output for unit step input is equal to

In the derivation of expression for peak percent overshoot, $M_{P}=exp(\frac{-\pi \xi }{\sqrt{1-\xi ^{2}}}) \times 100$ % Which one of the following conditions is NOT required ?

A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively

Despite the presence of negative feedback, control systems still have problems of instability because the

A causal system having the transfer function H(s)=1/(s+2) is excited with 10u(t). The time at which the output reaches 99% of its steady state value is

A system described by the following differential equation $\frac{d^{2}y}{dt^{2}}+3\frac{dy}{dt}+2y=x(t)$ is initially at rest. For input x(t)=2u(t), the output y(t) is

A second-order system has the transfer function $\frac{C(s)}{R(s)}=\frac{4}{s^{2}+4s+4}$ . With r(t) as the unit-step function, the response c(t) of the system is represented by

Consider a system with the transfer function $G(s)=\frac{s+6}{ks^{2}+s+6}$ . Its damping ratio will be 0.5 when the value of k is

The transfer function of a system is $G(s)=\frac{100}{(s+1)(s+100)}$ . For a unit step input to the system the approximate settling time for 2% criterion is

If the characteristic equation of a closed-loop system is $s^{2}+2s+2=0$ , then the system is

The open-loop DC gain of a unity negative feedback system with closed-loop transfer function $\frac{s+4}{s^{2}+7s+13}$ is