Answer True/False

The s-plane plot of the poles and zeros graphically portrays the character of the natural response of a system.

The roots of the characteristic equation are the zeros of the closed-loop system.

A linear system satisfies the properties of superposition and homogeneity.

Select one:

The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero.

The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero.

Consider the system in Figure 2.79 where

Gc(s) = 10, H(s) = l, and G(s) = (s + 50)/(s^2+60s_500)

If the input R(s) is a unit step input, Td(s) = 0, and N(s) = 0, the final value of the output

Y(s) is:

(use formula Yss=lim t->infinity y(t) = lim s->0 sY(s)

Consider the system in Figure 2.79 with Gc(s)=20, H(s) = 1, and G(s) = (s+4)/(s^2-12s-65). When all initial conditions are zero, the input R(s) is an impulse, the disturbance Td(s) = 0, and the noise N(s) = 0, the output y(t) is ...

Hint: First, you need to find the transfer function T(s) of the overall system

T(s) = GcG/(1+GcGH)

After substitution and simplification, you need to factorise and apply partial fraction.

Then, use Laplase Table to convert to time domain

Consider a differential equation

d^2y/dt^2 + 2 dy/dt + y(t) = u(t)

where initials conditions are zero and u(t) is a unit step. The poles of the systems are:

Select one:

Hint: First, you need to convert to Laplase Domain. Whenever you see dy/dt, replace with Y(s)

Then rearrange your equation

Factorise the denominator in order to find the roots.

Choose the right terminologies that describe the transfer function T(s) = A(s)/B(s).

The roots of the numerator A(s) are called ........

The roots of the denominator B(s) are called .......

The denominator of a transfer function is called ......