I Preamble

Noise Disturbance in Control Systems

Control engineering, as one of the cornerstones of automation, has contributed enormously to the

development of modern industrial society; and a control system is useful for regulating the behaviour

of industrial systems. In this assignment, you are required to analyze the following control

system in Figure 1 where X(s) is the signal input, N(s) the noise input and Y(s) the system

output.

G₁(s) = K

G₂ (s) =

G3(s)

=

G₁(s) =

H₂(s) =

1

s+2

X(s)

Figure 1

The gain values for the respective forward and feedback paths are given:

2

s+4

4

S

H₁(s) = 1

10

s + 10

H3(s) = 2

G₁

G₂

H₂

H₂

N(s)

G3

H3

G4

Y(s)

Task 1: Analytically determine the signal and noise transfer function of the control system in

Figure 1. If x(t) is a unit step input then how do the signal and noise vary at the

output for any change in the value of K as t → ∞o.

Task 2: Using Matlab determine the signal and noise transfer function of the control system

in Figure 1 assuming K = 1. Indicate clearly the Matlab code applicable to

appropriate block reduction. Plot the step response using Matlab to verify the final

steady-state value obtained in Task 1 y(t) as t→∞o for signal and noise.