Question 2

a. The block diagram of a plant is shown in figure 1.

X(s)

G₁(s)

G₂(s)

1

(s² + 3s +36)

H₁(s)

G₂(s)

H₂(s)

Figure 1

1

G₂(S) = ($+2)

G,(s)

G5(S) = (+5)

(s +6)

G.(s)

The sub systems have the following transfer functions;

G₁(S) = (s+8)

G4(S):

i. Use the appropriate Matlab commands to simplify the

block diagram and to find the overall transfer function of

the plant.

[16 marks]

[25 marks]

H₁=20

Y(s)

G3 (S) = (5+3)

ii. What are the order and type of the overall system?

H₂=1

[2 marks]

iii. Find the poles and zeros of the system, sketch the pole-

zero map and discuss which poles dominate the systems'

response.

[7 marks]