Problem 1 (Points 3): Consider a closed-loop control system shown in Fig. 1 where:

Ge(s) = Kp + K¹, Ga(s) = 1, H(s) = 1, G(s) =

1

2s +9

Find the values of the parameters Kp and K, to satisfy the following technical requirements:

• The natural frequency is wn = 6rad

• The damping ratio of the closed-loop system should be 0.5.

Simulate this control system in MATLAB/Simulink.

Error

Reference Signal

Input

e

7+

Controller

Gc(s)

Sensor

Signal

Control

Input

U

Actuator

Ga(s)

Sensor

H(s)

Actuating

Signal

ua System

G(s)

Figure 1: Closed-loop control system.

Output

y