Advanced Control Systems
23/02/2022
Assignment 01
Question 01
Derive state space model for the given system where 𝑓𝑎 (𝑡) is the input and 𝑧 is the output
Question 02
Determine the poles and zeros of the following system.
0
1
0
𝑥̇ = [
]𝑥 + [ ]𝑢
−20 −9
1
𝑦 = [−17 −5]𝑥 + 𝑢
Question 03
Obtain the state space representation of the given transfer function.
𝐶(𝑠)
10.4 𝑠 2 + 47𝑠 + 160
= 3
𝑅(𝑠) 𝑠 + 14𝑠 2 + 56𝑠 + 160
Question 04
For the state equation and initial state vector given below find the state transition matrix and solve for
𝑥(𝑡). 𝑢(𝑡) is the unit step input.
0
1
0
𝑥̇ = [
] 𝑥 + [ ] 𝑢(𝑡)
−8 −6
1
1
𝑥(0) = [ ]
0
Question 05
Given the following state space representation of the system, find 𝑌(𝑠).
𝑥̇ = [
1
3
1
] 𝑥 + [ ] sin 5𝑡
−3 −1
1
𝑦 = [1
2]𝑥 + 𝑢,
3
𝑥(0) = [ ]
0