Answer Happy

Given the system in Fig. 1:

a) Answer TRUE or FALSE to the following statements

i. The system states are the inputs, differentiated with respect to time.

(1 mark)

ii. The general form of the LTI (Linear Time-Invariant) state equation is 𝒙̇ = 𝐀𝒙 + 𝐁𝑢.

(1 mark)

b) What is the difference between a state space model and a transfer function?

(2 marks)

c) How many state equations are needed to represent a fourth-order system?

(1 mark)

d) Consider the system shown in Fig. 1. Derive a mathematical model in state space

form.

(15 marks)
F₁ = 2x₁ N 0000 -x₁(t) 1 N-s/m 1 kg: Fig. 1: A Mechanical system 1 kg - x₂(1) -f(t)

F₁ = 2x₁ N 0000 -x₁(t) 1 N-s/m 1 kg: Fig. 1: A Mechanical system 1 kg - x₂(1) -f(t)