An actuator in a manufacturing plant is represented schematically by Figure Q1: Control system analysis and design Assignment, UCD, Ireland

Question 1

An actuator in a manufacturing plant is represented schematically by Figure Q1

The actuator has a single input {the force f(t) acting on M2) and one output (position x;}. Four state variables are selected in order to model the system in state space:

X41 = X1 (position of My); x2 = Xz (position of M2); x3 = x1 (velocity of M1); x4 = 22 (velocity of M2}

Applying Newton’s Second Law {F=ma) to block M, gives:

Myf, = —d2, — Kyx1 + K2(x2 — X1)

Applying Newton’s Second Law {F=ma) to block M: gives:
M2¥2= —K2(x2 — x1) + F(t)

{a} Derive the state-space model of the system.

(b} tf Mi, = 10; M2 = 5; K; = 10; Ky = 5; d = 1, obtain the numerical state-space representation of the system.

{c) Give THREE advantages of a state-space approach relative to a Transfer Function approach to control design.