EE Assignment 2 Solution

Description

Question 1: A robot-arm drive system for one joint can be represented by the di erential equation

dv(t)

_dt ^{= k}1^{v(t) k}2^{y(t) + k}3^i(t)

where v(t) = velocity, y(t) = position, and i(t) is the control-motor current (Hint: i(t) = u(t)). Put the equations in state variable form and set up the matrix form for k₁ = k₂ = 1.

Question 2: The state space representation of a dynamical system is given as

X⁰ (t) = AX(t) + BU(t)

Y (t) = CX(t) + DU(t)

Prove that:

h ^Z t i

Y (t) = C (t)X(0) + (t ):B:U( )d + DU(t)

0

where (t) = e^At is the fundamental or state transition matrix.

Following problems are from the text book:

Question 3: 2.1

Question 4: 2.3

Question 5: 2.6

Question 6: 2.14

Question 7: 2.15

Question 8: 2.20

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