State Space Analysis and Controller Design EEE3001 – EEE8013 State Space Analysis and Controller Design This lecture will be recorded and you will be able to download it Dr Damian Giaouris http://www.staff.ncl.ac.uk/damian.giaouris/ EEE8044

Goals/Aims of Chapter 3 Basic form of a solution: Distinct eigenvalues Repeated eigenvalues Complex eigenvalues Eigenvalues/Eigenvectors Particular soln given ICs Response in the state space Fundamental Solution Matrix

SOLUTION OF SS MODELS EEE8044

Eigenvalues & Solutions a2=1 => a1=2 a1=2 => a2=-2 EEE8044

Example C1 = 0.4 >> C=inv([2 1;1 -2])*[1;0]; C2 = 0.2 >> C1=C(1), C2=C(2) EEE8044

Example EEE8044

General Procedure EEE8044

3 cases Distinct eigenvalues Repeated eigenvalues Complex eigenvalues EEE8044

Repeated Eigenvalues Proceed as before EEE8044

Example EEE8044

Example EEE8044

Solution Matrices Fundamental Solution Matrix (FSM) State Transition Matrix (STM) EEE8044

State Transition Matrix EEE8044

Exponential matrix Exercise: Starting from the FSM prove that EEE8044

Exponential matrix EEE8044