State Space Analysis

Week 15

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Professor Charlton S. InaoControl System Engineering,PE -3032

Defence Engineering College Bishoftu, Ethiopia

Instructional Objectives

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State Space Analysis Approach

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State Space Equation

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General State Space Representation

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State Space Model for Dynamic System

DuCxyBuAxx

Matrices: A is state matrix; B is input matrix; C is output matrix; and D is direct transmission matrix

Vectors: x is state vector; u is input vector; and y is output vector

Note: Only apply to system that is linear and time invariant 8

Terminology/Nomenclature

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State Space Block Diagram

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Sample Illustration: Mass Damper Spring/Translational Mechanical System(Review)

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Vector Matrix Form/State Space Model Standard Form

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Block Diagram

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Standard Vector Matrix Form

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Correlation Between Transfer Function and State Space

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Converting Transfer Function to State Space

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Practice problem

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Matlab Functions

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Using Matlab

Function: Use ss function creates state space models. For example:

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DCBAxxx

>>A = [0 1;-5 -2];>>B = [0;3];>>C = [0 1];>>D = [0];>>sys=ss(A,B,C,D)

a = x1 x2 x1 0 1 x2 -5 -2

Matlab Outputb = u1 x1 0 x2 3

c = x1 x2 y1 0 1

d = u1 y1 0

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