AKHIL MOHAMMED KK Asst.Prof. EEE,DCE Darbhanga

MODERN CONTROL THEORY (SEM-VIII:EEE)

DARBHANGA COLLEGE OF ENGINEERING,DARBHANGA

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Module 1 Lecture-2

State Space Systems

AKHIL MOHAMMED K K MODERN CONTROL THEORY

General Form of a linear time invariant state space model

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Obtaining state space equations from differential equations

AKHIL MOHAMMED K K MODERN CONTROL THEORY

consider an nth order linear plant model described by the differential equation

We can define a useful set of state variables as

Finally:

How does this look in matrix form?

Obtaining state space equations from differential equations

AKHIL MOHAMMED K K MODERN CONTROL THEORY

If we are measuring only one state, then we have

General Form of a linear time invariant state space model

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Example

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Simple RLC example

AKHIL MOHAMMED K K MODERN CONTROL THEORY

The final state space model will be as below

+ Vout

-

Example

AKHIL MOHAMMED K K MODERN CONTROL THEORY

The state space model will be

Example

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Example – coupled mass spring damper

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Example – coupled mass spring damper

AKHIL MOHAMMED K K MODERN CONTROL THEORY

Define new variables:

Example – coupled mass spring damper

AKHIL MOHAMMED K K MODERN CONTROL THEORY

The state space eqns in standard form are then:

States are position and velocity of each mass

Overview

• Summary: Lecture

Introduction Simple example (mass-spring-

• damper)

Definition of a state space system Three examples for state space modeling –

mechanical and electrical Relation between state space and transfer function

AKHIL MOHAMMED K K MODERN CONTROL THEORY