Lecture Control system design: State variable models - Nguyễn Công Phương

This chapter presents the following content: The state variables of a dynamic system, the state differential equation, signal – flow graph & block diagram models, alternative signal – flow graph & block diagram models, the transfer function from the state equation,...

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Nguyễn Công Phương

CONTROL SYSTEM DESIGN

State Variable Models

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I Introduction

II Mathematical Models of Systems

III State Variable Models

IV Feedback Control System Characteristics

V The Performance of Feedback Control Systems

VI The Stability of Linear Feedback Systems

VII The Root Locus Method

VIII.Frequency Response Methods

IX Stability in the Frequency Domain

X The Design of Feedback Control Systems

XI The Design of State Variable Feedback Systems

XII Robust Control Systems

XIII.Digital Control Systems

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1 The State Variables of a Dynamic System

2 The State Differential Equation

3 Signal – Flow Graph & Block Diagram Models

4 Alternative Signal – Flow Graph & Block

Diagram Models

5 The Transfer Function from the State Equation

6 The Time Response & the State Transition

Matrix

7 Analysis of State Variable Models Using Control

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The State Variables of a Dynamic

System (1)

• The state of a system is a set of variables

whose values, together with the input signals

& the equations describing the dynamics, will provide the future state & output of the system.

• The state variables describe the present

configuration of a system & can be used to

determine the future response, given the

excitation inputs & the equations describing

the dynamics.

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The State Variables of a Dynamic

System (2)

Mass

M k

Wall friction

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2 The State Differential Equation

Diagram Models

Matrix

Design Software

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The State Differential Equation

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( )1

00

C

u t C

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3 Signal – Flow Graph & Block Diagram

Models

Diagram Models

Matrix

Design Software

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Signal – Flow Graph

& Block Diagram Models (1)

 1

1

L

R L

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Sum of the forward-path factor

1 sum of the feedback loop factors1

k k N

q q

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3 4

x x

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q q

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y t b b b b

x x

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 10



9 3

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 10



9 3

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 10



9 3

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 10



9 3

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 10



9 3

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4 Alternative Signal – Flow Graph & Block

Diagram Models

Matrix

Design Software

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Alternative Signal – Flow Graph

Ex 1

1 5

5

s s



1 2

s 

6 3

Field current

Controller Motor & load

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Ex 1

1 5

5

s s



1 2

s 

6 3

Field current

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Ex 1

1 5

5

s s



1 2

s 

6 3

Field current

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The Transfer Function

from the State Equation (1)

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The Transfer Function from the State Equation (2)

00

1

00

C

C R

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The Transfer Function from the State Equation (3)

11

( )

R s

L C s

s

s L

1

00

C

C R

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Diagram Models

6 The Time Response & the State Transition

Matrix

Design Software

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The Time Response

& the State Transition Matrix (1)

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The Time Response

1

10

1

00

C

C R

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The Time Response

1

00

C

C R

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The Time Response

2 2

( )

t t

x1(t)

x 2

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Diagram Models

Matrix

7 Analysis of State Variable Models Using

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Analysis of State Variable Models Using Control Design Software

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