Multivariable Control Systems - Personal Datakarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/multivariab… · What is multivariable control? MIMO systems are considered as

Dr. Ali Karimpour Jan 2017

Lecture 1

Multivariable Control

Systems

Ali Karimpour

Associate Professor

Ferdowsi University of Mashhad

Lecture 1

References are appeared in the last slide.


Lecture 1

2

Introduction

Interaction

Stability

Analysis and design in multivariable systems

Some examples of multivariable systems

Evaluation and References

Introduction

Topics to be covered include:

Introduction


Lecture 1

3

Introduction

What is multivariable control?

MIMO systems are considered as multivariable systems.

A General multivariable plant

Why they are different from SISO?

Since of interaction and design procedure.


Lecture 1

4

Introduction

Interaction

Stability






Lecture 1

5

Interaction

Interaction


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6

Interaction

Interaction on a system

Loop 1

Loop 2

Direct effect: The first controller will get the first output ….

Indirect effect: The first controller will disturb the second output and ….

This is Interaction.


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7

Interaction

One way or single direction interaction (Neutralization process)


Lecture 1

8

Interaction

One way or single direction interaction (Stirred tank heater)

y1 is the level of tank.

y2 is the temperature of tank.


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Introduction

Interaction

Stability






Lecture 1

10

Stability

For stability analysis (BIBO) in the case of no interaction (g12(s)=g21(s)=0) check:

For stability analysis (BIBO) with interaction check:


Lecture 1

11

Introduction

Interaction

Stability






Lecture 1

12


Analysis of Multivariable Systems

• Multivariable system representation

• Multivariable poles and zeros

• Controllability and observability

• State space realization

• Multivariable system stability

• Multivariable system robustness analysis

• Control structure design

• Control system design strategy

Diagonal or decentralized

Block diagonal

Fully centralized


Lecture 1

13

Control system design strategy

Diagonal

or

decentralized

Block diagonal

Fully centralized

A multi machine power system

3

3

2

2

1

1

3

3

2

2

1

1

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Ex

Gov

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Gov

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t

t

t

3

3

2

2

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1

3

3

2

2

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1

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f

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......


Lecture 1

14

Multivariable Design Methodologies

• State space methods

• Multivariable root loci approach

• Rosenbrock frequency response approach

• Pole placement methods

• Eigenstructure assignment

• Multivariable PID controllers

• The classical robust control methods

• QFT

• Soft computing approach



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15

Introduction

Interaction

Stability






Lecture 1

16


Motor generator sets

Aero-engine

A multi machine power system


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17


A 3 inputs / 3 outputs chemical process


Lecture 1

18

Quadruple tank process

n.interactio No 121

?n!interactio No 021


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Example 1-1: Consider following two input two output system.

1175

1

1175

1185

13.2

185

17.2

)(

ss

sssG

s

ss

s

sGc 1.08

0

02.05

)(

Try a PI controller for g11

Try a PI controller for g22


Lecture 1

20


Exercise 1-1: Derive Matlab code(m-file) for above figure and plot them.

Exercise 1-2: Derive an MIMO example by yourself and explain it and plot

the step response. (m-file is necessary).


Lecture 1

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Introduction

Interaction

Stability


Some example of multivariable system




Lecture 1

22


• Control Configuration Selection in Multivariable Plants, A. Khaki-Sedigh, B. Moaveni, Springer Verlag, 2009.

References

• Multivariable Feedback Control, S.Skogestad, I. Postlethwaite, Wiley,2005.

• Multivariable Feedback Design, J M Maciejowski, Wesley,1989.

• http://saba.kntu.ac.ir/eecd/khakisedigh/Courses/mv/

Web References

• http://karimpor.profcms.um.ac.ir

• تحلیل و طراحی سیستم های چند متغیره، دکتر علی خاکی صدیق

Evaluation

• Exercises and Projects. • Midterms. • Final.

• Paper(Arbitrary). Good Journals after 2010 with model and simulation


Lecture 1

23

Exercises

1-3 Derive a linear state space model for quadruple tank process.

1-1 Mentioned in the lecture.

1-2 Mentioned in the lecture.

1-4 Derive transfer function model for quadruple tank process

Documents

Multivariable Control Systems - Personal Datakarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/multivariab… · What is multivariable control? MIMO systems are considered as