Dr. Ali Karimpour Feb 2016
Lecture 1
Multivariable Control
Systems
Ali Karimpour
Associate Professor
Ferdowsi University of Mashhad
Lecture 1
References are appeared in the last slide.
Dr. Ali Karimpour Feb 2016
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Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Introduction
Topics to be covered include:
Introduction
Dr. Ali Karimpour Feb 2016
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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.
Dr. Ali Karimpour Feb 2016
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Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
Dr. Ali Karimpour Feb 2016
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Interaction
Interaction
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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.
Dr. Ali Karimpour Feb 2016
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Interaction
One way or single direction interaction (Neutralized process)
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Interaction
One way or single direction interaction (Stirred tank hitter)
y1 is the level of tank.
y2 is the temperature of tank.
Dr. Ali Karimpour Feb 2016
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Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
Dr. Ali Karimpour Feb 2016
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Stability
For stability analysis (BIBO) in the case of no interaction (g12(s)=g21(s)=0) check:
For stability analysis (BIBO) with interaction check:
Dr. Ali Karimpour Feb 2016
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Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
Dr. Ali Karimpour Feb 2016
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Analysis and design in multivariable systems
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
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Control system design strategy
Diagonal
or
decentralized
Block diagonal
Fully centralized
A multi machine power system
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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
Analysis and design in multivariable systems
Dr. Ali Karimpour Feb 2016
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Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
Dr. Ali Karimpour Feb 2016
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Some example of multivariable system
Motor generator sets
Aero-engine
A multi machine power system
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Some example of multivariable system
A 3 inputs / 3 outputs chemical process
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Quadruple tank process
n.interactio No 121
?n!interactio No 021
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Some example of multivariable system
Example 1-1: Consider following two input two output system.
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1
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)(
ss
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sGc 1.08
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Try a PI controller for g11
Try a PI controller for g22
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Some example of multivariable system
Exercise 1-1: Derive Matlab code for above figure(m-file).
Exercise 1-2: Derive an MIMO example by yourself and explain it.
(m-file is necessary).
Dr. Ali Karimpour Feb 2016
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Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
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Evaluation and References
• 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. • Midterms. • Final. • Project.
• Paper(Arbitrary). Good Journals after 2010 with model and simulation
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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