multivariable control systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2....
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![Page 1: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/1.jpg)
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.
![Page 2: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/2.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
2
Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Introduction
Topics to be covered include:
Introduction
![Page 3: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/3.jpg)
Dr. Ali Karimpour Feb 2016
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.
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Dr. Ali Karimpour Feb 2016
Lecture 1
4
Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
![Page 5: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/5.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
5
Interaction
Interaction
![Page 6: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/6.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
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.
![Page 7: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/7.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
7
Interaction
One way or single direction interaction (Neutralized process)
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Dr. Ali Karimpour Feb 2016
Lecture 1
8
Interaction
One way or single direction interaction (Stirred tank hitter)
y1 is the level of tank.
y2 is the temperature of tank.
![Page 9: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/9.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
9
Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
![Page 10: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/10.jpg)
Dr. Ali Karimpour Feb 2016
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:
![Page 11: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/11.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
11
Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
![Page 12: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/12.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
12
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
![Page 13: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/13.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
13
Control system design strategy
Diagonal
or
decentralized
Block diagonal
Fully centralized
A multi machine power system
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![Page 14: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/14.jpg)
Dr. Ali Karimpour Feb 2016
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
Analysis and design in multivariable systems
![Page 15: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/15.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
15
Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
![Page 16: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/16.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
16
Some example of multivariable system
Motor generator sets
Aero-engine
A multi machine power system
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Dr. Ali Karimpour Feb 2016
Lecture 1
17
Some example of multivariable system
A 3 inputs / 3 outputs chemical process
![Page 18: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/18.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
18
Quadruple tank process
n.interactio No 121
?n!interactio No 021
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Dr. Ali Karimpour Feb 2016
Lecture 1
19
Some example of multivariable system
Example 1-1: Consider following two input two output system.
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Try a PI controller for g11
Try a PI controller for g22
![Page 20: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/20.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
20
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).
![Page 21: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/21.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
21
Introduction
Interaction
Stability
Analysis and design in multivariable systems
Some example of multivariable system
Evaluation and References
Topics to be covered include:
![Page 22: Multivariable Control Systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/mul_con/... · 2016. 2. 3. · Dr. Ali Karimpour Feb 2016 Lecture 1 3 Introduction What is multivariable](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fc114fdba91c411ce57aa43/html5/thumbnails/22.jpg)
Dr. Ali Karimpour Feb 2016
Lecture 1
22
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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Dr. Ali Karimpour Feb 2016
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