Multivariable Control Systems Syllabus

 

Course Description

 

This course studies the state-of-the-art computer-aided design methodologies for multivariable linear time invariant feedback control systems. Topics include:

 

  • Mathematical Language for Describing Design Objectives
  • Performance Limitation in MIMO Systems
  • Realization for MIMO Systems
  • How to Predict Qualities of Optimal Controller
  • Major Optimization Engines of Multivariable Design:
    • H2 and Linear-Quadratic
    • H-infinity
    • Decoupling
    • Loop Shaping Methodologies (Nyquist Like Techniques)
    • QFT

 

Prerequisites

 

  • Basic understanding of linear algebra.
  • Classical analysis and synthesis techniques (root locus, Bode).
  • Course assumes a working knowledge of MATLAB®.

 

It is a good idea to get hold of a copy of the MATLAB® manual for the Mu-Analysis and Synthesis Toolbox: this is a well-written "cookbook" style reference for those primarily interested in applications of H2 and H-Infinity optimization.

 

Lectures(January 2017):

  1. An Overview (Introduction, Interaction, Stability, Analysis and Design in Multivariable Systems, Some Example of Multivariable Systems)
  2. Linear Algebra (Vector Space, Norms, Unitary, Primitive, Hermition and Positive(Negative) Definite Matrices, Singular Value Decomposition, Relative Gain Array, Matrix Perturbation)
  3. Introduction in Multivariable Control Systems (Multivariable Connections, Multivariable Representation)
  4. Poles and Zeros in Multivariable Systems (Multivariable Poles and Zeros, Direction of Poles and Zeros, Smith-McMillan Form, Matrix Fraction Description, Transmission Zero Assignment)
  5. Performance Specification in Mulivariable Systems and Their Limitations ( A Brief Review of Linear Control System, Scaling and Performance, Shaping Closed-loop Transfer Function, Fundamental Limmitation on Performance)
  6. Stability of Multivariable Feedback Control Systems (Well-Posedness of Feedback Loop, Internal Stability, The Nyquist Stability Criterion, Coprime Factorization over Stable Transfer Functions, Stabilizing Controllers, Strong and Simultaneous Stabilization)
  7. Controllability and Observability and Realization in Mulivariable Systems (Controllability and Observability, Output Controllability, Realization, Model Order Reduction)
  8. Multivariable Control System Design ( Sequential Loop Closing, Characteristic-Locus Method, PI Controller for MIMO Systems)
  9. Multivariable Control System Design ( Decoupling, Diagonal Controller, Nyquist-Array Method)
  10. Uncertainty in Multivariable Systems and Quantitative Feedback Theory (Types of Uncertainty in Multivariable Systems, Robust Stability of Uncertain Systems, Quantitative Feedback Theory)

 

 

Lectures(2016):

  1. An Overview
  2. Linear Algebra
  3. Introduction in Multivariable Control Systems
  4. Poles and Zeros in Multivariable Systems
  5. Performance Specification in SISO Systems
  6. Performance Specification in Mulivariable Systems and Their Limitations
  7. Stability of Multivariable Feedback Control Systems
  8. Controllability and Observability and Realization in Mulivariable Systems
  9. Multivariable Control System Design( Sequential loop closing, Characteristic-locus method and PI controller)
  10. Multivariable Control System Design( Decoupling, Diagonal controller and Nyquist-array method)
  11. Uncertainty in Multivariable Systems and Quantitative Feedback Theory

Lectures(2015):

  1. An Overview
  2. Linear Algebra
  3. Introduction in Multivariable Control Systems
  4. Poles and Zeros in Multivariable Systems
  5. Performance Specification in SISO Systems
  6. Performance Specification in Mulivariable Systems and Their Limitations
  7. Stability of Multivariable Feedback Control Systems
  8. Controllability and Observability and Realization in Mulivariable Systems
  9. Decoupling Control
  10. Uncertainty in Multivariable Systems
  11. Multivariable Control System Design

 

Lectures:

  1. An Overview
  2. Linear Algebra
  3. Introduction in Multivariable Control Systems
  4. Poles and Zeros in Multivariable Systems
  5. Performance Specification in SISO Systems
  6. Performance Specification in Mulivariable Systems and Their Limitations
  7. Stability of Multivariable Feedback Control Systems
  8. Controllability and Observability and Realization in Mulivariable Systems
  9. Decoupling Control
  10. Uncertainty in Multivariable Systems
  11. Multivariable Control System Design

 

Assessment



  • Projects
  • Homework
  • Midterm 
  • Final  


 



Homework Policy


 

The homework’s are not intended as tests, but as vehicles for learning, complemented by the homework solutions that we hand out, and by any discussions that you have about the problems. Moderate collaboration on homework with your classmates is permitted. Discussions with the TAs and instructor are encouraged. There is no harm in seeking minor assistance from others who are knowledgeable but not involved in the class, although we would much prefer that your discussions be with those in the class.

We expect each of you to put in enough time alone to understand the specific difficulties and issues raised by each homework problem. We also expect that you will independently write up the actual solutions that you turn in, and not give us direct copies of a classmate's solutions!



 References:


 

Multivariable Feedback design by Maciejowski J.M., published by Adison-Wesley and

Multivariable Feedback Control by Sigurd Skogestad and Ian Postletwaite, published by Wiely.

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

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