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Multivariable Control Systems ECSE 6460. Fall 2009 Lecture 1: 1 September 2009. Information. Instructor: Agung Julius ( [email protected] ) Office hours: JEC 6044 Mon,Wed 2 – 3pm Textbook : S. Skogestad & I. Postlethwaite , Multivariable Feedback Control 2 n d ed , Wiley.

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Multivariable control systems ecse 6460

Multivariable Control SystemsECSE 6460

Fall 2009

Lecture 1: 1 September 2009


  • Instructor: Agung Julius ([email protected])

  • Office hours: JEC 6044 Mon,Wed2 – 3pm

  • Textbook: S. Skogestad & I. Postlethwaite, Multivariable Feedback Control 2nded, Wiley.

  • Additional reading: J. Doyle, B. Francis, A. Tannenbaum, Feedback Control Theory, Macmillan. Downloadable from Bruce Francis’ website (google)

    Online contents:

  •, HW sets)

  • RPI LMS (grades)

Prerequisite s

The course is for graduate or advanced undergraduate students with working knowledge in differential calculus, linear algebra, complex numbers, and classical linear systems/control theory.

Attendance background?


  • Homeworks (5 sets) = 40%

  • 2 x Exams = 30% + 30%

  • Homework sets are due one week after handout. Late submissions will get point deduction (no later than 1 week).

  • Exams are take home tests. Will include control design type of task.

Other issues
Other issues

  • Exchanging ideas is allowed for solving the homework sets, but not copying.

  • No collaboration is allowed for exams!

  • You will need MATLAB. An installer with campus license is available from software

  • Beware: Need to be connected to RPI network, use VPN client from outside. networking

Course outline
Course outline

  • Introduction

  • Classical Feedback Control

  • Loop Shaping

  • MIMO Control

  • Performance Limitations

  • Disturbance and Robustness

  • Controller Design

  • Model Reduction

Linear time invariant systems
Linear Time Invariant Systems


Time invariance:


Linear differential systems
Linear Differential Systems

With zero initial conditions. Why?

Two ways to describe the systems:

Time domain

Laplace transform

inverse transform

Frequency domain

Feedforward vs feedback
Feedforward vs feedback

  • Feedforward: use an inverse model of the plant to compute the control input.

  • Generally not a good idea! Why?

Feedforward vs feedback1
Feedforward vs feedback

  • Feedback: use output measurement to compute control input.

  • How to design a good controller?

  • What is a good controller?



Performance limitation
Performance limitation

  • Performance criteria: stability, speed of response, overshoot, disturbance rejection, etc.

  • Can we always attain any desired performance using feedback control?

  • Short answer: NO. Why?

Disturbance and robustness
Disturbance and Robustness





Design a controller that works, despite the presence of disturbances.

Disturbance and robustness1
Disturbance and robustness

  • How to best model the disturbance


Disturbance and robustness2
Disturbance and robustness

  • How to best model the disturbance


Square wheels!!!

Robustness issue
Robustness issue

  • Suppose that we know how to design a good controller ifwe know the plant (and disturbance) model.

  • It is still a very big IF !

  • In practice, we don’t know the model precisely. There’s always uncertainty, modeling error, parameter variation, etc.

  • Challenge: design a good controller, even though we don’t know the plant model.

  • Is it possible? How?

Model reduction
Model reduction

  • Reduce the complexity of the mathematical model, by throwing out the inessentials.

High order system

Fictitious application
Fictitious application

NOT a class project!!

Low order system

Model reduction1
Model reduction

  • Reduce the complexity of the mathematical model, by throwing out the inessentials.

  • We need to know how much detail is lost.


  • Input and output variables are multidimensional, i.e. vectors instead of scalars.

  • Consequences:

    • Different algebraic rules

    • Quantities have directions, in addition to magnitudes.

    • Controller topology can be important. (which output influences which input?)

  • How do we generalize SISO results to MIMO?