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Multivariable Control Systems ECSE 6460

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Multivariable Control SystemsECSE 6460

Fall 2009

Lecture 1: 1 September 2009

- Instructor: Agung Julius (agung@ecse)
- 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:

- www.ecse.rpi.edu/~agung(Notes, HW sets)
- RPI LMS (grades)

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.

- 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 http://helpdesk.rpi.edu software
- Beware: Need to be connected to RPI network, use VPN client from outside. http://helpdesk.rpi.edu networking

What is this course about?

- Introduction
- Classical Feedback Control
- Loop Shaping
- MIMO Control
- Performance Limitations
- Disturbance and Robustness
- Controller Design
- Model Reduction

S

Time invariance:

Linearity:

With zero initial conditions. Why?

Two ways to describe the systems:

Time domain

Laplace transform

inverse transform

Frequency domain

M

?

M

- Feedforward: use an inverse model of the plant to compute the control input.
- Generally not a good idea! Why?

- Feedback: use output measurement to compute control input.
- How to design a good controller?
- What is a good controller?

Controller

Plant

- 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

Controller

Plant

disturbance

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

- How to best model the disturbance

M

- How to best model the disturbance

M

Square wheels!!!

- 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?

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

High order system

NOT a class project!!

Low order system

- 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?