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# Multivariable Control Systems ECSE 6460 - PowerPoint PPT Presentation

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 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:

• 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

• 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

• 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?