Department of Electrical and
Computer Engineering

EEC 641 / 741

Multivariable Control

There are many ways to design a control system. Optimal control is a method that has been around since the 1950s and has seen a lot of successful applications, especially in the aerospace field. Adaptive control is a way of designing a control system to adjust to changes in the system that is being controlled. Fuzzy and neural control allow a designer to control a nonlinear system without having a mathematical model of the system.

In many practical cases, the designer has a model of the system, but the system parameters are subject to uncertainty. In this case robust control can be used to design a control system with a guaranteed level of disturbance rejection and a guaranteed level of performance (as long as the system uncertainties remain the assumed bounds). This course investigates various aspects of robust control, which is also sometimes referred to as multivariable control or H-infinity control. It is called multivariable control because it is a frequency-domain approach, but unlike classical frequency-domain control techniques, it is amenable to multiple-input and multiple-output systems. It is called H-infinity control because it can be used to minimize something called the infinity norm of the transfer function of the closed-loop system. Robust control is relatively recent control technology which began in the 1980s.

A related topic that we discuss is robust state estimation. There are various ways to estimate the state of a system. For instance, a Luenberger observer estimates system states using an eigenvalue assignment method. A Kalman filter is the best state estimator in that it minimizes the variance of the estimation error. (This is discussed in the optimal control course.) But if the system parameters are subject to uncertainty then the problem of state estimation is especially challenging. In this case we can often use H-infinity state estimation to obtain good results. You can see some basic tutorials that I have written on the topics of Kalman filtering (pdf, 425 KB - postscript, 1.26 MB) and H-infinity filtering (pdf, 432 KB - postscript, 1.47 MB).

You can view the syllabus and the homework assignments for the course on-line. This course uses MATLAB a lot and it may use Maple once in awhile. In particular, we use MATLAB’s Control System Toolbox, Robust Control Toolbox, and Simulink. You can find more information about MATLAB and Maple at the links below.

Sample Matlab files:

· PendCtrl.m - Inverted pendulum simulation

· RocketSim.m - Hovering rocket simulation (m-file)

· Rocket.mdl - Linearized hovering rocket simulation (Simulink file)

· Hydro.mdl - Hydroelectric generation simulation

· Hydro1.mdl - Hydroelectric generation simulation, controller designed for disturbance rejection

· Ex2_17.m - Example 2.17 in Skogestad’s book

· Principal.m - Principal gains for a MIMO system

· PendRGA.m - Relative gain array computation for inverted pendulum system

· BurlCE52.m - Check for robust stability and robust performance for structured uncertainty

· muBurlCE52.m - mu synthesis example

· SpringDamper.m - Example of full information H-infinity control

Department of Electrical and Computer Engineering

Last Revised: November 21, 2006