Short course on Asymptotic Tracking and Disturbance Rejection
The course is intended to students having attended RT I and RT II or equivalent lectures. Students can receive credit for 1 SWS within the Systemtheorie in the Diplom-Studiengang Technische Kybernetik or for the Hauptfach in other study programmes.
The course will be given in English.
Contact for further information: Marcus Reble .
Time and PlaceThe course takes place from 03.05.2010 to 07.05.2010.
All courses take place at Pfaffenwaldring 9, seminar room 3.243 .
Course contentsThe topic of this short course is the design of a feedback control system in which a specified regulated variable exhibit a prescribed steady-state response, to every exogenous input in a given family. This may include the problem of having the output of a controlled plant asymptotically track any prescribed reference signal in a certain class of functions of time, as well as the problem of having this output asymptotically reject any undesired disturbance in a certain class of disturbances. The family of exogenous inputs, against which asymptotic tracking/rejection is sought, consists in the set of all solutions a fixed ordinary differential equation. This situation is sufficiently distant from the ideal, but unrealistic, case of perfect knowledge of the exogenous input, and from the realistic, but conservative, case of totally unknown exogenous input. There is an abundance of design problems in which parameter uncertainties, reference commands and/or exogenous disturbances can be modeled as functions of time that satisfy an ordinary differential equation. Classical special cases are set the point control and the active suppression of vibrations. The course will initially review how the problem can be handled, in general terms, for linear systems and then will proceed with the description of a systematic design procedure for nonlinear systems.
1. The problem of asymptotic tracking/rejection of exosystem-generated command/disturbances
2. The case of linear systems as a design paradigm
3. Steady-state behavior and steady state response of nonlinear systems
4. Necessary conditions for regulation in nonlinear systems
5. The basic control structure: internal model and stabilizer
6. The design of the internal model
7. A digression on the small gain theorem for nonlinear systems
8. A digression on the theory of nonlinear observers
9. The design of a regulator for minimum-phase systems
10. The design of a regulator for some classes of non-minimum-phase systems