last modified 31/03/2004

Coursecode: wb2421
Coursename: Multivariable Control Systems

ECTS creditpoints: 6
Faculty of Mechanical Engineering and Marine Technology
Lecturer(s): Weiden, dr.ir. A.J.J. van der Tel.: 015-27 85609
Catalog data:
Review of single loop feedback design using frequency domain methods. Poles, zeros and stability of multivariable feedback systems. Decoupling by state-feedback for linear as well as nonlinear systems. The robust servomechanism problem for multivariable systems:
asymptotic tracking of reference signals in the presence of disturbances. Nyquist-like multivariable design techniques: the characteristic-locus method and Nyquist-array methods. Performance and robustness of multivariable systems. The use of singular values for assessing performance; generalization of the classical control theory. Representations of model uncertainties. The use of the H-infinity norm and the structured singular value to analyse robust stability and robust performance. The choice of suitable weighting functions to specify performance for obtaining an H-infinity controller.		 Course year: MSc 1st year
Semester: 1B
Hours p/w: 4
Other hours: -
Assessment: See remarks
Assessm.period(s):
(see academic calendar)
Prerequisites: wb2207
Follow up: wb2411
Detailed description of topics:
The lectures are divided into blocks. At first a review of elementary single-loop feedback design is given. A standard design problem is given and especially the limitations on performance are treated. In the second block of lectures a system theoretical approach is used to explain the properties and the computation of the poles and zeros of multivariable feedback systems. Furthermore internal stability and the generalized Nyquist stability is discussed. The third block treats performance and robustness of multivariable feedback systems. The use of principal gains (singular values) for assessing performance is introduced. Different representations of uncertainties are given. The use of the H-infinty norm and the structured singular value to analyse the robust stability and robust performance will be introduced. Examples are given of how to choose weighting functions to gain specified performance in the H-infinty control design context. Finally a block is spent on multivariable control design for real practical systems using Nyquist like techniques. In MATLAB implemented algorithms are explained and applied to different design examples.
Course material:
  • Multivariable Feedback Control Analysis and Design. S.Skogestad, I.Postlethwaite. John Wiley & Sons, ISBN 0-471-94330-4
  • Lecture notes: The poles and zeros of multivariable systems, A.J.J. van der Weiden.
References from literature:
Many references are available in the Central Library.
Remarks (specific information about assesment, entry requirements, etc.):
  • Assessment: Oral examination and excercises based on MATLAB.
  • Each year a new set-up of design examples is considered.
Goals:
The objective of the course is to gain a basic understanding of the problem formulation and solution for control design of (uncertain) multivariable systems. The mix of tutorial lectures and computer exercises on realistic examples provides a good learning environment.
Computer use:
MATLAB, the Control and mu-toolbox may be used for the exercises.
Laboratory project(s):
Design content:
Percentage of design: -