A Gramian-Based Controller for Linear Periodic Systems

Authors: 

Pierre Montagnier
Raymond J. Spiteri

Author Addresses: 

Pierre Montagnier (pierrem@cim.mcgill.ca)
Centre for Intelligent Machines,
McGill University,
Montreal, Quebec,
H3A 2K6 Canada.

Raymond J. Spiteri (spiteri@cs.dal.ca)
Faculty of Computer Science
Dalhousie University
6050 University Ave.
PO Box 15000
Halifax, Nova Scotia, Canada
B3H 4R2

Abstract: 

Many important real-world processes are best modelled by linear time-periodic systems. This paper proposes a new design method for the control of these systems. The method is based on the use of the controllability Gramian and a specific form for the feedback gain matrix to build a novel control law for the closed-loop system. The new controller can be full-state or observer-based and allows the control engineer to assign all the invariants of the system; i.e., the full monodromy matrix. Calculation of the feedback matrix requires first solving a matrix integral equation for the periodic Floquet factor of the new state-transition matrix of the closed-loop system. The effectiveness of the method is illustrated on a simple example.

Tech Report Number: 
CS-2002-05
Report Date: 
June 5, 2002
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