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OPTIMAL REJECTION WITH ZERO STEADY‐STATE ERROR OF SINUSOIDAL DISTURBANCES FOR TIME‐DELAY SYSTEMS
Author(s) -
Tang GongYou,
Zhang ShuMei
Publication year - 2006
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2006.tb00261.x
Subject(s) - control theory (sociology) , disturbance (geology) , compensation (psychology) , series (stratigraphy) , mathematics , sensitivity (control systems) , internal model , term (time) , steady state (chemistry) , optimal control , state vector , zero (linguistics) , computer science , control (management) , mathematical optimization , engineering , linguistics , philosophy , psychology , paleontology , chemistry , physics , classical mechanics , quantum mechanics , artificial intelligence , electronic engineering , psychoanalysis , biology
This paper studies the problem of optimal rejection with zero steady‐state error of sinusoidal disturbances for linear systems with time‐delay. Based on the internal model principle, a disturbance compensator is constructed to counterbalance the external sinusoidal disturbances, so that the original system can be transformed into an augmented system without disturbances. Then, with the introduction of a sensitivity parameter and expanding power series around it, the optimal disturbance rejection problem can be simplified to the problem of solving an infinite sum of a linear optimal control series without time‐delay or disturbance. The optimal control law for disturbance rejection with zero steady‐state error consists of accurate linear state feedback terms and a time‐delay compensating term, which is an infinite sum of an adjoint vector series. In the presented approach, iteration is required only for the time‐delay compensation series. By intercepting a finite sum of the compensation series, we obtain an approximate physically realizable optimal control law that avoids complex calculation. A numerical simulation shows that the algorithm is effective and easy to implement.