Optimal and robust control for linear state-delay systems |
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Authors: | Michael Basin Jesus Rodriguez-Gonzalez |
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Institution: | a Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Leon, Apdo postal 144-F, C.P. 66450, San Nicolas de los Garza, Nuevo Leon, Mexico b Department of Engineering, National Autonomous University of Mexico, Edificio “Bernardo Quintana”, Circulo Exterior, Cd. Universitaria, C.P. 04510, Mexico, D.F., Mexico |
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Abstract: | This paper presents the optimal regulator for a linear system with state delay and a quadratic criterion. The optimal regulator equations are obtained using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example. |
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Keywords: | Optimal control Robust control Integral sliding mode Linear time-delay system |
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