Synthesis of control for family of pseudolinear differential systems
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 77, Issue 1
Abstract
The work is devoted to development of methods of synthesis control for families of pseudolinear controlled systems. Construction of control in the form of static linear reverse connection foresees allocation of phase coordinates within the desired set, which is specified as invariant ellipsoid of a reference system. Ellipsoidal estimates solutions of systems of control and reference system are built using a matrix of comparison. Systems comparison methods in relevance with invariant sets are the development of the Lyapunov’s function method and have been successfully applied in the study of broad classes of solutions of differential and difference equations. This paper uses the connection between matrix comparison systems with the Lyapunov’s quadratic functions which provide invariant sets in phase space. Matrix differential equations of quasy monotony condition of the right-hand side with respect to the cone defined intrinsically symmetric matrices are being used as comparison matrix systems. Control is performed on the condition of equality of right matrix sides of the comparison for pseudolinear control and reference systems. Taking into account the proximity of estimations for such systems while synthesizing the regulator robustness can be obtained. There has been suggested an algorithm for synthesis control that is based on solving two optimization problems with constraints in the form of linear matrix inequalities. Synthesis control, being quite simple in the algorithm, is similar to the model control. The investigated method allows to specify an approach to solving problems of robust control, for example, for linear non-autonomous systems with uncertain parameters and external perturbations. The efficiency of the synthesis algorithm has been demonstrated on the example of the stabilization of double inverted pendulum. As a result of numerical calculations it has been shown that the method provides the desired arrangement of phase coordinates.
Authors and Affiliations
A. Aliluyko, Ivan Novosad
Keywords
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