WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 10, 2015
Application of Jordan Controlled Form for Nonlinear Optimal Control Systems Design
Authors: , ,
Abstract: The problem of optimal control system design for nonlinear control systems (plants) has been considered in many works. But the majority of the proposed design methods are focused on linear models which are received by the usual linearization. Therefore the real control systems are quasi optimal practically. Known methods of the optimal systems design on the basis of nonlinear models are very difficultly for practical use. Therefore new design methods of the nonlinear optimal control systems are claimed. This paper presents the application of a Jordan controlled form to analytical design of the optimal control system for nonlinear plants, equations of which are transformed to this form. For this reason the definition of Jordan controlled form and some features of the transformation to this form of the nonlinear systems equations are considered. The suggested method of the optimal control systems design includes two steps. At the first step a linearization control is designed on the base of the known stabilizing control and the nonlinear transformation of the plant state variables. In new variables the equations of the close system with the linearization control is linear. It gives possibility to apply the known method LQ to these linear equations on the second step. The resulting nonlinear control system is optimal in the sense of a minimum of nonlinear quadratic criteria. Coefficients values of the criteria can be chosen in accordance with the desired transients of the nonlinear optimal control system. The design problem has a solution if a plant is controllable. The optimal control is a feedback on the state variables of the plant. Efficiency of the stabilizing control and the suggested design method of nonlinear optimal control systems are shown on the examples of designing and simulation of nonlinear control systems.
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Keywords: Nonlinear plant, equation, Jordan controlled form, nonlinear transformation, linearization control, quadratic criteria, optimal control
Pages: 776-789
WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 10, 2015, Art. #82