Feedback linearization of mimo systems described by a nonlinear state space equation

Abstract

The idea of feedback linearization is to cancel the nonlinearities and imposing the desired linear dynamics via change of coordinates and feedback so that the linear control techniques can be applied. In this thesis feedback linearization is applied to a class of multivariable nonlinear systems; where the number of inputs divides exactly the number of state. The proposed method consists in converting a nonlinear multivariable system into block controller companion form that is suitable for block pole assignment which amounts to eigenstructure assignment. Necessary and sufficient conditions for input-state linearization have been developed. Comparison study has been achieved between the proposed approach and the feedback linearization for general form of multivariable nonlinear system. To verify the validity and effectiveness of the suggested method, a two-link robot manipulator has been implemented. When a nonlinear system presents a non-involutive property, the approximate feedback linearization is required. The idea of the proposed method consists in representing the original nonlinear system into a state-dependent coefficient form then applying block similarity transformations that allow getting the linearized system in block companion form. Examples have been used to illustrate the application and show the effectiveness of the given approach