Multivariate control system design using the theory of matrix polynomials

Abstract

The development of our mathematical work is based on state-space representations and matrix fraction descriptions as the mathematical models for physical systems. In this thesis, a design process is proposed to achieve block-structure assignment with a state-feedback and dynamic compensator for linear time invariant multiple inputs multiple outputs (MIMO) systems. A review of matrix polynomial theory is provided and a method to factorizing matrix polynomials into a complete set of linear factors has been developed. Furthermore, a study on feedback control has been undertaken; this includes a study on different feedback configuration and the development of the associated compensator equations. The input-output feedback configuration has been chosen to design the compensator which allows the placement of block roots of a desired denominator constructed from a desired latent structure. Moreover, a decoupling of the interactions between control loops in a multivariable plant has been developed; this proposed method is based on the ë-matrix (i.e. matrix polynomials) assignment. Finally, a novel MIMO intelligent predictive control design based on the matrix Diophantine equation resolution is presented, this later one is focalized on the adaptation mechanism made by merging the Adaptive Neuro-Fuzzy Inference System (ANFIS) and Maximum Likelihood identification method to the MIMO predictive scheme for controlling an uncertain stochastic two-wheeled self-balancing robot without requiring prior knowledge of the exact parameters