MIMO systems compensator dseign

Abstract

In this thesis a design process is proposed to achieve eigenstructure assignment using block poles placement with a dynamic compensator for linear invariant MIMO systems. Systems described in state space equations are transformed to systems in matrix fractions description and for such systems, eigenvalues are called latent values and eigenvectors are called latent vectors. The method proposed here allows the assignment of the whole set (and even more) of latent values and vectors obtained from a desired eigenstructure. A review of matrix polynomial theory has been achieved and a method to construct block roots of a matrix polynomial from latent values and vectors has been developed. Then the state space description and the matrix fraction description have been presented. The relationship between eigenstructure and latent structure has also been established. Additionally, a consequent result, consisting on a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials, has been obtained. 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 poles of a desired denominator constructed from a desired latent structure. Finally, to illustrate the proposed approach, a compensator for a helicopter flight control system has been designed