Design of regulators by Eigenstructure Assignment for linear multivariable systems

Abstract

In this dissertation, a problem of regulator design by eigenstructure assignment is first considered for linear time-invariant multivariable systems. The proposed technique of eigenstructure assignment generalizes the previous results of the closed-loop eigenstructure assignment via output feedback with no assumptions that eigenvalues of the closed-loop system are distinct or different from any eigenvalues of the open-loop system. Necessary and sufficient conditions for the closed-loop eigenstructure assignment by output feedback are presented. Some known results on entire eigenstructure assignment are deduced from this results. The design freedom, which remains after prespecified closed-loop eigenvalues for linear multi-input systems being assigned, is utilized to select optimal eigenvectors of the closed-loop system for better transient responses. It is shown that this proposed algorithm is considerably simpler and requires less computational time than that of the previous procedure. Using duality concept, this technique can be applied to determine unique observer gain matrix in the design of observers for multi-output systems. A problem of regulator design by the optimal constant feedback control is also considered for linear timeinvariant multivariable systems. Necessary conditions to be satisfied by an optimal output feedback controller using a time-weighted quadratic performance index are derived in the continuous-time and discrete-time domain, respectively. This design method of regulators using a time-weighted quadratic performance index provides an analytical design approach for better transient responses.