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 time-invariant 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.
본 논문에서는 선형 다변수 시스템에 있어서 Eigenstructure Assignment에 의한 안정기 설계 문제가 제시되었다. 제시된 Eigenstructure Assignment 기법은 페루프 시스템의 고유치가 독자적으로 다르다거나 혹은 폐루프 시스템의 고유치와는 다르다는 종전의 가정을 사용하지 않은 보다 일반화된 것이다. 이 결과는 출력 궤환에 의한 Eigenstructure Assignment에 대한 필요 충분 조건으로 제시되며 기존의 결과들은 이 결과로 부터 유도될 수 있게 된다. 선형 다입력 시스템에 있어서 Eigenvalue Assignment 문제를 다루었으며 이때 고유치를 설정하고 남는 자유도는 보다 나은 페루프 시스템의 과도응답을 얻기 위하여 최적화된 고유벡터를 선택하는데 사용되었으며 상대 개념을 이용하여 선형 다출력 시스템에 있어서 관찰기 설계 문제를 다루었다.
