OPTIMAL OUTPUT-FEEDBACK CONTROL OF ASYMMETRIC SYSTEMS USING COMPLEX-MODES

A Linear Quadratic Regulator (LQR)-based least-squares output feedback control procedure using a complex mode procedure is developed for the optimal vibration control of high-order asymmetric discrete system. A n LQ Regulator is designed for a reduced-order model obtained by negle cting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex mode coordina tes are derived. The complex mode approach appears to provide more acc urate reduced-order models than the normal mode approach for asymmetri c discrete systems. The proposed least-squares output feedback control procedure takes advantage of the fact that a full-state feedback cont rol is possible without using an observer. In addition, the lateral vi bration of a high-order rotor system can be effectively controlled by monitoring one single location along the rotor shaft, i.e., the number of measured states can be much less than the number of eigenvectors r etained in producing the reduced-order model while acceptable performa nce of the controller is maintained. The procedure is illustrated by m eans of a 52 degree-of-freedom finite element based rotordynamic syste m. Simulation results show that LQ regulators based on a reduced-order model with 12 retained eigenvalues can be accurately approximated by using feedback of four measured states from one location along the rot or shaft. The controlled and uncontrolled transient responses, using v arious numbers of measured states, of the original high-order system a re shown. Comparisons of reduced-order model results using normal mode s and complex modes are presented. The spillover problem is discussed for both collocated and noncollocated cases based on this same example .