Observer Design And Disturbance Suppression For Singular Linear Systems With Unknown Disturbance

As a kind of special systems which exist widely in practice,the singular systems have some characteristics that are different from ordinary normal systems.These char-acteristics make many theoretical research for normal systems not fully apply to such systems.Therefore,the study of singular systems is necessary and important.The ex-istence of unknown disturbances is very common in reality,so it is important to study the singular systems with unknown perturbations.In this paper,we first propose a simple method to design an observer for a sin-gular linear system with unknown perturbation.Considering the general perturbation which can be described as a polynomial and the system which can be observed,we the introduce integrable items into the observer.The observer can keep self-adjusting and finally achieve good observation performance.Sinusoidal disturbances are common disturbances which often occur in many en-gineering fields.Therefore,we choose an sinusoidal external disturbance whose di-mension is known,but the frequency,amplitude and phase are unknown to study.And our aim is to design a control law to reject the disturbances and to stabilize the system.We first design a state feedback controller for the system,in which the control input matches the perturbation,to satisfy the performance of the closed-loop system.In the design process,we first design a linear controller for the disturbance-free systems.And then we introduce the internal model principle and the adaptive control to obtain the disturbance estimation.Finally,the combination of them is the complete controller.While the first part of the controller stabilize the system,the second part reject the unknown disturbances completely.In fact,the input controller and the perturbation don't match and the states of system are not available in most of systems.Therefore,more general systems are con-sidered and the output control is studied.We first transformed the system and design a reduced-order observer to estimate the unknown states of transformed system.Then,we obtain the output feedback controller combining the observer and the state feedback controller.Finally,the theoretical analysis prove the reliability of the controller and the simulations illustrate the excellent performance of the controller.