Observer-based Stability Analysis And Controller Design Of Fractional Linear System

In practical research and calculation,the method is usually approximated by an integer order system.Of course,this is feasible for systems that require less information and less precision.But with the continuous development of science and technology,physical,chemical and other industries,the increasing demand,it was found that the use of fractional calculus to describe the actual system than the integer order classical method is more accurate and closer to the reality.The stable system is the premise of the normal operation of the physical object,and is the primary factor to be considered when designing the control system in the actual production process,and plays an extremely important role in the control theory.Therefore,the stability analysis of fractional order linear systems is very important in the study of dynamic behavior.As everyone knows,the state feedback control is an important means of comprehensive system,compared with other control methods have obvious advantages,in order to solve the physical realization of state feedback and not superior control performance cannot substitute,usually into the system of state observer state feedback control in the control system.Therefore,for the increasingly complex control systems,the observer based stability analysis and controller design of fractional linear systems have further enriched the study of control theory and control methods.The problems of stability analysis and controller design of observer based on fractional order linear systems,the main contents include the finite time fractional order linear observer system stability,based on the reduced order observer of fractional order linear systems with state feedback control and interference suppression disturbance observer system based on fractional time delay.The main research work is as follows:(1)Observer based finite time stability control for fractional order linear systems.For a class of fractional order linear systems,an observer is designed by reconstructing the state variables to analyze the finite time stability of the system in the case of no disturbance,and the finite time boundedness under disturbance,and by the observer to estimate the system state and disturbance.(2)State feedback control of fractional order linear systems based on reduced order observer.For the fractional order linear systems with order 0(27)?(27)1 and 1 ??(27)2respectively,a stabilizing control method based on reduced order observer is proposed.Part of the system state variables can be obtained directly from the output of the originalsystem,and the other part of state variables through the reconstruction of state variable design approach of reduced order observer is obtained,and by means of matrix singular value decomposition method and the linear matrix inequality(LMI)to get the system stability conditions and controller parameter solution technology.(3)Observer based disturbance rejection for fractional linear time-delay systems.A state feedback control method based on disturbance observer(DOB)is proposed for a class of fractional linear time-delay systems with external disturbances.By constructing disturbance observer,the output of the disturbance observer is introduced into the state feedback controller to counteract the influence of external disturbances on the system,so as to achieve the purpose of interference suppression.And the method of solving the system stability condition and the parameter of the controller is obtained by means of fractional model equivalent frequency domain transform method,Lyapunov method and matrix singular value decomposition technique.