The Observer Analysis And Design Research

With the rapid development of computer science, fractional theory has been widely used in fluid mechanics, signal analysis and power electronics and many other fields. Fractional-order calculus is the extension of integer order calculus in order,which has fractional-order. In terms of its memory and hereditary properties, the systems dynamic progress can be more accurately and more suitably described. On the one hand, the fractional-order controller provides more adjusted parameters, and the selection of the parameters setting is wider. Due to the properties of fractional-order calculus and the continuing breakthrough in theoretical research,applications of fractional-order control has been taken more and more attention.However, not all state variables of the systems are easily measured in practical applications. Thus, the design of observer for fractional-order differential systems has important significance and valuable applications, and it is also a problem need to be solved urgently in practical projects.In this paper, we investigate the design of fractional-order filter and fractional-order observer. The main contents include:(1) The design of fractional-order observer is presented for the fractional-order nonlinear system. By introducing a continuous frequency distribution equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of error dynamic system is presented, the stability condition is obtained in terms of LMI tools.(2) A fractional-order filter method is put forward. Discretization approximation processing is the key to the digital implementation of the fractional-order filter,Discretization approximation processing is the choice for generating and development for fractional-order function. Several common discretization method can be used for filter to design. Requirements of the filter designing and the filter’s order are obtained by analysing the performance of several discretization methods.(3) A mathematical model of motor speed control system is adapted. An anti-interference fractional-order observer is designed based on the fractional-order filter to illustrated the performance of the resistance to disturbance. And by comparing with the traditional PID controller shows the superiority of fractional-order disturbance observer.