Control Theory And Its Applications Of Fractional Order Sliding Mode

Sliding mode control, which has strong robustness and anti-disturbance ability, has become an important branch of the modern control theory, and it is deeply applied in the aerospace field. With the rapid development of space technology and the gradual improvement of of space strategic position, in order to be able to better master the spacecraft on-orbit control technology, to realize the high-precision advanced robust attitude control for modern complex spacecraft is a quite hard mission with profound application prospect. Fractional order sliding mode control incorporates the advantages of fractional order differential and sliding mode control, which could achieve further better control performance of the system on the basis of traditional sliding mode control; Therefore, it has becomes an important research line of modern nonlinear control theory.This paper took the problem of complex spacecraft attitude control as the background. It deeply studied the sliding mode control theory by introducing the fractional differential operator, which possess the information memory and genetic characteristics, into the traditional sliding mode control. After that, it also did much work on the applications of the sliding mode control through using the fractional order hyperchaotic system, spacecraft attitude control system and ground experiment simulation platform of spacecraft as the control objects.(1) On the basis of traditional sliding mode control, the characteristics of applying fractional calculus operator in sliding mode control theory were studied from the aspects of fractional order mode reaching law and fractional order sliding mode control. With a simple mechanical system model as the control object, a traditional and a fractional order sliding mode control laws were designed, respectively, and then numerical simulations were performed to demonstrate the favorable control performance of the proposed fractional order sliding mode control.(2) On the basis of the existing achievements of output feedback sliding mode control for integer order system, an output feedback sliding mode control with engineering practical significance was studied for fractional order system. Firstly, an output feedback sliding mode control is researched for fractional order linear system by studying the structure decomposition theory and output feedback sliding mode control theory. Secondly, with a general fractional order hyperchaotic system as the control object, an output feedback sliding mode control was study by using MATLAB LMI toolbox. Finally, on the basis of the auxiliary system, a sliding mode control law and an adaptive sliding mode control with output feedback characteristics are designed for the synchronization of fractional order hyperchaotic systems.(3) Taking the problem of spacecraft attitude control for an example, different fractional order sliding mode control approaches were studied from three aspects. Several different sliding mode control methods with traditional sliding mode reaching law and fractional order sliding mode reaching law were researched. The fractional order sliding mode control has better anti-interference and strong robustness compared with traditional sliding mode control. Secondly, a fractional order sliding mode control was studied, and superior properties of fractional order sliding mode control were showed compared with the existing literature. Finally, a fractional sliding mode control law was designed for the problem of Micro-spacecraft attitude control by using linearization theory for nonlinear systems, which has better strong robustness.(4) On the basis of research achievement (3), comprehensively considering the influences of parametric uncertainty, flexible modal and external disturbances, several different fractional sliding mode control methods with better anti-interference and strong robustness were designed. Firstly, a fractional order sliding mode control law was studied on the premise of considering norm bounded of flexible modal and external disturbances as known conditions. The better control performance was given from stability region and convergence rate. Secondly, the integrated disturbance was approximated by the fuzzy adaptive theory and the universal approximation, and a fuzzy adaptive fractional order sliding mode control law was designed by reducing the assumed condition of norm bounded of flexible modal and external disturbances. Finally, on the basis of traditional spacecraft attitude control model, the equivalent spacecraft attitude control model with Lagrange form was deduced. And then a fractional order terminal sliding mode control law with finite time convergence characteristics was researched under certain allowable assumption conditions.(5) Regarding the network spacecraft ground experiment simulation platform of5-DOF air-bearing simulator as the research object, a control model of5-DOF air-bearing simulator was given by considering the effect of the deviation between the air-bearing sphere center and gravity center of attitude platform. A fractional PID control law and a fractional sliding mode control law were designed for translational platform and attitude platform, respectively. The operating performance and the coupling effects between translational and attitude were showed by considering the actual operating characteristics of the actuator. Finally, the implementation principles of some program of control systems for5-DOF air-bearing simulator were given.