Fast Terminal Sliding Mode Control Of Discrete-time Nonlinear Systems

Due to the advantages of robustness, invariance and convenient implementation, the method of sliding mode control has been widely studied. Fast terminal sliding mode control provides faster transient response and meets the needs of rapidity in physical systems in the field of engineering. Hence, fast terminal sliding mode control is used to deal with the control problems in the real systems, for instance, the satellite attitude system, the mechanical arm system and the wind power generation system, etc..In the last few decades, with the theoretical development and widespread appli-cation of computer control, there has been a growing interest in discrete-time sliding mode control. Corresponding results have been obtained to further increase the tran-sient response and to prove the stability of the systems under discrete-time fast terminal sliding mode control. Although these results have extended the method of fast terminal sliding mode control to the discrete-time domain, there still exist many problems to be solved. For example, the existence of quasi-sliding mode, the system chattering, the boundedness and the estimation of the bounds for the discrete-time systems under fast terminal sliding mode control still remain to be explored.In view of these problems, this thesis will study and discuss the method of discrete-time fast terminal sliding mode control. First, the boundedness of the undisturbed discrete-time nonlinear system under fast terminal sliding mode control is analysed. And the corresponding bounds are derived. Second, the disturbance compensator based reaching law is proposed for the disturbed discrete-time nonlinear system to alleviate chattering. The boundedness of the system is established and the corresponding bounds are obtained. The specific work in this thesis is as follows:? For the undisturbed discrete-time nonlinear system, the boundedness of the sys-tem under fast terminal sliding mode control is established. First, it is demon-strated that the system trajectory will enter in the bounded neighbourhoods of fast terminal sliding mode surfaces (i.e. quasi-sliding mode bands). Widths of the quasi-sliding mode bands are obtained and the system trajectory is proven to remain in the quasi-sliding mode bands. Second, the relationship between the fast terminal sliding mode parameters and the bounds of the quasi-sliding mode bands is analysed, it is proven that the widths of the quasi-sliding mode band-s can be made arbitrarily small. Third, boundedness of the system steady-state is established and the bounds are given. Finally, the relationship between the fast terminal sliding mode parameters and the bounds of the system steady-state is analysed, it is proven that the bounds of the system steady-state can be made arbitrarily small.? For the disturbed discrete-time nonlinear system, the disturbance compensator based reaching law is proposed, and the boundedness of the system is proven. First, the disturbance compensator based reaching law is proposed, and the fast terminal sliding mode control law is derived based on the reaching law. Second, it is demonstrated that the system trajectory will enter and remain in the quasi-sliding mode bands in finite sampling periods, and the widths of the quasi-sliding mode bands are obtained. Third, the boundedness of the system steady-state is established and the corresponding bounds are derived. Finally, comparing with the existing results, it is concluded that the chattering is alleviated and the transient response is increased based on the proposed reaching law in this thesis.