The Research For Sliding-mode Control Of Nonlinear Discrete-time Systems With Time-delay

It is well known that nonlinear systems with time-delay exist in every field ofnatural science and social science. Meantime, with the fast development of scienceand technology, the analysis and design of discrete-time systems have become oneimportant part of control theory. So, the research of discrete-time nonlinear systemswith time-delay is meaningful.The thesis first reviews the relative studies on the discrete-time systems and time-delay systems and sliding mode variable structure control. Then the sliding modecontrol problems of two classes of discrete-time nonlinear systems with time-delay arestudied. Tracking control strategy and integral sliding mode control (DISMC) schemeare proposed which eliminate the chattering from control switching, then the stabilityof the systems is analyzed. The major results are summarized as follows.Firstly, the sliding mode control method is studied for discrete-time nonlinear sys-tems with known structure disturbance. The good character in sliding mode of slidingsurface is reserved and the sliding surface can be designed as the expected characters.Then the tracking control strategy is proposed based on Internal Model Principal. Thismakes real system track ideal sliding mode system and the chattering from controlswitching is avoided. And the tracking error system is asymptotically stable by thestability analysis of the real sliding mode system. Thus the original system becomeasymptotically stable. Then a numerical example for the simulation is given to showthe possibility of the design method. Then this method is applied on a kind of discrete-time nonlinear systems with constant state time-delay; by the so-called lifting method,the system with time-delay is transformed into the system without time-delay; then thecontrol law is designed and finally the asymptotical stability is obtained for the orig-inal system with time-delay. Last, The discrete-time nonlinear systems with variablestate time-delay and control time-delay is studied; by designing a sliding surface withtime-delay, the asymptotical stability is obtained at last. And numerical examples forthe simulation are given to show the possibility of the design method. Secondly, The sample-data nonlinear systems with time-delay are discussed. Adiscrete-time integral sliding mode control (DISMC) scheme is proposed for sample-data nonlinear systems. A variable replacement is applied to transform the originalsystem with time-delay to a new delay-free system. This control scheme consists ofa feedback control component and a component for disturbance compensation. Thiscontrol achieves O(T2) steady-state error for the new state regulation under some con-ditions and eliminates the reaching phase. Last, for the assumption on the relationshipbetween the new system and the original one, the whole control can make the originalstates go into the region magnitude of O(T2). Then, the sample-data nonlinear sys-tems with control time-delay is discussed. The same conclusion is obtained. A goodmethod is provided for engineers to deal with the time-delay systems, especially forthe systems with unmatched time-delay.Lastly, the conclusions are given and a proposition is indicated on the researchwork in the future.