Research On The Integral Sliding-mode Control Problems For Classes Of Control Systems

The System chattering is usually produced by the time-delay, systemperturbation, external disturbance and unknown of the system states, so theapplication of variable structure control is influenced. Therefore in this paper, firstlyan improved method of observer designing is given. Secondly, based upon compositenonlinear feedback technology, the design problem of integral sliding mode controlleris studied for the uncertain continuous system with mismatched disturbance. Lastly,according to LMI, the design problem of integral sliding mode controller isconsidered for a class of uncertain system with multiple time-delay. Andcorrespondingly, the feasibility and effectiveness of above conclusions are illustratedby a simulation example is given in every chapter.The main contents summed up as follows.1.The variable structure controls are reduced and the research status of integralsliding mode control and multiple time-delay are analyzed, then the main researchworks are summarized.2. An improved design procedure of state observer is proposed for a class ofMulti-Input and Multi-Output (MIMO) Discrete-Time Systems (DTS) withunmatched external disturbance in this paper, and the state observer is not affected byexternal disturbances. This method can also be used into the MIMO-DTS which issatisfied matched condition of external disturbances. A design scheme for the slidingmode controller is put forward based on the state observer and the disturbanceestimator for a class of MIMO-DTS which some external disturbances satisfy thematched condition. The system states and the upper bound of external disturbancesare not required to know in the design scheme. Finally, a simulation example ispresented to demonstrate the feasibility and effectively of the proposed method in thispaper.3. A design method of the integral sliding mode controller(ISMC) is proposed based on linear matrix inequalities(LMIs) for a kind of the uncertain system withmultiple time-delay, the state matrix and the input matrix of the system have boundedmismatching perturbations. A sufficient condition for the existence of a sliding surfaceis given to guarantee asymptotic stability of the state trajectory on the sliding mode,and a sliding surface is designed by some LMIs characterization, at the same time, anintegral control law is obtained to guarantee the existence of a sliding mode from theinitial time. Finally, a simulation is given to show the effectiveness of the proposedmethod in this paper.4. A design method of the ISMC is proposed based on linear LMIs for a kind ofthe uncertain system with multiple time-delay, the state matrix and the input matrix ofthe system have bounded mismatching perturbations. A sufficient condition for theexistence of a sliding surface is given to guarantee asymptotic stability of the statetrajectory on the sliding mode, and a sliding surface is designed by some LMIscharacterization, at the same time, an integral control law is obtained to guarantee theexistence of a sliding mode from the initial time. Finally, a simulation is given toshow the effectiveness of the proposed method in this paper.