Study On Variable Structure Control Strategy And Its Design For Singular Systems And Delta Operator Systems

In modern control technologies, variable structure control (VSC) is an advancednonlinear control strategy, which mainly contain three kinds of control strategies:VSC precluding sliding mode, sliding mode control (SMC) and switching supervisorycontrol. Soft variable structure control (SVSC) is based on a continuous selectionstrategy to achieve variational signals by altering system structure, which is part ofVSC precluding sliding mode. It has many advantages such as high regulating rates,fast response, and scarcely any chattering. The SMC strategy make the system driftdown a specified switching plane towards the equilibrium state, if the system involvedis controlled in the sliding modes. It is complete robustness to the internal parameterperturbation and external disturbance under certain matching conditions but it maycause certain system chattering. The VSC strategy has been promoted and applied to awide variety of practical program, such as robot models, aerospace controls, chemicalprocess, electric motors and power systems et al. Singular system is much moregeneral than normal system because the controller must be designed so that the systemis not only robust and stable, but also regular and impulse-free, or causal, while thelatter two issues do not arise in the normal system. The continuous system and thediscrete system can be presented in a unified framework by Delta operator. Deltaoperator theory is widely applied in high speed signal processing and digital samplecontrol system.The dissertation first reviews the origin and the development of VSC strategy, aswell as the relative studies on the VSC design for singular systems and Delta operatorsystems up to now are given in detail. Due to the above reasons, the dissertationsystematically investigates the problems of the SVSC strategy for continuous systemswith input constraints, the SMC strategy for uncertain discrete systems based on reaching laws, and the VSC design for singular systems and Delta operator systems.The main results are shown as follows.1. The SVSC strategy for continuous systems with input constraints is presented.The definition of SVSC and the structure feature of its controller are given. SVSC forunrestricted controls and restricted controls based on implicit Lyapunov functions ispresented, as well as the SVSC system with state observer is discussed. The dynamicSVSC strategy is discussed. The SVSC strategy with S-class functions is presented.The SVSC with hyperbolic tangent functions is designed. The SVSC for autonomousunderwater vehicle (AUV) based on sigmoid functions is presented, and simulationexperiment is carried out to verify the effectiveness of the proposed strategy.2. The SMC strategy for uncertain discrete systems based on reaching laws ispresented. The conventional discrete reaching laws are summarized, and the definitionof ideal reaching law is given. The uncertain discrete SMC system is designed by theideal reaching law with disturbance compensator. The S-class variable rate reachinglaw is designed, and the performance of the law is better than that of the exponentialreaching law and the variable rate reaching law. Finally, a knowledge worker dynamicsystem by the SMC strategy in high technology enterprises is presented.3. The problem of the dynamic SVSC design for continuous singular systemswith input constraints is presented. The singular system and its solution are described.The structure mode of SVSC controller is given. The stability of singular systemswith the dynamic SVSC is proposed. The dynamic soft variable structure controller isdesigned, and the concrete algorithm on the dynamic SVSC is given.4. The problem of the SMC design for mismatched uncertain discrete singularsystems is presented. The dynamic switching function with last step state is given toguarantee the stability of the control systems in switching band. Two types of discretesingular reaching laws with disturbance compensator are designed to eliminate therestriction that the system uncertainties is bounded and the satisfaction of matchingconditions compared with conventional SMC. Essential conditions of quasi-slidingmode which can cross the switching plane step by step is provided, and the switchingband of quasi-sliding mode is reduced. 5. The problem of the SMC strategy for Delta operator systems is presented. Asufficient condition for the existence of the switching plane in terms of linear matrixinequality (LMI) is given, and the reaching condition of sliding mode is analyzed. Thedifferences and similarities of designing sliding mode controller based on the idealreaching law and the exponential reaching law. The SMC design for uncertain Deltaoperator systems with internal parameter perturbation and external disturbance isdesigned, and the asymptotic stability of quasi-sliding mode is proved. Finally, theoptimal sliding mode controller for Delta operator systems is designed.