Research On Integral Sliding Mode Control For Multi-Time-Scale Systems

Multi-time-scale systems widely exist in many fields,such as chemical processes,motor systems,power systems and electric circuit systems,etc.Applying the traditional control theory and method to design the controller and analyze the stability for multi-time-scale systems,usually result in high dimensionality and ill-conditioned numerical problems.In recent years,sliding mode control has attracted much attention for its strong ability of rejecting disturbances.However,the sliding mode control theory for multi-time-scale systems is still immature,and there are many open problems.This thesis study the design and analysis problems of integral sliding mode control for multi-time-scale systems based on singularly perturbation theory.The proposed results will improve and promote the control theory for multi-time-scale systems.The main results are summarized as follows:1.A reduced order model-based integral sliding mode control method is proposed for multi-time-scale systems.Firstly,as for multi-time-scale systems affected by matched disturbances,the eigenvalue placement technique is used to stabilize the fast subsystem,and the integral sliding mode controller is designed based on reduced order slow subsystem model.Secondly,for the case of systems with mismatched disturbances,applying the fast subsystem dynamics to design the disturbance observer-based integral sliding mode controller after stabilizing the slow subsystem.Finally,the advantages and effectiveness of the proposed methods are demonstrated by the simulation results.2.A full order model-based integral sliding mode control method is proposed for multi-time-scale systems.Firstly,a singular perturbation parameter-dependent disturbance observer is constructed to estimate disturbances.And then,the disturbance estimation is taken into account in the design of integral sliding mode controller.Secondly,applying the robust H_?control theory and Lyapunov stability theory,the integral sliding mode controller gain is designed by solving a set of linear matrix inequalities,which is aimed at rejecting the disturbances.Finally,the advantages and effectiveness of the proposed methods are illustrated by two examples for multi-time-scale systems affected by matched disturbances and mismatched disturbances,respectively.Compared with the existing method,the proposed method has less overshoot and faster response speed.At the same time,systems have strong ability to reject external disturbances.3.A the passivity-based integral sliding mode control method is proposed foruncertainmulti-time-scalesystems.Firstly,asingularperturbation parameter-dependent integral sliding surface is designed,and the reachability condition is guaranteed.And then,by passivity theory,the integral sliding mode controller gain is designed by solving a set of linear matrix inequalities,such that the closed-loop multi-time-scale systems under the resulting integral sliding mode controller are passive and exponentially stable.Secondly,a singular perturbation parameter upper bound value estimation method is proposed,such that the passivity and exponential stability are preserved for any admissible singular perturbation parameter.Finally,the advantages and effectiveness of the proposed methods are demonstrated by an example.The proposed approaches have less conservatism than the existing results,which lead to a more optimal singular perturbation parameter bound,and the systems can tolerate larger uncertainties.