Research On Second-Order Sliding Mode Control Theory Subject To Disturbances Bounded By Positive Constants/Functions

Among the nonlinear robust control methods,traditional sliding mode control(SMC)has received extensive attention owing to its fast dynamic response and strong antiinterference ability.Nevertheless,the restriction of relative degree and the chattering problem existing in conventional SMC greatly limit its application and development.To this end,second-order sliding mode(SOSM)is proposed to overcome these drawbacks with inheriting the inherent merits of conventional SMC.Note that the current SOSM control theory remains in the development stage,and hence there still exist many problems to be urgently settled and improved.This dissertation will investigate several issues concerning SOSM control for nonlinear systems.It mainly includes the four aspects:how to improve the control performance of conventional super-twisting algorithm;how to handle the control design problem of SOSM dynamics subject to mismatched disturbances;how to solve the issue of control design for SOSM systems under state or output constraints and how to design SOSM controllers under the premise of not requiring the bounds of uncertainties to be known.Aiming at these problems,this dissertation will study the issues of SOSM control design for nonlinear systems from the two viewpoints.One is that the system disturbances are bounded by known positive constants or functions,while the other is that the system disturbances are bounded by unknown positive constants or functions.The corresponding research results and innovations are listed as follows:(1)A super-twisting-like algorithm is developed under the case of matched disturbances bounded by known positive constants.Firstly,a super-twisting-like controller is designed by using a non-smooth term to replace the discontinuous term in the traditional super-twisting controller.Then,under this controller,it is verified by taking advantage of Lyapunov stability theory that the sliding variables can finite-time converge to a domain of attraction.Meanwhile,with the aid of the constructed Lyapunov function,the domain of attraction is explicitly given.Finally,the simulation studies are performed,where the conventional super-twisting algorithm is employed to compare with the presented supertwisting-like algorithm.The simulation results show that the proposed super-twisting-like algorithm significantly improves the control performance of the traditional super-twisting algorithm.(2)An approach to the SOSM control design subject to mismatched disturbances is proposed under the case of matched disturbances bounded by known positive functions.The primary benefit of this method is that some terms contained in the derivatives of the sliding variable can be preserved in the mismatched channel.This will obviously decrease the disturbances in the control channel.Accordingly,the control performance of the closed-loop system can be improved in the presence of actuator saturation.However,in such a circumstance,the SOSM dynamics is a typical nonlinear system with a triangular structure.Firstly,when the SOSM dynamics features the lower-triangular structure,by adopting adding a power integrator technique,a SOSM controller is constructed from the perspective of disturbance suppression,and the finite-time stability of the closedloop system is proved based on Lyapunov method.Secondly,when the SOSM dynamics possesses the lower-triangular structure,a SOSM controller is first designed such that the sliding variables can be locally stabilized in a finite time.And then,by imposing a saturation function on the local SOSM controller,a SOSM controller with an adjustable saturation level is derived.Under the proposed controller,the sliding variables will be driven to a small region including the origin,which is determined by the saturation level.In this region,this controller will reduce to the local one and guarantee the finite-time stability of the closed-loop system.Finally,the numerical simulation results are given to verify the validity of the presented method.(3)The problems of SOSM control design under state or output constraints are investigated under the case of matched disturbances bounded by known positive constants or functions.Firstly,in the case of matched disturbances bounded by known positive constants,for nonlinear systems with state constraints,a SOSM control algorithm based on the saturation technique is proposed.The feature of the proposed algorithm lies in that the resultant controller includes a state saturation term,which can change the phase trajectory of the closed-loop sliding mode dynamics.Moreover,a maximum domain of attraction is also obtained for the considered nonlinear systems under preset state constraints.Secondly,in the case of matched disturbances bounded by known positive functions,by constructing a barrier Lyapunov function and applying the technique of adding a power integrator,a SOSM control algorithm,which can be used to deal with the output constraint problem,is developed.The theoretical analysis and simulation results demonstrate that under the output constraints,the sliding variables can still be stabilized to zero in a finite time.(4)The issues of adaptive SOSM control design are studied under the case of matched disturbances bounded by unknown positive constants or functions.Firstly,in the case of matched disturbances bounded by unknown positive constants,a Lyapunov-based adaptive SOSM control strategy is presented.The key feature of the approach is that the bounds of the uncertainties and their derivatives are not required to be known beforehand.Under the proposed control scheme,a non-overestimated adaptive control gain can be provided,which efficiently weakens the chattering effect.Moreover,a domain is given to reveal a detection mechanism that as soon as this domain is reached,the control gain starts decreasing dynamically,while when the system trajectories leave the domain,the control gain begins to increase in order to bring back the trajectories to the domain in a finite time.Secondly,in the case of matched disturbances bounded by unknown positive functions,an adaptive fuzzy SOSM control strategy is proposed.The main merit of the presented method lies in that the fuzzy logic systems are adopted to dynamically approximate the unknown functional bounds of uncertainties such that the chattering phenomenon can be dramatically attenuated.Finally,the simulation results are shown to substantiate the obtained theoretical analysis.