Theory And Application Of Adaptive Second-order Sliding Mode Control

Sliding mode control(SMC)has always been favored by scholars due to its strong robustness and insensitivity to system parameter perturbations.However,traditional SMC suffers from relative degree limitations and chattering problems.Second-order sliding mode(SOSM)not only addresses the issues of chattering and relative-degree limitations in traditional SMC,but also retains the strong robustness.However,the development of SOSM is still in progress,and there remain numerous unresolved challenges.Most SOSM control algorithms are designed based on the assumption that the upper bound of the system uncertainties is known.However,in practical control systems,this upper bound is often difficult to determine,which can result in the problem of selecting overly large control gains.In addition,the system output often needs to be constrained within a specific range to meet control requirements and ensure safety.Therefore,this paper proposes an adaptive SOSM control algorithm with output constraints,and conducts research on mismatched terms.By introducing a fixed-time term,the control system achieves fixed-time stability.Additionally,some theoretical results are applied to the active safety control system of in-wheel electric vehicles.The specific research content and innovation points are as follows:(1)A novel adaptive finite-time SOSM control algorithm is proposed to solve the problem of unknown upper bounds of uncertainties in SOSM dynamic systems.The proposed method achieves this by designing a new adaptive mechanism that relaxes the constraint on the uncertain terms of the system from being limited by known constants or functions to being limited by unknown positive constants,thereby avoiding overestimation of control gains and effectively reducing chattering.(2)A novel adaptive fixed-time SOSM control algorithm considering mismatched terms is proposed.Generally,the SOSM dynamic system is obtained by differentiating the sliding variable twice.However,this method not only includes some nondifferentiable terms in the derivative of the sliding variable,but also causes some useful terms to be transferred to the control channel.Therefore,this paper reconstructs the first-order derivative of the sliding variable as a combination of mismatched terms and state variables.In addition,a fixed-time term is introduced to achieve fixed-time stability of the system,and the convergence time of the state variables will no longer be affected by the initial values.(3)The issue of output constraints in adaptive SOSM control is addressed.A novel barrier Lyapunov function is constructed in this paper.The controller is designed based on the technique of adding a power integrator and the backstepping-like method.Based on this,a piecewise Tangent barrier Lyapunov function is introduced to solve the problem of asymmetric output constraints.The two methods of solving output constraints are combined with adaptive SOSM to design the controller.(4)The adaptive SOSM control algorithm is applied to the active safety control system of in-wheel electric vehicles,and a combined control strategy of active front steering and direct yaw moment control is proposed.Firstly,an active front steering controller is designed,but it cannot solve the problem of vehicle motion in extreme road conditions.Thus,direct yaw moment control is introduced for combined control.Therefore,based on the adaptive SOSM control algorithm,a direct yaw moment controller is constructed to provide the necessary yaw moment for vehicle steering,thereby ensuring driving safety and comfort.A Car Sim/Simulink joint simulation experiment platform is established,and experiments with and without crosswind are designed to verify the robustness of the controller.