Study On Several Problems Of High-order Sliding Mode Control Theory

The sliding mode control(SMC)algorithm is derived from the variable structure control systems,which has strong robustness to the uncertainty and disturbance of the nonlinear system.As is known,there often exist some differences between the considered system and its mathematical model,such as the external disturbance,the unmodeled dynamics,the parameter perturbation,and so on.The SMC has been widely concerned since it can effectively deal with the uncertainties caused by these differences.After years of development,SMC algorithm has become an independent and complete research branch in the nonlinear control field,and it is also a widely-used nonlinear control method in the field of control theory and engineering application.However,most of the existing SMC algorithms are investigated based on the traditional SMC algorithm,whose disadvantages lie in the chattering problem and relative degree limitation.To this end,the high-order sliding mode(HOSM)control is developed to solve these problems.However,due to the fact that HOSM is in the development stage,there still exist unsolved problems in HOSM algorithm,such as variable gain,output constraint,and mismatched uncertainty.To this end,the dissertation,which is funded by the National Natural Science Foundation of China “High-order sliding mode theory and application with the disturbance limited by function” and “High-order sliding mode control theory and application with mismatched disturbance” under Grant 61573170 and 61973142,is aimed to investigate the problems of variable gain,output constraint,and mismatched uncertainty on the basis of the HOSM control algorithm.Furthermore,the resulting control algorithms are applied to Buck converters,pendulum systems,and robotic systems.The main research contents and innovations of the dissertation are listed as follows:(1)The adaptive-based SMC algorithm is investigated to solve the constant control gain problem in the SMC algorithm.First of all,a sliding-mode-based filter is constructed to avoid the parameter lamination in the low-pass filter.Furthermore,with the help of the equivalent control,an adaptive law is developed by using the sliding-mode-based filter to track the disturbance.Then,an adaptive non-singular terminal sliding mode(NTSM)controller is constructed based on the adaptive law for the electric vehicle.Finally,an adaptive second-order sliding mode(SOSM)control algorithm is presented by using the adaptive law,whose effectiveness is verified by a Buck converter.(2)Introducing the mismatched term into SOSM dynamics attenuates the chattering problem.Saving some information in the mismatched channel can reduce the uncertainty in the control channel,resulting that the chattering can be reduced by decreasing the control gain.Furthermore,in order to eliminate the effect of the disturbance in the mismatched channel,the stabilization problem of the SOSM dynamics with mismatched disturbance is investigated by using a disturbance observer.First of all,when the system state is known,the disturbance can be directly estimated by the Levant's differentiator,thereby designing the compensating controller.Secondly,if the system state is unknown,one can first let the disturbance and the sliding variable as a new sliding variable to construct an auxiliary system,and then design the compensating controller for the auxiliary system by using a state observer.On this basis,the disturbance observer is used to estimate the disturbance in the new sliding variable to construct the compensating SOSM controller for the original system.This method effectively deals with the mismatched disturbance by means of the combination of the observer technique and SMC algorithm.(3)A general method is proposed to solve the control problem of HOSM dynamics with mismatched terms.The HOSM dynamics with mismatched uncertainties can be divided into two types,i.e.,the HOSM dynamics with lower-triangular uncertainties and the HOSM dynamics with upper-triangular uncertainties.Firstly,the control design of HOSM dynamics with lower-triangular uncertainties is carried out by using the backstepping method and mathematical induction,where the finite-time convergence of the closed-loop system is proved by Lyapunov method.However,by using the same method,a local sliding mode controller is only obtained for the HOSM dynamics with upper-triangular uncertainties such that the closed-loop system is finite-time stabilized in a fixed region.Then,by introducing the saturation technique into the local sliding mode controller,a saturation-like SMC is designed to drive the sliding variables to a small region.On this basis,one can let the small region belongs to the fixed region by adjusting the saturation level so as to globally finite-time stabilize the considered system.(4)Aiming at the output constraint problem existing in the actual systems,the SOSM dynamics with the output constraint is investigated by introducing the barrier Lyapunov function.First of all,a barrier Lyapunov function,whose value is inversely proportional to the distance of the output from the boundary of the constraint,is proposed based on the homogeneity of SOSM algorithm.Secondly,by combining the barrier function with the backstepping method,a SOSM controller is designed to finite-time stabilize the considered system with output constraint.Furthermore,since the mismatched term can be used to attenuate the chattering,the control problem for the SOSM dynamics with mismatched term under output constraint is studied.The effectiveness of the methods is verified by pendulum system.