Higher-order Sliding Mode Control Theory And Its Application On Underactuated Systems

In the robust methods for resisting system uncertainties, the traditional sliding mode control(SMC) method is widely used for its advantages such as: the invariance to matched uncertainty, simple controller implementation and so on. However, it has two big disadvantages: the appearance of chattering phenomenon and the constraint to the relative degree of the system. Therefore, higher-order sliding mode(HOSM) control is proposed for these shortcomings. When the relative degree of the system is one, the second-order sliding mode(SOSM) in HOSM can make the control input continuous, the high gain switching is eliminated, thus the chattering phenomenon is weakened. When the relative degree of the system is more than 1, the HOSM can be directly used, remove the constraint of relative degeree of SMC. However, there are also disadvantages in the HOSM such as: the bounds of system uncertainties is hard to be obtained; parameters selection, Lyapunov function chosen, convergence time estimation and the constraint of relative degree of the SOSM.According to the disadvantages above, some important problems encountered in the application of SOSM are studied and solved. The underactuated systems with strong nonlinearity, parameter uncertainties and external disturbance are the object of study. The research work and innovation of this paper mainly includes the following several aspects:(1) The current SOSM doesn’t have robustness to the uncertainties with unknown upper bounds, the improved homogeneous SOSM based on adaptive method is proposed. the uncertainties with unknown upper bounds are totally compenstated by adding of adaptive compensate controller. Finite-time stability proof is given. The improved method is used for the stability control of nonlinear and underactuated ball and beam(BAB) system and TORA system. Exact dynamic model of the systems have been employed in design. Virtual controllers have been introduced to control the second order subsystems. An improved SOSM controller has also been presented to obtain the finite-time tracking to virtual controllers. The stability of the whole systems is obtained at last. Theory, simulation and experiment results verify the efficiency of the controller.(2) The parameters selection is difficult because of the unknown of the uncertainties bounds in the SOSM. An adaptive control method is introduced to improve the performance of the SOSM Twisting algorithm. Adaptive parameter controller is designed to make the automatic adjustment of the parameters realized, at the same time, unknown uncertainties are totally compensated. Finite-time stability proof is given. The improved twisting algorithm is applied in the underactuated wheeled mobile robot trajectory tracking system. The wheeled mobile robot system with many kinds of uncertainties tracks the given trajectory successfully in finite-time.(3) Aiming at the difficulties in the SOSM like: the obtain of the bounds of uncertainties, parameters selection, and the estimation of the convergence time, the SOSM Super-Twisting Algorithm(STA) is improved, the compensation controller is added to compensate the uncertainties with unknown upper bounds. Adaptive parameter controller is designed to make the automatic adjustment of the parameters. Finite-time convergence theoretical proof of the improved controller is given by using of quadratic form Lyapunov function, and the form of convergence time is also obtained. The convergence time can be adjusted by the changing of paramters. The robustness and superiority of our improved algorithm are verified by the further simulation comparisons with other paper.(4) Regarding the relative degree constraint of the SOSM Super-Twisting Algorithm(STA), the STA is extended. Two kinds of second order STAs are presented: The first one is based on quadratic form Lyapunov function, the convergence time can be estimated. Another one is based on homogeneous theory. Furthermore, the first method is improved by adapitve method, upper bounds of uncertainties are needed not to be known and parameters can be adjusted themselves. The second method is extended to random order system. The effectiveness of the extended and improved STAs are also verified by the path tracking control of underactuated surface vessel.