Research On Nonsingular Terminal Sliding Mode Control Method For Flexible Manipulator

With the development of aeronautics and robotics, flexible manipulators exhibit wider application foreground in comparison with conventional rigid manipulators for their advantages, such as high load-to-weight ratio, low energy consumption, high speed and so on. However, structural flexibility, model parameter uncertainties, external disturbances combined with inherent nonlinear dynamics makes flexible manipulators a class of complicated nonlinear uncertain system. Thus, the control of flexible manipulators is of both theoretical and practical importance.In the last decades, sliding mode control evolved into nonsingular terminal sliding mode (NTSM), which owns advantages of both traditional linear sliding mode (LSM) and terminal sliding mode (TSM), such as strong robustness, convergence in a finite time and high steady precision. Meanwhile, NTSM changes the mathematical form of switching surface, purposively avoids the singularity problem of TSM and makes the control signal globally nonsingular. However, chattering is the biggest drawback restricting the real application of NTSM. Thus, this thesis emphasizes on the NTSM controller design for flexible manipulator and chattering elimination.This thesis firstly discusses distinctly the characteristics of NTSM by theoretical analyses and simulation comparison with LSM, TSM and NTSM. Then, in order to solve chattering problem, a free-chattering two-order NTSM control method is proposed and further applied into a class of multivariable system with uncertain systemic matrix and input matrix. This thesis discusses how to change the general multivariable system to decomposition block-controllable form after nonsingular state transformation and decomposition, which consists of an input-output subsystem and a zero-dynamics subsystem. Later, an auxiliary system is introduced to eliminate uncertainty of input matrix. By applying the proposed two-order NTSM control method, the input-output subsystem tracks the auxiliary system, and the auxiliary system converges to zero in a finite time, respectively. Therefore, the input-output subsystem indirectly realizes convergence in a finite time. Finally, by pole assignment, the zero-dynamics subsystem converges to zero asymptotically. Therefore, the proposed method guarantees the convergence of the whole system.This thesis regards the two-link flexible manipulator as an example to research on its regulation and tracking control. In order to solve non-minimum phase control problem and realize end-point regulation of flexible manipulator system, a NTSM control strategy is proposed based on genetic algorithm (GA). Redefined system output as the combination of joint position and flexible modes, the flexible manipulator system is decomposed into input-output subsystem and internal subsystem. Therefore, the system is transformed into a minimum phase system around equilibrium point by input-output linearization. NTSM controller is designed to make the input-output subsystem converge to zero in a finite time. Moreover, the internal subsystem is transformed into zero-dynamics subsystem. The relationship between the zero dynamics and parameters of the redefined output is analyzed by graphic. Then GA is further adopted to optimize combined parameters, aimed to make zero-dynamics subsystem converge to zero. Meanwhile, the end-point of flexible manipulator converges to zero. Additionally, model parameter uncertainty is considered for flexible manipulators. By analyzing the uncertainties evolved from original system, the error range of end-tip output is calculated by Lyapunov stability theorem. In order to eliminate chattering, combining high-order sliding mode, LSM and the proposed two-order NTSM, a three-order NTSM control strategy is proposed for the redefined input-output subsystem to guarantee its convergence and elimination chattering by filtering. The validity of the proposed method is proved by theory analysis and simulation.In order to deal with the problem of trajectory tracking control with oscillation elimination for flexible manipulators, a composite control strategy is proposed based on fuzzy NTSM. Based on the singular perturbation method and two time-scale decomposition, the flexible manipulator system is decomposed into two subsystems by modeling the joint angles and the corrected flexible modes as the slow and fast variables, respectively. For the slow subsystem, a composite controller is designed by combining NTSM and fuzzy control. NTSM controller is used to realize global stability, fast convergence and better tracking precision, while fuzzy controller is used to eliminate chattering phenomenon, according to the designed fuzzy rules and the distance from system states to switching surface. For the fast subsystem, an observer-based state-feedback control method is proposed. A reduced-order observer is proposed to estimate the corrected flexible mode variables that can not be measured directly. Therefore, the fast subsystem is stabilized by a simple LQR control around the equilibrium trajectory defined by the slow subsystem.The above researches are all based on NTSM control, and the simulation results are presented to validate the design methods.