Robust Second-Order Sliding Mode Control Law Design and Realization for Nonlinear Mechanical Systems

Abstract

The purpose of this study is to apply the robust second-order sliding mode theory in the trajectory tracking control law design for nonlinear mechanical systems The first of the thesis begins from the conventional sliding mode control (CSMC) theory the robustness to the matched perturbations finite-time stability and reduced-order property are observed However the price of robust properties is that the designed switching control will induce the high-frequency switching of the control signal which is the chattering phenomenon One of the second-order sliding mode control approaches namely the super-twisting sliding mode algorithm (STSMA) is introduced to obtain a continuous control signal and preserve the robust property to the matched perturbations Comparing the STSMA to the other second-order sliding mode control algorithms only needs to feedback the sliding variable but its derivatives one does not This characteristic so that the STSMA is often applied in the systems with the relative degree equal to one Multiple numerical examples are provided about the super-twisting algorithm to illustrate its robustness finite-time property and stability interpretations in the frequency-domain From the realistic engineering problem point of view firstly consider the well-known positioning control of the servo motor The nonlinear unsymmetrical Coulomb friction model is introduced The corresponding system parameter identification techniques are also conducted Based on the identified dynamic model the robust super-twisting positioning controller is designed Comparative numerical simulations and experiment validations are carried on The results reveal the robustness and the high-precise tracking performance of the super-twisting controller concerning the traditional linear controller Remarkably the implementation of a super-twisting controller is not difficult For the environment with the unknown complex disturbance the super-twisting controller still can derive the linear/nonlinear system to the desired trajectory As the preliminary research of the redundant reaction wheel driven attitude control system the single-axis reaction wheel driven positioning module is firstly discussed The simulations/experiments results show that the effectiveness of the proposed control scheme To realize the fully orientational attitude control of the spacecraft the quaternion-based attitude representation is introduced and the associating quaternion-based control is conducted Based on the optimal control theory the optimal force distribution matrix (FDM) to minimize the control energy for the redundant reaction wheels configuration is presented It should be noted that the stability and the convergent behavior of the nonlinear reduced-order dynamics are addressed utilizing an analytic solution From the space mission scenario point of view the tangent-normal-binormal (TNB) frame attitude command follow strategy is proposed The simulation results illustrate that the superior tracking performance and effectiveness of the super-twisting controller

Date of Award	2021
Original language	English
Supervisor	Chao-Chung Peng (Supervisor)