A linear matrix inequality–based proportional-derivative sliding mode control tuning method in robotic systems subjected to external disturbance

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2297-2315
Author(s):  
Valiollah Ghaffari
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequality ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
External Disturbance ◽  
Inequality Constraints ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Tuning Method ◽  
Mode Control

The proportional-derivative sliding-mode control will be designed and tuned in the trajectory tracking of a robot manipulator which operates on uncertain dynamic environments. For achieving these goals, first, a linear matrix inequality–based framework is suggested to design a robust proportional-derivative sliding-mode control in the presence of external disturbances. Next, the parameters of the proportional-derivative sliding-mode control law will be tuned via another minimization problem subjected to some linear matrix inequality constraints. Thus, the controller parameters can be automatically updated via the solution of the optimization problem. The results are successfully used in the robot manipulator with considering two reference paths and some different loads. The simulation results show the effectiveness of the proposed method in comparison with the same technique.

Global Sliding Mode Control Via Linear Matrix Inequality Approach for Uncertain Chaotic Systems With Input Nonlinearities and Multiple Delays

2018 ◽  
Vol 13 (3) ◽  
Author(s):  
Mona Afshari ◽  
Saleh Mobayen ◽  
Rahman Hajmohammadi ◽  
Dumitru Baleanu
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequality ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequality ◽  
Mode Control ◽  
Global Sliding Mode Control ◽  
Uncertain Chaotic Systems

This paper considers a global sliding mode control (GSMC) approach for the stabilization of uncertain chaotic systems with multiple delays and input nonlinearities. By designing the global sliding mode surface, the offered scheme eliminates reaching phase problem. The offered control law is formulated based on state estimation, Lyapunov–Krasovskii stability theory, and linear matrix inequality (LMI) technique which present the asymptotic stability conditions. Moreover, the proposed design approach guarantees the robustness against multiple delays, nonlinear inputs, nonlinear functions, external disturbances, and parametric uncertainties. Simulation results for the presented controller demonstrate the efficiency and feasibility of the suggested procedure.

Nonsingular terminal sliding mode control for micro-electro-mechanical gyroscope based on disturbance observer: Linear matrix inequality approach

2021 ◽  
pp. 107754632098819
Author(s):  
Maryam Jafari ◽  
Saleh Mobayen ◽  
Hubert Roth ◽  
Farhad Bayat
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Terminal Sliding Mode Control ◽  
Matrix Inequality ◽  
Terminal Sliding Mode ◽  
Mode Control ◽  
Nonsingular Terminal Sliding Mode

The aim of this article is to design a nonsingular terminal sliding mode control method based on disturbance observer for the stabilization of the micro-electro-mechanical systems under lumped perturbation. By using the nonsingular terminal sliding mode control scheme, the state trajectories of the system achieve the switching surface and approach to the origin in the finite time. Also, by utilizing the disturbance observer, the finite-time convergence of disturbance error is assured. In the process of design, the optimized coefficients of the sliding surface are calculated in the form of linear matrix inequality. Simulation results for a micro-electro-mechanical gyroscope are illustrated to exhibit the validity of the planned approach in comparison with the other methods.

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