Sliding mode control for non-linear systems with global invariance

1997 ◽  
Vol 211 (1) ◽  
pp. 75-82 ◽  
Author(s):  
C-L Chen ◽  
W-Y Lin
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Parametric Uncertainty ◽  
Invariance Property ◽  
Control Law ◽  
Continuous Control ◽  
Mode Control ◽  
Non Linear Systems ◽  
The Cost

In the conventional sliding mode control, a discontinuous control signal is applied to achieve the sliding condition. This control makes the system invariant to parametric uncertainty and external disturbance, but also causes chattering. Modified approaches are introduced to eliminate chattering at the cost of the invariance property or accuracy. This paper describes the use of the concept of extended systems, such that a continuous control is obtained using a sliding mode control design scheme. A sliding surface is assigned so that the sliding mode motion will occur while the proposed control law is applied. This results in a system with global invariance.

A novel constraint tracking control with sliding mode control for industrial robots

2021 ◽  
Vol 18 (4) ◽  
pp. 172988142110297
Author(s):  
Yaru Xu ◽  
Rong Liu ◽  
Jia Liu ◽  
Jiancheng Zhang
Keyword(s):  
Convergence Rate ◽  
Sliding Mode Control ◽  
Tracking Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Industrial Robots ◽  
Special Method ◽  
Control Law ◽  
Reaching Law ◽  
Mode Control

As industrial robots are characterized by flexibility, load variation, and unknown interference, it is necessary to develop a control strategy with strong robustness and adaptability, fast convergence rate, and simple structure. Sliding mode control is a special method widely used to handle nonlinear robot control. However, the existing control law for sliding mode control has limitations in the chattering and convergence rate. The sliding mode manifold and reaching law are firstly discussed in this article. In the meanwhile, a proposed control law for sliding mode control combining linear sliding mode manifold and double-power reaching law is developed, which is based on the robot dynamic equation derived by the Udwadia–Kalaba theory. Furthermore, a compared control law for sliding mode control combining linear sliding mode manifold with exponential reaching law is presented to test the proposed control law for sliding mode control. The comparison indicates that the proposed law effectively improves the performance in convergence rate and the chattering of constraint tracking control. Finally, the two control laws for sliding mode control are applied to the Selective Compliance Articulated Robot Arm robot system with modeling error and uncertain external disturbance to demonstrate the merit and validation of the proposed scheme.

scholarly journals Trajectory tracking of a mobile robot using adaptive sliding mode control

2021 ◽  
Author(s):  
Seyyed Mohammad Hosseini Rostami ◽  
Fatemeh Jahangiri
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Parametric Uncertainty ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
External Disturbances ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Angular Velocities ◽  
Robust Adaptive

Abstract The purpose of this paper is to design a control system for a mobile four-wheeled robot, whose task is to achieve stability and proper operation in the execution of commands. As a result of the nonlinear dynamics, structural and parametric uncertainty of this robot, various control approaches are used in order to achieve stability, proper performance, minimize modeling errors and uncertainties, etc. By adjusting linear and angular velocities in the presence of external disturbances and parametric uncertainty, this algorithm is able to follow a predetermined trajectory based on the information contained in the signals received by the sensor from the trajectory.. In previous articles, the upper bound of uncertainty was assumed to be known. This paper makes the assumption that the upper band of uncertainty and disturbances in robotic systems is unknown, since, in many cases, we cannot know the extent of these uncertainties in practice. In our recent paper, we generalized the sliding mode control law and proved its effectiveness, so that by including an adaptive part to the control law, we transformed it into a robust-adaptive sliding mode control, and we could estimate the upper band uncertainties online based on these adaptive laws. This typology can be expressed as a distinct theorem with stable results. Simulations with MATLAB software demonstrate that the controller ensures optimal performance under external disturbances and parametric uncertainty with less fluctuations.

Adaptive sliding mode formation control for multiple flight vehicles with considering autopilot dynamic

2021 ◽  
pp. 1-21
Author(s):  
W. Li ◽  
Q. Wen ◽  
H. Zhou
Keyword(s):  
Sliding Mode Control ◽  
Formation Control ◽  
Control Method ◽  
Sliding Mode ◽  
Dimensional Space ◽  
External Disturbance ◽  
Control Law ◽  
Terminal Sliding Mode ◽  
Mode Control ◽  
Flight Vehicles

ABSTRACT This paper mainly focuses on the cooperative control of formation configuration for multiple flight vehicles in the three-dimensional space. Considering the external disturbance of the system, the adaptive non-singular terminal sliding mode control law (NTSMC) is designed based on the virtual leader-follower method, which aims to ensure that each flight vehicle reaches the expected terminal position in a limited time and meet the configuration constraints. Further considering the first-order dynamic characteristic of the autopilot, a novel second-order sliding mode control (SOSMC) law is deduced with using the estimated information of sliding mode disturbance observer. The proposed control method ensures that all flight vehicles form the required space formation configuration simultaneously at a pre-designed time, and the chattering phenomenon of the sliding mode surface and acceleration response that nears the equilibrium point is effectively weaken. The stability of the proposed control law is verified by theoretical analysis and lots of mathematical simulations. The results show that the control algorithm in this paper can be used to guidance the formation controller design of multiple flight vehicles in the mid-guidance phase to some extent, and thus the cooperative flight stability of the system can be effectively improved.

scholarly journals A fuzzy adaptive sliding mode controller for uncertain nonlinear multi motor systems

2018 ◽  
Vol 161 ◽  
pp. 02013
Author(s):  
Tran Xuan Tinh ◽  
Pham Tuan Thanh ◽  
Tran Van Tuyen ◽  
Nguyen Van Tien ◽  
Dao Phuong Nam
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Adaptive Sliding Mode Controller ◽  
Pressure Meter ◽  
Fuzzy Adaptive

Multi-motor drive systems are nonlinear, multi-input multi-output (MIMO) and strong-coupling complicated system, including the effect of friction and elastic, backlash. They have been widely used in many modern industries. The control law for this dive system much depend on the determining of the tension being hard to obtain this tension in practice based on a load cell or a pressure meter due to the accuracy of sensors or external disturbance. An emerging proposed technique in the control law is the use of adaptive sliding mode control scheme to stabilize closed system. However, the control system would be affected by chattering phenomenon. In order to eliminate this term, fuzzy technique is proposed by adjusting equivalent coefficients. The theory analysis and simulation results point out the good performance of the proposed fuzzy adaptive sliding mode control for the drive system.

Dynamic sliding mode-based attitude stabilisation control of satellites with angular velocity and control constraints

2018 ◽  
Vol 41 (4) ◽  
pp. 934-941 ◽  
Author(s):  
Chunmei Yu ◽  
Xun Xie
Keyword(s):  
Angular Velocity ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Convergence Time ◽  
Small Radius ◽  
Control Law ◽  
Control Approach ◽  
Mode Control ◽  
Dynamic Sliding Mode

This work presents a novel control approach to the attitude stabilisation problem of rigid satellites with external disturbance, control constraint, and angular velocity constraint. The controller is developed in the framework of dynamic sliding mode control. A dynamic sliding mode surface is preliminarily chosen, and then a structure-simple sliding mode control law is synthesised. It is proved that the proposed control law can successfully accomplish the attitude stabilisation manoeuvre. The attitude is exponentially stabilised, and the angular velocity is stabilised with an exponential rate to a ball with a small radius. In comparison with the static sliding mode surface-based controllers, the proposed approach can provide a fast convergence rate. The system convergence time can be shortened by dynamically updating the control parameters in the sliding mode. Simulation results are presented to examine the feasibility of the presented solution.

Sliding Mode Control for Wheeled Inverted Pendulum

2014 ◽  
Vol 971-973 ◽  
pp. 714-717 ◽  
Author(s):  
Xiang Shi ◽  
Zhe Xu ◽  
Qing Yi He ◽  
Ka Tian
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
High Performance ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Experimental Results ◽  
Control Law ◽  
Collaborative Simulation ◽  
Mode Control ◽  
Wheeled Inverted Pendulum

To control wheeled inverted pendulum is a good way to test all kinds of theories of control. The control law is designed, and it based on the collaborative simulation of MATLAB and ADAMS is used to control wheeled inverted pendulum. Then, with own design of hardware and software of control system, sliding mode control is used to wheeled inverted pendulum, and the experimental results of it indicate short adjusting time, the small overshoot and high performance.

Conditional integrator sliding mode control of an unmanned quadrotor helicopter

2021 ◽  
pp. 095965182110498
Author(s):  
Yohan Díaz-Méndez ◽  
Leandro Diniz de Jesus ◽  
Marcelo Santiago de Sousa ◽  
Sebastião Simões Cunha ◽  
Alexandre Brandão Ramos
Keyword(s):  
Sliding Mode Control ◽  
Transient Response ◽  
Tracking Control ◽  
Position Control ◽  
Sliding Mode ◽  
Control Technique ◽  
Control Law ◽  
Control Problems ◽  
Control Activity ◽  
Mode Control

Sliding mode control (SMC) is a widely used control law for quadrotor regulation and tracking control problems. The purpose of this article is to solve the tracking problem of quadrotors using a relatively novel nonlinear control law based on SMC that makes use of a conditional integrator. It is demonstrated by a motivation example that the proposed control law can improve the transient response and chattering shortcomings of the previous approaches of similar SMC based controllers. The adopted Newton–Euler model of quadrotor dynamics and controller design is treated separately in two subsystems: attitude and position control loops. The stability of the control technique is demonstrated by Lyapunov’s analysis and the effectiveness and performance of the proposed method are compared with a similar integral law, also based on SMC, and validated by tracking control problems using numerical simulations. Simulations were developed in the presence of external disturbances in order to evaluate the controller robustness. The effectiveness of the proposed controller was verified by performance indexes, demonstrating less accumulated tracking errors and control activity and improvement in the transient response and disturbance rejection when compared to a conventional integrator sliding mode controller.

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