Terminal sliding mode control strategy design for second-order nonlinear system (original) (raw)
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IEEE Access
This paper proposes a controller-observer strategy for a class of second-order uncertain nonlinear systems with only available position measurement. The third-order sliding mode observer is first introduced to estimate both velocities and the lumped uncertain terms of system with high accuracy, less chattering, and finite time convergency of estimation errors. Then, the proposed controller-observer strategy is designed based on non-singular fast terminal sliding mode sliding control and proposed observer. Thanks to this combination, the proposed strategy has some superior properties such as high tracking accuracy, chattering phenomenon reduction, robustness against the effects of the lumped uncertain terms, velocity measurement elimination, finite time convergence, and faster reaching sliding motion. Especially, two period times, before and after the convergence of the velocity estimation takes place, are considered. The finite time stability of proposed controller-observer method is proved by using the Lyapunov stability theory. Final, the proposed strategy is applied to robot manipulator system and its effectiveness is verified by simulation results, in which a PUMA560 robot manipulator is employed.
Mathematical Problems in Engineering, 2014
A continuous nonsingular fast terminal sliding mode (NFTSM) control scheme with the extended state observer (ESO) and the tracking differentiator (TD) is proposed for second-order uncertain SISO nonlinear systems. The system’s disturbances and states can be estimated by introducing the ESO, then the disturbances are compensated effectively, and the ideal transient process of the system can be arranged based on TD to provide the target tracking signal and its high-order derivatives. The proposed controller obtains finite-time convergence property and keeps good robustness of sliding mode control (SMC) for disturbances. Moreover, compared with conventional SMC, the proposed control law is continuous and no chattering phenomenon exists. The property of system stability is guaranteed by Lyapunov stability theory. The simulation results show that the proposed method can be employed to shorten the system reaching time, improve the system tracking precision, and suppress the system chatter...
Fast second-order sliding mode control design based on lyapunov function
We design a new kind of fast terminal sliding mode controller for second-order uncertain systems with a single control input. In contrast to the reported techniques, which are based on the Terminal Sliding Mode Control, the proposed controller design is based on Lyapunov methods. Sufficient conditions are given to ensure the finite-time stability of the close-loop system with the proposed discontinuous controller. The performance is compared with others Fast Terminal Sliding Mode controllers by means of a simulation example.
Nonsingular Terminal Sliding Mode Control Based on Novel Reaching Law for Nonlinear Uncertain System
Applied Mechanics and Materials, 2013
Novel reaching law to nonsingular terminal sliding mode control for the control of the second order nonlinear uncertain system is introduced in this paper. The problems of singularity, chattering and slow convergence of the terminal sliding mode control, and verify the stability of the new controller is analyzed. Due to the premise of eliminating the singular value in the nonsingular terminal sliding mode control, the new reaching law based on the power reaching law enables the finite time convergence of the system equilibrium. By applying the new controller to the inverted pendulum system, the sliding surface had been proved fast and the system chattering had been reduced at the same time. Simulation results indict that the system converges to the equilibrium in a short time and the proposed method is feasible and effective.
International Journal of Modelling, Identification and Control, 2017
The sliding mode control concept has been extensively investigated during the last decade, where it has been proved that such a control strategy is not so simple to be efficiently applied in dynamical and mechanical systems, because of the too strong sensitivity of such systems to the chattering phenomenon. In this paper, a reformulated second order sliding mode controller has been implemented into a robotic system for a trajectory tracking task, both in the case of ideal operation as well as for real systems submitted to parameter uncertainties. A comparative study performed through the obtained simulation results has been presented. Then, an adaptive extension of the second order sliding mode control has been treated seeking to resolve the challenging problems of real systems reflected by the presence of physical and environmental disturbances and especially parametric uncertainties. The proposed adaptive second order SMC has the advantage that it allows not only to remedy disturbing phenomena but also to retain all properties and system performances. Simulation results performed on a robotic manipulator system have illustrated improved performances with the proposed adaptive second order sliding mode control design.
Non-singular terminal sliding mode control and its application for robot manipulators
2001
A global non-singular terminal sliding mode controller for second order uncertain nonlinear dynamic systems, which enables enables finite time reachibility and elimination of the singularity problem associated with conventional terminal sliding mode control. The tracking precision problem is also explored. The relationship between the tracking precision and the width of the saturation function used for elimination of chattering is formulated. The proposed controller is then applied to the control of a rigid manipulator. Simulation results are presented to validate the analysis.
Adaptive Neural Integral Full-Order Terminal Sliding Mode Control for an Uncertain Nonlinear System
IEEE Access
This study reports the design of a control system for a class of general nonlinear second-order systems. The significant problems of singularity and chattering phenomenon, which limit the use of the conventional terminal sliding mode control (TSMC) in real applications due to the order of the sliding surface, need to be addressed. Additionally, the effects of disturbances and uncertainties need to be removed, and the response rates increased. Therefore, the integral full-order terminal sliding mode (IFOTSM) surface was proposed. To track the specified trajectories with high accuracy, a control approach is developed for the class of general nonlinear second-order systems by utilizing an IFOTSM surface and an adaptive compensator. The unknown dynamic model is derived based on a radial basis function neural network (RBFNN). Consequently, our controller provides good performance with minimum position errors, robustness against uncertainties, and work without a precise dynamic model. Simulated examples were performed to analyze the effectiveness of the control approach for position pathway tracking control of a 2-DOF parallel manipulator.
Nonsingular terminal sliding mode control of nonlinear second-order systems with input saturation
International Journal of Robust and Nonlinear Control, 2015
This paper proposes the use of a novel nonsingular Terminal Sliding surface for the finite-time robust stabilization of second order nonlinear plants with matched uncertainties. Mathematical characteristics of the proposed surface are such that a fixed bound naturally exists for the settling time of the state variable, once the surface has been reached. A simple redesign of the control input able to ensure the feature of fixed-time reaching of the sliding surface will be also presented, and fixed-time stability will be guaranteed by the proposed Terminal Sliding Mode Control design method. A careful simulation study has been performed using a benchmark system taken from the literature.
A Finite-time Adaptive Fuzzy Terminal Sliding Mode Control for Uncertain Nonlinear Systems
International Journal of Control, Automation and Systems, 2018
In this study, a new adaptive fuzzy terminal sliding mode (AFTSM) control is presented for control of uncertain nonlinear systems with disturbances. The proposed controller incorporates terminal-based gradient descent (GD) algorithm and fuzzy logic system into a continuous nonsingular terminal sliding mode. The nonlinear dynamics of the system to be controlled are approximated with the fuzzy logic system and an adaptive law based on the terminal-based GD is proposed for online updating the parameters. The most advantage of the proposed terminal-based GD is the finite-time convergence compared to the conventional GD learning algorithm. It is proved that under the proposed terminal sliding mode and updating law, the tracking and approximation errors converge to the neighbourhood of zero in a very short time. Simulation results are given to illustrate the performance of the proposed AFTSM control through the control of a second-order system and a two-link rigid robotic manipulator. The simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous terminal sliding mode control methods. Moreover, the proposed terminal sliding mode is applied to control of joint movement generated by functional electrical stimulation. The experiment results verify that accurate control of movement is obtained using the proposed control scheme.
Scientia Iranica
This paper investigates fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems in the presence of matched and mismatched disturbances. Using estimation of the mismatched disturbance estimated by a fixed-time disturbance observer, a novel nonlinear dynamic sliding surface is designed. The convergence time of the closed-loop system including disturbance observer and control system is guaranteed to be uniform with respect to initial conditions. Moreover, the proposed controller avoids chattering phenomenon by producing a continuous control signal.