Continuous fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems with matched and mismatched disturbances (original) (raw)
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Nonsingular terminal sliding mode control of nonlinear second-order systems with input saturation
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This paper investigates a novel nonsingular fast terminal sliding-mode control method for the stabilization of the uncertain time-varying and nonlinear thirdorder systems. The designed disturbance observer satis es the nite-time convergence of the disturbance approximation error and the suggested nite-time stabilizer assures the presence of the switching behavior around the switching curve in the nite time. Furthermore, this approach can overcome the singularity problem of the fast terminal sliding-mode control technique. Moreover, knowledge about the upper bounds of the disturbances is not required and the chattering problem is eliminated. Usefulness and e ectiveness of the o ered procedure are con rmed by numerical simulation results.
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IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, 2012
This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.
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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.
Advanced Control for Applications, 2021
It is essential to consider chattering alleviation of Sliding Mode Control (SMC) design along with providing the system convergence regardless of initial states utilizing the fixed‐time stability notion. Unknown states and disturbance are two major issues in practical applications, which can be effectively solved by using sliding mode observers. This paper deals with state and disturbance Observers‐based Chattering‐Free Fixed‐time SMC (OCFFSMC) design for a class of high‐order nonlinear systems with unknown disturbance, while only the first state is measured physically. A new form of the combined observer‐controller is designed to provide estimated data of unknown disturbance and unmeasured states in the control law. The designed disturbance observer‐based sliding mode controller is not only capable of estimating unknown disturbance but also capable of alleviating the chattering problem in the control signal. Based on defining a new form of the sliding surface, a new control law is ...
Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances
Automatica, 2013
We have developed a continuous nonsingular terminal sliding-mode control with time delay estimation (TDE) for Shape memory alloys (SMA) actuators. The proposed method does not need to describe a mathematical model of a hysteresis effect and other nonlinearities; thus, it is simple and model-free. The proposed control consists of three elements which have clear meaning: a TDE element that cancels nonlinearities in the SMA dynamics, an injection element that specifies desired terminal sliding-mode (TSM) dynamics, and a reaching element using a fast terminal sliding manifold that is activated accordingly when the system trajectory is not confined in the TSM. The proposed control has been successfully implemented in an SMA actuated system and experimental results show the proposed control is easily implementable and highly accurate. Once the TSM and the reaching condition are suitably specified, the tracking performance of the proposed control is improved compared with a conventional time delay control with a linear error dynamics.
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.
International Journal of Control, Automation and Systems, 2020
Using state observer has attracted a notable interest of researchers in control community to provide an on-line state estimator for control systems instead of measuring them physically by sensors which is costly, inaccurate, and easy to contaminate by noise. Some challenges ahead to design state observer in control systems are using estimated data by observer in the designed controller as well as the system stability analysis by using controller and observer simultaneously. This paper proposes Fuzzy Adaptive Fixed-time Sliding Mode Control (FAFSMC) technique for trajectory tracking of a class of high-order nonlinear systems with mismatched external disturbances and uncertainties. Meanwhile, the fixed-time state observer is proposed to incorporate with the controller for estimating the unmeasured even states (velocity) and providing on-line data in the controller. A proper candidate Lyapunov function is defined to verify the system global fixed-time stability by considering designed control law, state observer term, and adaptive law, simultaneously. The simulation results of three simulation examples, ship course system, two-link robotic manipulator, and three-link robotic manipulator, are carried out in Simulink/MATLAB to reveal the effectiveness of the proposed FAFSMC scheme compared with the other three conventional methods for solving trajectory tracking problem. Two performance criteria, Integral of the Square Value (ISV) and Integral of the Absolute value of the Error (IAE), are used to make a comprehensive comparison among the proposed FAFSMC method with state observer and the other three methods.
Applied Sciences
This paper describes a design scheme for terminal sliding mode controllers of certain types of non-linear dynamical systems. Two classes of such systems are considered: the dynamic behavior of the first class of systems is described by non-linear second-order matrix differential equations, and the other class is described by non-linear first-order matrix differential equations. These two classes of non-linear systems are not completely disjointed, and are, therefore, investigated together; however, they are certainly not equivalent. In both cases, the systems experience unknown disturbances which are considered bounded. Sliding surfaces are defined by equations combining the state of the system and the expected trajectory. The control laws are drawn to force the system trajectory from an initial condition to the defined sliding surface in finite time. After reaching the sliding surface, the system trajectory remains on it. The effectiveness of the approaches proposed is verified by ...