scholarly journals Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Aldo-Jonathan Muñoz-Vázquez ◽  
Vicente Parra-Vega ◽  
Anand Sánchez-Orta ◽  
Gerardo Romero-Galván
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Finite Time ◽  
Sliding Mode ◽  
Practical Interest ◽  
Mathematical Framework ◽  
Continuous Control ◽  
Formidable Challenge ◽  
Full State ◽  
Fractional Order Controller

The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

scholarly journals Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Yaoyao Wang ◽  
Jiawang Chen ◽  
Linyi Gu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Output Feedback ◽  
Finite Time ◽  
Sliding Mode ◽  
Terminal Sliding Mode Control ◽  
Remotely Operated Vehicles ◽  
Terminal Sliding Mode ◽  
Mode Control ◽  
Nonsingular Terminal Sliding Mode

For the 4-DOF (degrees of freedom) trajectory tracking control problem of underwater remotely operated vehicles (ROVs) in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC) technique is introduced in light of the equivalent output injection sliding mode observer (SMO) and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time.

A New Finite Time Control Solution for Robotic Manipulators Based on Nonsingular Fast Terminal Sliding Variables and the Adaptive Super-Twisting Scheme

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Vo Anh Tuan ◽  
Hee-Jun Kang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Robotic Manipulators ◽  
Control Law ◽  
Continuous Control ◽  
Terminal Sliding Mode ◽  
Finite Time Convergence ◽  
Position Errors ◽  
Time Control

In this study, a new finite time control method is suggested for robotic manipulators based on nonsingular fast terminal sliding variables and the adaptive super-twisting method. First, to avoid the singularity drawback and achieve the finite time convergence of positional errors with a fast transient response rate, nonsingular fast terminal sliding variables are constructed in the position errors' state space. Next, adaptive tuning laws based on the super-twisting scheme are presented for the switching control law of terminal sliding mode control (TSMC) so that a continuous control law is extended to reject the effects of chattering behavior. Finally, a new finite time control method ensures that sliding motion will take place, regardless of the effects of the perturbations and uncertainties on the robot system. Accordingly, the stabilization and robustness of the suggested control system can be guaranteed with high-precision performance. The robustness issue and the finite time convergence of the suggested system are totally confirmed by the Lyapunov stability principle. In simulation studies, the experimental results exhibit the effectiveness and viability of our proposed scheme for joint position tracking control of a 3DOF PUMA560 robot.

scholarly journals Finite-Time Output Feedback Controller Based on Observer for the Time-Varying Delayed Systems: A Moore-Penrose Inverse Approach

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Cong-Trang Nguyen ◽  
Yao-Wen Tsai
Keyword(s):  
Asymptotic Stability ◽  
Output Feedback ◽  
Finite Time ◽  
Sliding Mode ◽  
Feedback Controller ◽  
Delay Systems ◽  
Linear Matrix ◽  
Invariance Property ◽  
Time Varying ◽  
Output Feedback Controller

This study proposes a novel variable structure control (VSC) for the mismatched uncertain systems with unknown time-varying delay. The novel VSC includes the finite-time convergence sliding mode, invariance property, asymptotic stability, and measured output only. A necessary and sufficient condition guaranteeing the existence of sliding surface is given. A novel lemma is established to deal with the control design problem for a wider class of time-delay systems. A suitable reduced-order observer (ROO) is constructed to estimate unmeasured state variables of the systems. A novel finite-time output feedback controller (FTOFC) is investigated, which is based on the ROO tool and the Moore-Penrose inverse technique. Moreover, with the help of this lemma and the proposed FTOFC, restrictions on most existing works are also eliminated. In addition, an asymptotic stability analysis is implemented by means of the feasibility of the linear matrix inequalities (LMIs) and given desirable sliding mode dynamics. Finally, a MATLAB simulation result on a numerical example is performed to show the effectiveness and advantage of the proposed method.

Fractional-order nonsingular terminal sliding mode control via a disturbance observer for a class of nonlinear systems with mismatched disturbances

2020 ◽  
pp. 107754632092526
Author(s):  
Amir Razzaghian ◽  
Reihaneh Kardehi Moghaddam ◽  
Naser Pariz
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Finite Time ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Terminal Sliding Mode Control ◽  
Terminal Sliding Mode ◽  
Nonsingular Terminal Sliding Mode

This study investigates a novel fractional-order nonsingular terminal sliding mode controller via a finite-time disturbance observer for a class of mismatched uncertain nonlinear systems. For this purpose, a finite-time disturbance observer–based fractional-order nonsingular terminal sliding surface is proposed, and the corresponding control law is designed using the Lyapunov stability theory to satisfy the sliding condition in finite time. The proposed fractional-order nonsingular terminal sliding mode control based on a finite-time disturbance observer exhibits better control performance; guarantees finite-time convergence, robust stability of the closed-loop system, and mismatched disturbance rejection; and alleviates the chattering problem. Finally, the effectiveness of the proposed fractional-order robust controller is illustrated via simulation results of both the numerical and application examples which are compared with the fractional-order nonsingular terminal sliding mode controller, sliding mode controller based on a disturbance observer, and integral sliding mode controller methods.

Fixed-time fractional-order sliding mode control for nonlinear power systems

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1425-1434 ◽  
Author(s):  
Sunhua Huang ◽  
Jie Wang
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Fixed Time ◽  
Sliding Mode Controller ◽  
Mode Control ◽  
Time Control

In this study, a fractional-order sliding mode controller is effectively proposed to stabilize a nonlinear power system in a fixed time. State trajectories of a nonlinear power system show nonlinear behaviors on the angle and frequency of the generator, phase angle, and magnitude of the load voltage, which would seriously affect the safe and stable operation of the power grid. Therefore, fractional calculus is applied to design a fractional-order sliding mode controller which can effectively suppress the inherent chattering phenomenon in sliding mode control to make the nonlinear power system converge to the equilibrium point in a fixed time based on the fixed-time stability theory. Compared with the finite-time control method, the convergence time of the proposed fixed-time fractional-order sliding mode controller is not dependent on the initial conditions and can be exactly evaluated, thus overcoming the shortcomings of the finite-time control method. Finally, superior performances of the fractional-order sliding mode controller are effectively verified by comparing with the existing finite-time control methods and integral order sliding mode control through numerical simulations.

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