Asymptotic stabilization in fixed time via sliding mode control

Abstract The hydraulic turbine regulating system (HTRS) plays an important role in the safe and stable operation of hydropower stations. In this paper, a fixed-time integral sliding mode controller (FTISMC) is designed to make the nonlinear HTRS with disturbances stable in a fixed time. The HTRS is a highly complex, strongly coupled, nonlinear nonminimum phase system, which can ensure the frequency and rotor angle of generator stability by adjusting the guide vane opening. In order to decouple the nonlinear HTRS, the input/output feedback linearization is applied to establish the relationship between the control input and the output of the HTRS. Based on sliding mode control (SMC) theory and fixed-time stability theory, FTISMC is proposed to stabilize the HTRS in a fixed time. Compared with the finite time control method (FTCM), the convergence time of nonlinear HTRS under FTISMC is independent of initial conditions and can be exactly estimated. Meanwhile, the integral sliding surface can avoid singularity, thus eliminating the chattering phenomenon. Finally, the numerical simulation is implemented to demonstrate the superior performances of the proposed FTISMC than the existing PID, SMC, and FTMC.

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

Journal of Vibration and Control ◽

10.1177/1077546319898311 ◽

2020 ◽

Vol 26 (17-18) ◽

pp. 1425-1434 ◽

Cited By ~ 2

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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New fixed-time sliding mode control for a mismatched second-order system

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220952305 ◽

2020 ◽

pp. 014233122095230

Author(s):

Guo Jianguo ◽

Yang Shengjiang

Keyword(s):

Sliding Mode Control ◽

Sliding Mode ◽

Initial Conditions ◽

Nonlinear Function ◽

Fixed Time ◽

Second Order ◽

Order System ◽

Time Stability ◽

Mode Control ◽

Mismatched Uncertainties

A fixed-time sliding mode control (FTSMC) method is proposed for a second-order system with mismatched uncertainties in this paper. A new sliding mode, which is insensitive to the mismatched disturbance, is present to eliminate the effect of mismatched uncertainties by adopting the differentiable nonlinear function, and to obtain the fixed time stability independent of initial conditions by using the fraction-order function. In order to improve the performance of control system, the extended disturbance-observer-based fixed-time sliding mode control (EDO-FTSMC) approach is investigated to obtain the fixed-time stability subject to the mismatched uncertainties. Finally, the performance of the proposed control method is illustrated to compare other control approaches with numerical simulation results and application examples.

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