Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Abstract

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

“…where , > 0 and 0 ≤ 2 < 1, 1 > 1; by using ( / )(| 1 | sign( 1 )) = | 1 | −1̇1 , the time derivative of (27) can be derived aṡ…”

“…The adaptive controller of system (25) is designed as (33) and the corresponding updated laws are chosen as (34)-(36). If the sliding mode manifold is expressed as (27), then the system state trajectories converge to the sliding surface within a finite time bounded by…”

“…Compared with the finite-time stability, fixed-time stability possesses a faster convergence rate, higher precision estimation, and stronger disturbance rejection. The fixed-time stability of nonlinear systems with uncertain parameters, unmodeled dynamics, and unknown disturbances has been a well-established area [26][27][28]. Ma et al [29] proposed an adaptive fixed-time fast terminal sliding mode control method for the second-order chaotic oscillation power system.…”

Adaptive Sliding Mode Control Based on Equivalence Principle and Its Application to Chaos Control in a Seven-Dimensional Power System

“…Some scholars have also designed chaos controllers for a classical four-dimensional power system model. At present, the main control methods proposed for the model include finite-time feedback control [14], finite-time integral sliding mode control [15], finite-time passive control [16], chattering-free time scale separation sliding mode control [17], fixed-time integral sliding mode control [18], feedback linearization based sliding mode control [19], discrete time sliding mode control [20], fractional order sliding mode control [21], fast fixed-time nonsingular terminal sliding mode control [22], and fixed-time dynamic surface highorder sliding mode control [23]. However, it is worth noting that most of these controllers are abstract control inputs without considering realizability of the controller and there are also too many control inputs (see [14][15][16][17][18][19][20][21]), which make the proposed control methods impractical.…”

Sliding mode control with mismatched disturbance observer for chaotic oscillation in a seven‐dimensional power system model

“…Therefore, how to control its chaos has become a common problem to be solved in recent years. Many chaos control methods have been proposed for chaotic oscillation in power system, such as time‐delay feedback control, 7 variable speed synergetic control, 8 direct feedback linearization control, 9,10 finite time feedback control, 11 adaptive feedback control, 12,13 fixed time integral sliding mode control (SMC), 14 fixed time nonsingular terminal SMC, 15 fixed time dynamic surface SMC, 16 relay characteristic function based SMC, 17 disturbance observer based SMC, 18 chattering free time scale separation SMC, 19 integral SMC, 20 and so on. However, all aforementioned methods are mainly aimed at a simple two‐dimensional or a four‐dimensional model, which makes poor universality of the proposed control methods.…”