Time-Varying Second-Order Sliding Mode Control for Systems Subject to External Disturbance

Abstract

In this paper, the design problem of a class of novel second-order sliding mode controller for systems subject to external disturbance is investigated, where the sliding variable is affected by a timevarying regulation. On the one hand, for the unmatched disturbance bounded by positive functions, a secondorder sliding mode controller is proposed to prove the finite-time stability of aforementioned system through the backstepping-like method and virtual control strategy. On the other hand, for the non-vanishing bounded disturbance, a non-singular terminal sliding mode surface containing disturbance observations is designed via a finite-time disturbance observation method and the finite-time stability of the system controlled output is realized. The claimed performances of the proposed methods are validated by two simulation examples. INDEX TERMS Finite-time stability, Second-order sliding mode, Time-varying systems, External disturbance, Virtual control, Backstepping-like method.

Single phase second order sliding mode controller for complex interconnected systems with extended disturbances and unknown time-varying delays

“…Now, we are in position to show that the system's trajectories hit the sliding manifold (2) from beginning of the motion. With these aims, a new control signal is established as (14):…”

“…Theorem 2. Study the interconnected system (1) with the proposed controller (14) where the switching manifold is demarcated by (2). Then, the state variables of (1) forward to the switching manifold (2) in finite time and stay on sliding mode under the controller (14) when scalar gains filling the following settings:…”

“…For the above second mission which will consider the unknown exogenous perturbations, this issue has been examined by researchers [8], [12]- [14]. In [12], a second order sliding mode algorithm was established to solve the nonlinear plants with disturbances limited by positive functions via a backsteppinglike technique.…”

“…In [12], a second order sliding mode algorithm was established to solve the nonlinear plants with disturbances limited by positive functions via a backsteppinglike technique. Also, this approach, Wu et al [14] suggested a new controller for systems subject to external disturbance. Based on super-twisting, twisting, or homogeneous procedures, Shi et al [13] proposed a new variable-gain fixed-time SOSMC signal for a general class of uncertain nonlinear plants.…”

Single Phase Second Order Sliding Mode Controller for Mismatched Uncertain Systems with Extended Disturbances and Unknown Time-Varying Delays

“…Also, based on this technique, a new SOSMC was synthesized for nonlinear systems with mismatched term and time-varying output constraint [20]. In [21], a new SOSMC was proposed for the nonlinear system by using the backstepping-like method and virtual control strategy. Based on the Lyapunov method, an adaptive SOSMC was designed in [22] for nonlinear systems with uncertainties.…”