Abstract
A recursive continuous higher order nonsingular terminal sliding-mode (TSM) controller is proposed in this article for nonlinear systems. A new integral TSM manifold is constructed in a recursive manner by modifying the tool of adding a power of integrator instead of exploring nonrecursive design directly. A super-twisting like reaching law is designed to achieve continuous control action without sacrificing disturbance rejection specification as that in boundary-layer approaches. By the new Lyapunov-based design, the proposed control method admits the following new features: first, rather than imposing some existence condition for nonrecursive design, the proposed method admits the certainty for chosen fractional power to guarantee the finite-time stability of the closed-loop system; second, an explicit Lyapunov function approach is proposed to establish finite-time stability of the closed-loop system; and, third, the proposed method is shown to be tunable to exhibit desired transient performance and control energy restriction.
Highlights
S LIDING-mode control (SMC) is recognized as one of the most efficient nonlinear robust control approaches in control systems for uncertain nonlinear systems subject to external disturbances [1,2,3,4,5,6]
Among the SMC methods, the terminal sliding mode (TSM) control has attracted a great deal of attention due to the prosperous property of finite-time convergence in the sliding phase, which brings about many advantages such as smaller steady-state tracking error and faster convergence rate [7]
A key drawback of TSM control is the singularity problem of the control law [8], which can be addressed by the so-called nonsingular TSM control approach [8,9,10,11,12,13]
Summary
S LIDING-mode control (SMC) is recognized as one of the most efficient nonlinear robust control approaches in control systems for uncertain nonlinear systems subject to external disturbances [1,2,3,4,5,6]. The new sliding manifold and controller are constructed by means of modifying the tool of adding a power integrator [15] instead of utilizing the nonrecursive design directly This admits the certainty for choosing fractional power that guarantees the finite-time stability of the closed-loop system. The resultant reaching law admits a continuous control action that substantially alleviate the chattering influence The dynamics of both the reaching and sliding phases are combined together and a composite Lyapunov function is constructed for stability analysis. The main contributions and merits of the proposed work are summarized as follows: 1) To overcome the existence condition on power selection in existing nonsingular TSM manifolds [9, 13], a novel higher-order nonsingular TSM manifold is proposed by using a new principle for fractional power design, which provides sufficient conditions on finite-time stability with given power factor. It is shown to be tunable to exhibit desired transient performance and control energy restriction
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