Fractional-order sliding mode control for deployment of tethered spacecraft system

Abstract

This paper proposes a fractional-order integral sliding mode control with the order 0 < ν < 1 to stabilize the deployment of tethered spacecraft system with only tension regulation. The work in this paper is partially based on integer-order nonlinear sliding mode controller and improves its performance with fractional-order calculus. The proposed scheme makes use of integral sliding surface to obtain smaller convergence regions of state errors, and the fractional derivative is synthesized to enhance the flexibility of controller design by fining parameters for better dynamic and steady-state performance. Fractional-order observers help to eliminate external disturbances while the adaptive law is presented to remove the adverse effect in stability analyses, and fractional-order uniform ultimate boundedness is proved to guarantee the existence of the proposed sliding surface. According to theoretical analyses, the fractional order will indeed affect the dynamic and steady-state performance of control system, and the proposed method will be verified in numerical simulations compared with the nonlinear sliding mode counterpart.

Adaptive super‐twisting algorithm‐based fractional‐order sliding mode control of redundantly actuated cable driving parallel robot with uncertainty and disturbance estimation

“…where 𝜷 i = diag(𝛽 1i , … 𝛽 ni ) with i = 1, 2, 3. From the analysis of the above two cases and the results of [23,44], we can conclude that the position tracking error e 1 is uniformly ultimately bounded.…”

“…From the analysis of the above two cases and the results of [23, 44], we can conclude that the position tracking error is uniformly ultimately bounded.Remark According to [45], the fractional‐order system cannot reach equilibrium in finite time. If a fractional‐order system satisfies the result of [23, 44], its uniformly ultimate boundedness can be guaranteed.…”

“…According to [45], the fractional-order system cannot reach equilibrium in finite time. If a fractional-order system satisfies the result of [23,44], its uniformly ultimate boundedness can be guaranteed.…”

Fractional-Order Adaptive Integral Hierarchical Sliding Mode Control Method for High-Speed Linear Motion of Spherical Robot

“…For the second-order sliding mode control, if the sliding surface and its first and second derivatives are equal to 0, the motion error can converge to 0. Therefore, letS 1 = 0 andS 2 = 0, we can get the control laws of two subsystems, as shown in (24).…”

“…Fractional calculus is an arbitrary order of ordinary derivatives and integrals. The application of fractional calculus can help eliminate external interference and steady-state error, improve convergence speed and trajectory tracking performance of the spherical robot during linear motion [23], [24]. Some studies use the control method that incorporates fractional calculus, but the adaptivity of this control method is not considered, and only simulation results are given [25].…”