Model-free finite-time robust control using fractional-order ultra-local model and prescribed performance sliding surface for upper-limb rehabilitation exoskeleton

Abstract

To address the trajectory tracking issue of upper-limb rehabilitation exoskeleton with uncertainties and external disturbances, this paper proposes a fractional-order ultra-local model-based model-free finite-time robust controller (FO-FTRC) using predefined performance sliding surface. Different from previous model-free control strategies, a novel multi-input multi-output (MIMO) fractional-order ultra-local model which is a virtual model is proposed to approximate the complex uncertain nonlinear exoskeleton dynamics in a short sliding time window. This allows the design of controller to be independent of any exoskeleton model information and reduces the difficulty of controller design. The developed robust model-free control method incorporates a fractional-order quasi-time delay estimator (FO-QTDE), unknown disturbance estimator (UDE) as well as prescribed performance sliding mode control (PPSMC). The FO-QTDE is utilized to estimate the unknown lumped uncertainties which employs short time delayed knowledge only about the control input. However, the low-pass filter is always added for FO-QTDE when disturbances change fast, which leads to unavoidable estimation error. Then, UDE is designed to further eliminate the estimation error of FO-QTDE to enhance control performance. The PPSMC is constructed to converge sliding surface to zero in a finite time. Besides, the sliding surface is always limited in performance boundaries. After that, the overall system stability and convergence analyses are demonstrated by using the Lyapunov theorem. Finally, with the comparison to other methods of α-variable adaptive model free control (α-AMFC), time-delay estimation-based continuous nonsingular fast terminal sliding mode controller (TDE-CNFTSMC), time delay estimation (TDE)-based model-free fractional-order nonsingular fast terminal sliding mode control (MFF-TSM) and fractional-order proportion–differential (PDβ), the co-simulation results on 7-degree-of-freedom (DOF) iReHave upper-limb exoskeleton virtual prototype and experiment results on 2-DOF upper-limb exoskeleton are obtained to illustrate the effectiveness and superiority of the proposed FO-FTRC method.