A Fast Finite-Time Composite Control With Dynamic Prescribed Performance for Tracking in Task Space of Stewart Parallel Mechanism

To improve tracking control performance in the task space of the Stewart parallel mechanism (SPM) with uncertainties of modeling errors and external disturbances in our developed rust removal sandblasting robot for steel box girder, a fast finite-time composite control method with dynamic prescribed performance (DPP) is proposed. Firstly, by introducing only one exponential power regulation term with a variable exponent coefficient (VEC) into Lyapunov differential inclusion, a VEC finite-time stability theorem for the multi-input multi-output nonlinear system is proposed. Secondly, based on the proposed theorem, a VEC finite-time disturbance observer and a VEC finite-time super-twisting control are respectively designed and combined into a fast finite-time composite control, to enhance system robustness and achieve fast and smooth finite-time convergence for SPM tracking in task space. Finally, the fast finite-time composite control with DPP is formed by devising a dynamic asymmetric prescribed performance function and a modified barrier-function-based constraint transformation function and integrating them into the fast finite-time composite control, to effectively constrain the tracking error into small ranges under time-varying uncertainties, achieve non-overshoot transient performance and high steady-state tracking accuracy, provide continuous and smooth control input torque, and reduce input energy consumption. The effectiveness is validated by simulation and prototype experiments. Note to Practitioners—To improve the control performance of the Stewart parallel mechanism (SPM) with uncertainties of modeling error and external disturbances, a variable exponent coefficient (VEC) finite-time stability theorem is firstly proposed. On this basis, a VEC finite-time disturbance observer and a VEC finite-time super-twisting control algorithm are respectively designed and combined into a fast finite-time composite control method, in order to achieve fast and smooth bounded-time convergence performance for the SPM tracking in task space. Furthermore, a dynamic asymmetric prescribed performance function and a modified barrier-function-based constraint transformation function are respectively devised and introduced into the fast finite-time composite control, aiming to make it further realize non-overshoot transient performance while providing smooth and non-excessive control inputs and reducing input energy consumption.