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This paper presents an adaptive proportional-integral-derivative fractional-order nonsingular terminal sliding mode (PID-FONTSM) control for the cable-driven manipulators using time-delay estimation (TDE). The proposed control uses TDE technique to obtain the lumped system dynamics and brings in an effective model-free structure. Then, a PID-FONTSM surface is designed to further enhance the control performance. The proposed PID-FONTSM surface uses the FONTSM error dynamic as its inner loop and utilises a PID-type surface with FONTSM variable as its outer loop. Benefitting from this structure, the proposed PID-FONTSM surface enjoys the advantages from both PID and FONTSM simultaneously. Afterwards, an adaptive algorithm is developed, to timely and precisely regulate the control gain for the robust term. The proposed control method is model-free, highly accurate and essentially continuous thanks to the TDE technique and developed PID-FONTSM surface and adaptive algorithm. The stability of the closed-loop control system under TDE and PID-FONTSM dynamics is proved using Lyapunov stability theory. Finally, comparative simulations were conducted to verify the effectiveness and superiorities of our proposed control method over the existing methods. [ABSTRACT FROM AUTHOR]

Parallel micropositioning piezostages are widely used in the micro-/nano-manipulation applications, but also subject to the nonlinear disturbances, like hysteresis, creep and cross-coupling effects. In this paper, a new fractional robust adaptive decoupled control (FRADC) is synthesized for a six-axis parallel micropositioning piezostage to improve the positioning accuracy. The proposed FRADC contains three intuitional terms: (1) a decoupling term that alleviates the coupled motions among different axes, making the controller implementation more convenient and efficient; (2) a feedforward compensation term based on a fractional normalized Bouc-Wen (FONBW) model, compensating for the rate-dependent hysteresis effect induced by the piezoelectric actuators; (3) a feedback model reference adaptive control (MRAC) term with fractional proportional-plus-integral-type updating rules that suppresses the creep effect, parameters uncertainty and external disturbances, further enhancing the robustness and positioning accuracy. The stability of the closed-loop system is analyzed in theory. The effectiveness of the proposed FRADC is experimentally validated by comparing with the standalone inverse-FONBW-based feedforward control, the standalone feedback fractional MRAC, and the traditional integer-order control methods. Results demonstrate that the proposed FRADC can guarantee higher positioning accuracy for the piezostage system in wider control bandwidth. [ABSTRACT FROM AUTHOR]