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Improving the control performance of active vibration isolation systems is crucial to provide an ultra-quiet environment for precision instruments. This paper presents a new fractional-order robust model reference adaptive controller for the piezo-actuated active vibration isolation systems with a relative-degree-one model. One advantage of the proposed controller lies in that its controller parameters are adjusted online by fractional proportional–integral-type adaptive laws, which not only speeds up the convergence of the closed-loop system, but also improves the control energy efficiency. Moreover, the proposed controller only uses the measurable input and output of the plant as feedback signals, which is convenient for controller implementation. The stability of the closed-loop system is proved based on the Lyapunov theory in detail. The optimal values of the fractional order and adaptive gains for adaptive laws are determined using the multi-objective genetic algorithm through off-line simulation. Comparative experiments on the piezo-actuated active vibration isolation systems are conducted to verify the effectiveness of the proposed controller. Results show that the proposed controller achieves satisfactory isolation performance in a wider frequency band of 20–500 Hz, and simultaneously reduces the control effort compared with the traditional MRAC 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]