External force estimation of a piezo-actuated compliant mechanism based on a fractional order hysteresis model

Sensing of external forces applied on piezo-actuated compliant mechanisms plays a key role in state monitoring, process control and feedback strategy design in a variety of fields, including micro-/nanopositioning, micro-/nanomanipulation, and micro-/nanomanufacturing. In this paper, a force estimation strategy is proposed by comparing the practically measured displacement with the estimated free one without external forces, when subjecting to any given actuation voltages. To have an accurate prediction of the free displacement relating to the actuation voltage, an improved fractional order model is proposed. With this model, the system response is decomposed into a basic linear component and a nonlinear hysteresis component, and the extracted hysteresis is then described by an ordinary fractional order differential model using a modified voltage signal as the model input, which extracts a linear time-delay component from the original voltage. Comparative study with other two differential type hysteresis models are experimentally conducted on a piezo-actuated bridge-type compliant mechanism, demonstrating well the effectiveness and superiority of the proposed model for both system response modeling and external force estimation.