Design, modeling, and experimental validation of a fully decoupled piezoelectrically actuated compliant nano-positioning stage

Abstract This paper presents the design, modeling, and experimental validation of a fully decoupled piezoelectrically actuated compliant nano-positioning stage (CNS). To accurately capture the stiffness and dynamic behavior characteristics of the stage, an adaptive triangular finite element modeling strategy is introduced, which integrates both rigid bodies and flexure hinges into a globally partitioned mesh framework with regionally optimized mesh densities. In the static model, the direct relationship between applied forces and resulting displacements is established via the stiffness characteristics of the stage. In the dynamic model, natural frequencies are derived by solving the eigenvalue problem formed from the stiffness and equivalent modal mass matrices. Thus, the proposed modeling approach can accurately predict both the working stroke and natural frequencies of the piezoelectrically actuated CNS. The analytical model is further verified by comparing its results with those obtained from finite element analysis (FEA). The final stiffness estimation obtained using this method exhibits only a 7% deviation compared to conventional FEA results, demonstrating its validity and reliability. The experimental evaluation reveals that the proposed modeling technique offers a substantial improvement in prediction accuracy relative to prior methods. Moreover, to further reduce motion errors caused by actuator hysteresis and external interferences, a composite control architecture combining PID regulation and a disturbance observer is developed. The system achieves a tracking error of 2.75% for a 100 Hz sinusoidal waveform motion with 4 μ m amplitude.