Final-state control for a system with load displacement-dependent stiffness in a two-inertia system - Mitsuo HIRATA; Rikuto NOMURA; Masayasu SUZUKI; Hiroshi ARAYA; Yoichi IGARASHI (Mechanical Engineering Journal, 2025)
Actuators capable of performing both rotational and vertical movements are being developed in the manufacturing industry to enhance the area productivity. These actuators exhibit nonlinear characteristics in which the torsional stiffness of the rotational axis changes with the vertical displacement, causing variations in the mechanical resonance frequency. Applying final-state control (FSC) to such nonlinear systems typically requires repeated calculations, resulting in a high computational load. However, if a system with a torsional stiffness that is dependent on the vertical displacement can be modeled as a time-varying system, repeated calculations become unnecessary. This study investigates the effectiveness of time-varying final-state control (TVFSC) for such actuators. An experimental setup simulating the actuator is constructed, and its performance is evaluated through simulations and experiments. First, FSC and frequency-shaped FSC (FFSC) inputs are designed based on a rigid-body model, demonstrating that while FFSC effectively suppresses residual vibrations, it increases the feedforward (FF) input amplitude compared to FSC. Furthermore, when the FFSC input is designed to have the same amplitude as the FSC input, the positioning time increases, revealing a trade-off between vibration suppression and FF input amplitude. In contrast, the TVFSC input maintains a waveform nearly identical to that of the FSC input while avoiding an increase in amplitude. Experimental results confirm that, although the TVFSC input does not completely eliminate residual vibrations as in simulations, it achieves vibration suppression comparable to FFSC. Moreover, TVFSC eliminates the need for trial-and-error tuning for frequency shaping, making it more practical for implementation. These findings suggest that TVFSC provides an effective and computationally efficient alternative to vibration-suppressed positioning control in actuators with displacement-dependent stiffness.