(untitled) (ASEAN Engineering Journal, 2025)
Suppression of residual vibrations in position control of flexible systems is a challenging problem, especially in the presence of high nonlinearities or diverse operating points. Input shaping, a technique for designing shaped commands to minimize system residual vibration during point-to-point movements, is crucial. Traditional input shapers like zero-vibration and zero-vibration-and-derivative shapers, designed based on the superposition principle, perform well for linear systems but have limitations in highly nonlinear systems. This paper revisits nonlinear input shapers, including three-impulse and robust shapers, providing a comprehensive energy-based analysis. Additionally, a novel fast three-impulse shaper is proposed to improve the time-delay of traditional input shapers. The amplitudes and time locations of all designed shapers are proven in the same closed-form solution for the undamped case, suitable for analyzing sensitivity to variations in plant parameters. Demonstrations on a two-mass flexible system with nonlinear spring and damper show that the proposed fast-three shaper outperforms the two-impulse shaper in robustness, with similar performance in rise time. However, robust shapers, while slower, exhibit superior robustness as increasing impulse numbers decrease residual total energy. The effect of nonlinear damping force is demonstrated in simulations, providing suggestions for designing robust shapers for damped flexible systems.