Command shaping control with robustness and smoothness adjustability for time-variant systems

Abstract

A new command-shaping technique for vibration control is proposed to command a time-variant system from a known initial state to a predefined target state without inducing residual vibration and independently of the time-varying system parameters. Shaped commands based on equally-spaced steps, monomial functions, and Fourier basis are constructed to satisfy predefined system constraints and input targets while accommodating the parameter variations during the maneuver. Unlike classical input shapers with fixed duration, the proposed method features an adjustable maneuver time that enables a balance between motion speed and transient vibration reduction. The shaped commands are obtained by solving simultaneous linear equations without the need for optimization. The proposed formulations are compared with robust classical shapers and validated numerically and experimentally on a pendulum system with linear and nonlinear hoisting/lowering maneuvers. The added time penalty associated with using smooth robust shaped inputs is negligible relative to the significant reduction in transient vibrations, the complete suppression of residual vibrations, and the improved robustness under parameter uncertainties.