Polynomial Chaos-based Input Shaper Design under Time-Varying Uncertainty

TL;DR

This paper introduces a polynomial chaos expansion method for designing input shapers that are robust to time-varying uncertainties in dynamical systems, validated through simulations showing improved efficiency over Monte Carlo methods.

Contribution

It develops an intrusive polynomial chaos expansion approach for input shaper design under time-varying uncertainty, enhancing robustness and efficiency.

Findings

Achieves vibration mitigation with similar accuracy to Monte Carlo methods

Demonstrates higher computational efficiency in simulations

Validates approach on spring-mass system with varying stiffness

Abstract

The work presented here investigates the application of polynomial chaos expansion toward input shaper design in order to maintain robustness in dynamical systems subject to uncertainty. Furthermore, this work intends to specifically address time-varying uncertainty by employing intrusive polynomial chaos expansion. The methodology presented is validated through numerical simulation of intrusive polynomial chaos expansion formulation applied to spring mass system experiencing time-varying uncertainty in the spring stiffness. The system also evaluates non-robust and robust input shapers through the framework in order to identify designs that minimize residual energy. Results indicate that vibration mitigation is achieved at a similar accuracy, yet at higher efficiency compared to a Monte Carlo framework.