Abstract
The focus of this paper is on the design of input shapers for systems with uncertainties in the parameters of the vibratory modes which need to be attenuated. A probabilistic framework is proposed for the design of the robust input shaper, when the uncertain modal parameters are characterized by probability density functions. A convex chance constrained optimization problem is posed to determine the parameters of input shapers (time-delay filter) which can accommodate the users acceptable risk levels for a prescribed residual energy threshold. Robust input shapers are developed for various compact support distributions to illustrate the ability of the proposed formulation to synthesize input shapers which can satisfy a residual energy threshold with a given risk level. This problem formulation can conceivably reduce the conservative nature of worst case controllers which have to ensure that all realizations of the uncertain system have to satisfy a prescribed performance index. The chance constrained input shaper is designed for a spring-mass-dashpot system with three different distributions for the uncertain spring stiffness. Results provide encouragement for the extension of the proposed approach to multi-dimensional and multi-model uncertainties.
Published Version
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