Rigorous treatment of wave‐based control concept, structured procedures and critical observations

Abstract

The concept of wave-based control (WBC) has been around for about two decades. It is designed primarily for controlling the end-point motions of one-dimensional lumped mass flexible chains. The systems under consideration are, therefore, severely underactuated. Typical control objective for such systems is a point-to-point motion without unwanted residual oscillations. These oscillations, however, become troublesome especially for the lightly damped cases. The only way to attenuate them is to ‘shape’ the control input. For this WBC concept considers a set of hypothetical (forward and backward) motion waves, which combine to form the actual motions. This document critically investigates wonderful properties of WBC which are claimed over the years and presents a completely new mathematical and rigorous treatment of the method. We rectify several misconceptions, especially on the level of a priori knowledge which is required on the system dynamics. Second, the authors present a novel step-by-step procedure to design a WBC law which ultimately leads to a number of opportunities for future explorations. Finally, the necessary and sufficient conditions in system parameter space for the stability of WBC are rigorously elucidated for the first time in the literature to the best of our knowledge.