A Structured Treatment of Wave-Based Control (WBC) and Discussions on Earlier Misconceptions

An interesting concept of wave-based control (WBC) has been around for about two decades now. Its core objective is to control the end- point motions of 1-D lumped mass flexible chains using one single base actuator and a motion sensor from the immediately adjacent mass. This severely underactuated mechanism is shown to achieve a benchmark point-to-point motion without (or with considerably attenuated) residual oscillations. WBC strategy is based on a set of hypothetical motion waves (in forward and backward directions) as the decomposition of physical motion of the masses. This paper revisits the concept in order to rectify several misconceptions, especially the earlier claim that such a control strategy can be created without any prior knowledge on the system dynamics. In particular the stability of the controlled system is revisited. Furthermore we offer one well-defined step-by-step procedures for formulating a WBC law and suggest vast opportunities for future explorations. An example parametric optimization pathway is also presented.