Wave-based control of planar motion of beam-like mass-spring arrays

Wave-based control (WBC) is a simple and relatively new technique for motion control of under-actuated flexible systems. To date it has been mainly applied to rectilinear lumped flexible systems. The current work focuses on a development of WBC to control two-dimensional beam-like structures in which an actuator, attached to one end, acts to translate and rotate the structure through an arbitrary path in the plane. In this work, first a lumped model of a beam is developed using mass-spring arrays. The lumped beam model is of interest here as a benchmark control challenge. It can also be considered as a model of various lumped or distributed mass structures. To check the latter, the mode shapes and frequencies are first compared with those of classical beam theory. This involved a new technique to find mode shapes and frequencies for arrays. The control strategy is then presented and tested for a range of manoeuvres. As a system to be controlled, the mass-spring array presents many challenges. It has many degrees of freedom, many undamped vibration modes, is highly under-actuated, and sensing of system states is difficult. Despite these challenges, WBC performs well, combining a fairly rapid response with active vibration damping and zero steady-state error. The controller is simple to implement and of low order. It does not need or use any system model and is very robust to system changes. (C) 2017 Elsevier B.V. All rights reserved.