Optimal centralized and decentralized velocity feedback control on a beam

摘要

This paper considers the optimization of a velocity feedback controller with a collocated force actuator, to minimize the kinetic energy of a simply supported beam. If the beam is excited at a single location, the optimum feedback gain varies with the position of the control system. It is shown that this variation depends partly on the location of the control force relative to the exciting force. If a distributed excitation is assumed, that is random in both time and space, a unique optimum value of the feedback gain can be found for a given control location. The effect of the control location on performance and the optimal feedback gain can then be examined and is found to be limited provided the control locations are not close to the ends of the beam. The optimization can also be performed for a multichannel velocity feedback system. Both a centralized and a decentralized controller are considered. It is shown that the difference in performance between a centralized and a decentralized controller is small, unless the control locations are closely spaced. In this case the centralized controller effectively feeds back a moment proportional to angular velocity as well as a force proportional to a velocity. It is also shown that the optimal feedback gain can be approximated on the basis of a limited model and that similar results can be achieved.