Optimal negative derivative feedback controller design for collocated systems based on [formula omitted] and [formula omitted] method

Abstract

In this paper, a direct procedure is presented in order to design negative derivative feedback (NDF) controller for collocated systems. Collocated systems have embedded sensors and actuators, which have an alternating poles and zeroes in frequency domain, which creates asymptotic stability. NDF is a band-pass filter, cutting off the control action far from the natural frequencies associated with the controlled modes, which reduces the spillover effect. Since it is a band-pass filter, it can effectively control the lower and higher frequency disturbances. Also, it is very efficient controller for higher frequencies’ vibration mitigation. An approach for an optimal design of NDF controller to implement on collocated system is presented. A simple, collocated system is considered and a mode of it is targeted to damp. Maximum damping method is used to extract all of the controller constants dependent on closed-loop damping value. Afterward, H2 and H∞ methods are utilized to determine the closed-loop damping value optimally. The results show that NDF not only can easily damp the targeted mode impactfully but also can reduce some level of vibrations in the modes after that as well. This shows the power of NDF filter on vibration mitigation of modes located in a band of frequency. The proposed method is applicable for any general system and for any zero/pole patterns of collocated system, easily. It can be applied for any collocated system with zero before pole pattern or zero after pole pattern.