Vibration suppression in smart structures using fractional order PD controllers

Abstract

Several important domains, such as the aerospace industry, are confronted with problems related to vibration. The solutions for reducing these vibrations are numerous, but are limited to a large number of passive methods, while the active solutions involve classical and intelligent control techniques. The present paper proposes a fractional order PD controller, for which the control parameters are computed in order to directly limit the vibrations at the resonance frequencies. The case study consists in a beam containing smart sensors and actuators using piezoelectric materials. The simulation results, considering both free and forced vibrations responses of the smart beam, show that the proposed method is simple and leads to an improvement of the closed loop behavior.

A Comparison between Integer and Fractional Order PD μ Controllers for Vibration Suppression

“…In the case of smart beam vibration suppression, fractional order PID controllers were proposed [11,12] with good results, as well as fractional order PD controllers [13][14][15]. In the case of the fractional PID, its complexity represents a great disadvantage since there are five parameters that need to be tuned leading to solving a system of minimum five equations [16].…”

Vibration suppression with fractional-order PIλDμ controller

“…This novel tuning approach is based on solving a set of nonlinear complex equations that directly aim at reducing the resonant peak, rather than the very simple tuning procedure used in [11], which is based on a trial and error method for selecting the optimal fractional order controller parameters. A similar approach to the one proposed in this paper has been used for the tuning of a fractional order PD controller [2]. In this paper, a fractional order PID controller is used instead.…”

“…In this paper, a fractional order PID controller is used instead. Additionally, the proposed fractional order PID controller is also tested experimentally, rather than considering solely Matlab simulations as in [2].…”

“…Previous research on active vibration suppression in smart beams include direct proportional feedback, constant gain velocity feedback and constant amplitude velocity feedback control, optimal control strategies [3], [4], [5], [6]. One of the major issues associated with these control strategies is that they are highly sensitive to modeling errors and require an exact mathematical model of the smart beam [2]. A better choice from this point of view consists in the robust control strategies due to their intrinsic ability of ensuring a robust closed loop behavior, despite modeling uncertainties and estimation errors [7].…”

“…This justifies the need of advanced controller usage. The closed loop performance of smart structures depends considerably upon the choice of the control algorithm [2]. Previous research on active vibration suppression in smart beams include direct proportional feedback, constant gain velocity feedback and constant amplitude velocity feedback control, optimal control strategies [3], [4], [5], [6].…”