ACTIVE VIBRATION CONTROL FOR EULER-BERNOULLI
CANTILEVER BEAM
Ronaldo Carrion, rcarrion@sc.usp.br
University of São Paulo – São Carlos School of Engineering – Mechanical Engineering Department
Ivando S. Diniz, ivando@sorocaba.unesp.br
São Paulo State University, Control and Automation Engineering Department, Sorocaba
Ricardo Ferreira
São Paulo State University, Control and Automation Engineering Department, Sorocaba
Abstract. It is quite common in flexible structures analysis the needs of attenuating vibration to desired levels or even
to eliminate them. To achieve this goal, there are three control techniques: the passive, the active and the semi-passive
control. Active control uses external actuators, controlled by a loop in real time to eliminate or mitigate the forces
responsible for these vibrations. However for this technique to provide satisfactory results, there are several factors to
take into consideration, among them the type of actuator and sensor being used and the type of controller. There are
many studies related to this issue and one of them is the use of a piezoelectric material, which acts both as sensors and
actuators. These materials have some advantages like the little added weight to the structure, associated to good
performance. Most flexible structures are distributed parameter systems and therefore, problems with infinite
dimensions are not practical for control design, so some mathematical techniques are used to bring such systems to
finite dimensions, and one of the most used is the Finite Element Method. This paper proposes to model an Euler-
Bernoulli cantilever beam and incorporate the piezoelectric sensors and actuators dynamics, using the Finite Element
Method. It will be developed a control design, both in time and in frequency domains in order to compare the results
obtained by both approaches.
Keywords: Active Vibration Control, Finite Element Method, Modal Analysis
1. INTRODUCTION
Currently, due to the demands of quality and performance on the market, it becomes necessary the use of efficient
equipments and structures as well low-cost manufacturing, maintenance and operation. Accordingly, various researches
are focused on developing techniques for active vibration control. This technique use external actuators, in real time
control loop, which act to eliminate or to reduce the forces responsible for the undesirable vibrations. The active control
main idea is presented in Figure 1
Figure 1: Active control scheme.
However, for this technique to show satisfactory results, there are several factors to be considered, among them the
type of actuator and sensor used as well the type of controller. Thus there are many researches related to this issues and
one of them concerns piezoelectric material, which acts both as sensor or actuator. Some advantages of these materials
are the low weight added to the structure, combined to the fast response.
Most flexible structures are distributed parameters systems and these infinite-dimension problems are not practical
for control design, so some mathematical techniques are used to bring these systems to finite dimensions and one of the
most used is the Finite Element Method.
This paper proposes to model an Euler-Bernoulli cantilever beam as well to incorporate the piezoelectric sensors and
actuators dynamics using the Finite Element Method. Afterwards it will be developed a control design, both in the time
and in the frequency domains in order to compare the results obtained by them.
structure
controller
sensor actuator
ABCM Symposium Series in Mechatronics - Vol. 5
Copyright © 2012 by ABCM
Section II – Control Systems
Page 166