JOURNAL OF AIRCRAFT Vol. 40, No. 2, March–April 2003 Vibration Control Using Fuzzy-Logic-Based Active Damping Kelly Cohen ¤ Israel Defence Forces, Tel Aviv 61909, Israel and Joseph Z. Ben-Asher † and Tanchum Weller ‡ Technion—Israel Institute of Technology, 32000 Haifa, Israel In this study a general approach is introduced for the design of a robust control law for suppression of structure borne vibration. This control law is based on a passive design in the form of dynamic vibration absorbers. Passive absorbers minimize vibration at a specic frequency, but their performance is improved by introducing adaptive tuning of the absorber. An adaptive dynamic vibration absorber is tuned to the forcing frequency, using classical methods. The tuning ratio is time varying and adapts itself to variations in the forcing frequency. However, the uniqueness of the approach in this study is that the damping parameter of the absorber is continuously varied by means of a fuzzy-logic control algorithm to provide a lower sound pressure level. The inputs of the fuzzy control law are the displacement and velocity of the main structure. The effectiveness of the control algorithm for active vibration control is demonstrated using MATLAB ® simulations of a single-degree-of-freedom plant. This methodology provides superior performance in the presence of signicant mistuning compared to a more conventional approach. I. Introduction A MAJOR issue in the cabin design of commercial transport air- craft concerns the reduction of noise for improved passenger comfort. Cabin noise usually results from either airborne sources, such as engine fan, propeller tones, propwash or engine exhaust noise, or from structure-bornesources such as engine spool imbal- ance. In additionto cabin noise, the precedingdisturbancescan also cause material fatigue. The sound pressure level can be attenuated by the incorporationof structural acoustic control. Structuralacousticcontrolcan be achievedby usinga passivede- sign like the passivedynamic vibrationabsorber(DVA). This device typically consists of a second-orderdynamic system comprising of mass, spring, and dash-pot elements (Fig. 1), whose main purpose is to transfer and dissipate the energy of the system, thereby reduc- ing the sound pressure level. George 1 reports on the introductionof DVAs for sound suppressionin C90B and King Air B2000 business aircraft. The DVAs, tuned to the low-frequencystructural vibration that results from the turboprop engines, provided 17-dB noise re- duction in the center of the C90B cabin. The main drawback of this approach is that the DVA is effective only in the immediate vicinity of its tuned frequency, whereas in practice there are uctuations in the frequency of vibration that can result from the throttling of the engines. The controller proposed by Ryan 2 acts to alter the stiffness of the adaptive absorber (see schematic conguration in Fig. 2). The accelerometer mounted on the main system mass provides an ac signal that is fed through a frequency-to-voltageconverter. The dc output of the converter,which is proportionalto the frequencyof the input signal,yields the desiredtuned frequencyof the absorber.The desired stiffness k 2 is then determined from the value of the desired tuned frequency. The error between the desired stiffness and the actual stiffness is then fed back to alter the length of a variable Received 9 February 2001; revision received 22 July 2002; accepted for publication 1 August 2002. Copyright c ° 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose- wood Drive, Danvers, MA 01923; include the code 0021-8669/03 $10.00 in correspondence with the CCC. ¤ Ofcer. † Associate Professor, Department of Aerospace Engineering. Associate Fellow AIAA. ‡ Professor and Dean, Department of Aerospace Engineering. Associate Fellow AIAA. length cantilever-typeabsorber that utilizes a length change in the beam to alter the absorber stiffness. More details of the actuation mechanism are provided by Ryan. 2 The case for a tunable passive vibration absorber has led to hardware solutions such as a discrete stiffness spring proposed by Walsh and Lamancusa. 3 A promising hardware design, intro- duced by Davis and Lesieutre, 4 incorporates a shunted piezoce- ramic inertial actuator.The electrical tuning of this absorber,which changes the mass or stiffness of the device, is enabled by the piezo- electromechanical coupling. The electromechanical properties of the piezoceramic forcing element within the adaptive absorber in conjunction with an external passive electrical shunt circuit can be used to alter the natural frequency and damping of the device. The natural frequency of the device can be altered by capacitive shunt- ing, whereasresistiveshuntingaltersboth the naturalfrequencyand damping. II. Objective of This Study This research effort addresses the incorporation of an adaptive vibration absorber in which continuous tuning of the damping pa- rameter of the absorber is achieved by a fuzzy-logic control (FLC) algorithm. The main objective of this study is to determine the ef- fectivenessof the developedmethodology,basedon numericalsim- ulations of an experimental model used to test adaptive absorbers. 2 The performance robustness and the closed-loop performance of the developed approach are examined by comparing the simulation results with those obtainedusing the approachsuggestedby Ryan. 2 The main reasons for selecting variable damping and fuzzy logic are also explained. The current effort does not go into the details of hardware imple- mentation. A schematic description of the proposed conguration is providedin Fig. 3. The displacementand the velocity of the main system mass are measured. Based on these two sensor readings, the desired values for the variable stiffness k 2 and the variable damping coefcient c 2 are calculated as follows: 1) The forcing frequency is extracted from the sensor readings, and, using Den Hartog’s tuning scheme described next, the desired value of k 2 is calculated. 2) The sensor readings are fed into the adaptive fuzzy control algorithm (AFCA) as inputs. The output of this algorithm is the desired value of the variable damper c 2 . Finally the errors between the desired and the actual value of the preceding design variables are fed back to direct the respective 384