5. ANKARA INTERNATIONAL AEROSPACE CONFERENCE AIAC August METU, Ankara TURKEY

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1 5. ANKARA INTERNATIONAL AEROSPACE CONFERENCE AIAC Augut METU, Ankara TURKEY ACTIVE VIBRATION SUPPRESSION OF A SMART BEAM VIA SELF-SENSING PIEZOELECTRIC ACTUATOR Uğur Arıdoğan 1 Havelan Ankara, Turkey Melin Şahin 2 Middle Eat Technical Univerity Ankara, Turkey Volkan Nalbantoğlu 3 Aelan Ankara, Turkey Yavuz Yaman 4 Middle Eat Technical Univerity Ankara, Turkey ABSTRACT In thi aer, an active vibration ureion of a mart beam uing elf-ening iezoelectric actuator i reented. The mart beam i comoed of a cantilever aluminium beam with four urface-bonded iezoelectric atche ymmetrically located both ide of the beam. Piezoelectric material can tranform mechanical deformation to electric ignal and vice vera. Thi roerty of iezoelectric material enable them to be ued a an actuator and a enor. In elf-ening actuator configuration, the iezoelectric material can be ued a an actuator and a enor imultaneouly. A ecial bridge circuit i ued to decomoe actuator and enor ignal. Thi bridge circuit include the electrical model of the iezoelectric material and in general iezoelectric material i modelled a a voltage ource with a erie caacitor or a charge ource with a arallel caacitor. In our tudy, thi bridge circuit i deigned and built for voltage ource model of iezoelectric material. Following thi, frequency reone of the ytem i obtained by uing iezoelectric atche a a elf-ening actuator. Then, analytical ytem model i obtained from the meaured frequency reone and robut controller i deigned for the active vibration control of mart beam. Finally, both free and the firt reonance frequency forced vibration reult of oen and cloed loo are reented. INTRODUCTION Severe tructural vibration can damage comonent of aeroace vehicle becaue of their aeroelatic roertie. In order to ure tructural vibration of aeroace tructure, active vibration control method are invetigated and alied by cientit and engineer. The technological advance in iezoelectric material motivated cientit and engineer to ue thee material in the area of active vibration control. The atomic lattice tructure of iezoelectric material rovide the tranformation of mechanical deformation to electric ignal and vice vera. Thi roerty of iezoelectric material enable them to be ued an actuator and a enor in active vibration control. In the former reearch tudie in the Deartment of Aeroace Engineering of METU, iezoelectric material are ued a enor and actuator for active vibration ureion of cantilever beam-like and late-like tructure. In the tudie where iezoelectric material are ued a actuator, train gauge and laer dilacement enor are choen a ening device. [3,4]. Following thee reearch activitie, iezoelectric material are alo emloyed a enor to invetigate vibration characteritic of mart beam [2] a an initiative tudy for an active vibration ureion of mart beam via iezoelectric enor and actuator [1]. In thi tudy, on the other hand, elf-ening iezoelectric actuator i conidered for the active vibration control of mart beam. For thi uroe, at firt, a ecial bridge circuit i deigned and built to decomoe actuator and enor ignal of elf-ening iezoelectric actuation. After thi, frequency reone of the ytem i obtained by uing thi elf-ening iezoelectric actuator. Having acquired the analytical model from the meaured frequency reone, robut controller i deigned for the active vibration control of mart beam. Finally, free and the firt reonance frequency forced vibration reult of oen and cloed loo are reented. 1 Aeroace Engineer in STS Grou, maridogan@havelan.com.tr 2 At. Prof. in Deartment of Aeroace Engineering, mahin@metu.edu.tr 3 Aeroace Engineer in MGEO Diviion, vnalbant@mgeo.aelan.com.tr 4 Prof. in Deartment of Aeroace Engineering, yyaman@metu.edu.tr

2 SMART BEAM The mart beam (Figure 1) conit cantilever aluminium beam ( mm) with eight urface bonded SenorTech - BM500 ( mm) PZT (Lead - Zirconate -Titanate) atche (Figure 2). A thin iolation layer i laced between the aluminium beam and iezoelectric atche o that each iezoelectric atch may be emloyed a a enor and an actuator indeendently. In our tudy, iezoelectric atche are labelled according to their oition on each urface of the aluminium beam (Figure 3). In order to have more actuation ability, iezoelectric atche (1A-1B and 4A-4B) are configured a bimorh and ued a elf-ening actuator. Figure 1: Smart Beam Figure 2: SenorTech - BM500 PZT Patch Figure 3: Piezoelectric Patche on Smart Beam SELF SENSING PIEZOELECTRIC ACTUATOR CONFIGURATION Our aim i to ue four of the iezoelectric atche imultaneouly a a enor and an actuator for the active vibration control. Piezoelectric material generate electrical ignal when they are under mechanical tre. Thi roerty of iezoelectric material enable them to be ued a a enor. On the other hand, iezoelectric material are mechanically deformed when electric field i alied to them. In conequence of thi roerty, iezoelectric material can be alo ued a actuator [6]. Beide thee, a iezoelectric material can be imultaneouly ued a a enor and an actuator when actuation and ening ignal are decomoed. For thi uroe, a ecial bridge circuit can be ued [5,7]. The bridge circuit hown in Figure 4 include the electrical model of the iezoelectric material with additional circuit element. The iezoelectric material i modelled a a voltage ource (V P ) with a erie caacitor (C P ). When the value of caacitor (C 1 and C 2 ) and reitor (R 1 and R 2 ) are elected a identical, and the amount of caacitance (C A ) i et to caacitance of iezoelectric material, the ubtraction of the voltage V 1 and V 2 indicate the ening ignal (V S ) indeendent from actuation ignal (V A ). 2 Ankara International Aeroace Conference

3 Figure 4: Bridge Circuit for Self-Sening Actuator The relationhi between the iezoelectric voltage (V P ) and the ening ignal (V 2 V 1 ) i determined by alying Kirchhoff current and voltage law. Equation 1 how the Lalace tranform of the ubtraction of voltage V 2 and V 1. V C R C R C R V2 V1 V (1) ) A Va Va 1 ( C2R2 C AR2 ) 1 ( C1R1 C R1 ) 1 ( C1R1 C R1 In Equation 1, the ening ignal become indeendent from actuation ignal when the following equilibrium are atified. C A C, C C and R R (2) The ening voltage i obtained by auring the condition in Equation 2. V C R V2 V1 V (3) ) 1 1 ( C1R1 C R1 The ening ignal in Equation 3 i the high-a filtered form of the iezoelectric material voltage. The cut-off frequency of thi high-a filter i determined by election of reitance and caacitance value. In order to cature low frequency dynamic of the ytem, the cut-off frequency of the high a filter hould be ket very low. In our tudy, the total caacitance of the iezoelectric atche (1A-1B-4A-4B) i meaured a 75 nf. The value of reitance and caacitance are elected a 3.3 MΩ and 72 nf. In addition to thee, the amount of caacitance (C A ) i adjuted in order to atify the Equation 2. VIBRATION CHARACTERISTICS OF SMART BEAM Uing the elf-ening iezoelectric actuator, the mart beam i excited with the inuoidal ignal within in the bandwidth of 2 Hz -115 Hz while the reone of mart beam i meaured uing enor voltage acquired by the bridge circuit. The frequency reone of the ytem i then obtained uing Brüel & Kjaer PULSE latform from the decomoed actuation and ening ignal. A linear model of the ytem i fitted to the meaured frequency reone by uing leat quare algorithm in MATLAB R2007b [8] and reented in Figure 5. The correonding eight order tranfer function including the firt three reonance mode of the ytem and the coefficient of thi function are given in Equation 4 and Table 1 reectively. 3 Ankara International Aeroace Conference

4 Figure 5: Exerimental Frequency Reone and Linear Model for Smart Beam uing Self-Sening Piezoelectric Actuator G( ) a (4) b0 b1 b2 b3 b4 b5 b6 b7 b8 Table 1: Coefficient of Tranfer Function G() Coefficient Value Coefficient Value a x 10-1 b a x 10 2 b x 10 2 a x 10 5 b x 10 5 a x 10 8 b x 10 8 a x b x a x b x a x b x a x b x a x b x DESIGN OF ROBUST CONTROLLER In thi ection, the deign of robut controller for ureion of free and the firt reonance frequency forced vibration i exlained. The objective of robut controller i to minimize H-infinity norm of tranfer function between the ytem inut and ytem outut. The block diagram ued for deign of robut controller i given in Figure 6. In thi diagram, ytem and controller block are hown with the weighted erformance and uncertainty block. The high frequency dynamic of the ytem are comried in the multilicative uncertainty block (W m ). The diturbance weight (W d ) and noie weight (W n ) are alo included. In addition to thee, exected ytem erformance i alo conidered within the erformance block (W P ). 4 Ankara International Aeroace Conference

5 Figure 6: Block Diagram of Robut Controller The diturbance, erformance and uncertainty block are deigned in order to have a table and effective ureion of free and the firt reonance frequency forced vibration. The frequency reone of oen and cloed loo are hown in Figure 7. Alying robut controller, a coniderable reduction (4 db) in the firt mode i achieved for the elf-ening iezoelectric actuator. Figure 7: Frequency Reone of the Oen Loo and Cloed Loo EXPERIMENTAL SETUP Robut controller i alied to ure vibration of the mart with the exerimental etu hown in Figure 8. In thi etu, four-channel rogrammable controller i included with actuator and enor voltage. The outut of rogrammable controller (actuator voltage) i amlified 30 time with the SenorTech SA10 high voltage amlifier. Thi high voltage amlifier i owered by SenorTech SA21 high voltage ower uly. Beide thee, the exerimental etu contain the elf-ening circuit ued for decomoition of actuator and enor ignal. A mentioned above, iezoelectric atche (1A- 1B and 4A-4B) are ued a elf-ening actuator. Meanwhile, the vibration of the mart beam i alo monitored by iezoelectric atch 2A. Brüel & Kjaer PULSE latform i ued to record the voltage meaurement from thi iezoelectric atch 2A. 5 Ankara International Aeroace Conference

6 Figure 8: Exerimental Setu EXPERIMENTAL RESULTS OF ACTIVE VIBRATION CONTROL The iezoelectric atche on urface of cantilever-beam like tructure are ued a elf-ening actuator to ure free and forced vibration. Active vibration control i archived by uing four iezoelectric atche a elf-ening actuator. During the exeriment, another iezoelectric atch, 2A, i alo ued to monitor the vibration of the mart beam. For cantilever-beam tructure, maximum curvature at the clamed-end correond with the maximum ti dilacement in the firt bending mode. Therefore, monitoring of voltage of iezoelectric atch 2A reflect the ti dilacement of mart beam for the free and firt reonance forced vibration. Sureion of Free Vibration At the firt art of active vibration control, analye of oen-loo and cloed-loo time reone are erformed by alying a 6 mm initial ti dilacement with zero initial ti velocity which correond aroximately to 600 mv monitored voltage of atch 2A. The oen-loo time reone are obtained when robut controller via elf-ening actuator i inactive while the cloed-loo time reone are acquired when robut controller via elf-ening actuator i active. Correonding time reone are given in Figure 9. Figure 9: Oen and Cloed Loo Time Reone of Free Vibration (Monitored by Piezoelectric Patch 2A) 6 Ankara International Aeroace Conference

7 Sureion of Forced Vibration At the econd art of active vibration control, analye of oen-loo and cloed-loo time reone are erformed by alying a 150 V(-) inuoidal ignal to bimorh configured iezoelectric atche (3A and 3B) at the firt reonance frequency (7 Hz). Similar to the ureion of free vibration reult, the oen-loo time reone correond to the ituation where the robut controller via elfening actuator i inactive wherea the cloed-loo time reone correond to the active robut controller via elf-ening actuator. Correonding forced-vibration time reone are given in Figure 10. Figure 10: Oen and Cloed Loo Time Reone of Firt Mode Forced Vibration (Monitored by Piezoelectric Patch 2A) CONCLUSION In thi tudy, elf-ening iezoelectric actuator i ued for an active vibration ureion of the mart beam with robut controller which i deigned for the table and the effective ureion of free and the firt reonance forced vibration. For the free vibration ureion, reduction of one-quarter of the maximum voltage take more than 13 econd at the oen-loo, however at the cloed-loo, ureion of free vibration to the onequarter of the maximum voltage take only 7 econd. In the cae of forced vibration ureion, the monitored voltage at cloed-loo i half of the monitored voltage at oen-loo. Thi mean that the robut controller via elf-ening actuator can ure half of the amlitude of vibration in the forced vibration. A a concluion, with thi tudy, active vibration control of a mart beam i achieved with emloyment of iezoelectric atche a elf-ening actuator via deigned robut controller. The exerimental work erformed on the ureion of free and forced vibration how the effectivene of thee elfening actuator with the robut controller. Reference [1] U. Arıdoğan, M. Şahin, V. Nalbantoğlu, and Y. Yaman, "Piezoelektrik Yamaların Akıllı Bir Kirişin Titreşim Kontrolünde Algılayıcı ve Uyarıcı Olarak Kullanılmaı", UMTS2009, 14. Ulual Makina Teorii Semozyumu, Güzelyurt, KKTC, , July [2] U. Arıdoğan, M. Şahin, V. Nalbantoğlu, and Y. Yaman, "Piezoelektrik Yamaların Akıllı Bir Kirişin Titreşim Özelliklerinin Bulunmaında Algılayıcı Olarak Kullanılmaı", XVI. Ulual Mekanik Kongrei, Kayeri, June [3] M. Şahin, F. M. Karadal, Y. Yaman, O. F. Kırcalı, V. Nalbantoğlu, D.F. Ülker, and T. Çalışkan, "Smart Structure and Their Alication on Active Vibration Control: Studie in the Deartment of Aeroace Engineering, METU ", Journal of Electroceramic, vol. 20, , [4] O. F. Kırcalı, Y. Yaman, V. Nalbantoğlu, M. Şahin, F.M. Karadal, and F. D. Ülker, "Satial Control of a Smart Beam", Journal of Electroceramic, vol. 20, , Ankara International Aeroace Conference

8 [5] A. S. Putra, S. Huang, K. K. Tan, S. K. Panda and T. H. Lee, "Self-ening Actuation with Adative Control in Alication with Switching Trajectory", IEEE/ASME Tranaction on Mechatronic, vol. 13, , 2008 [6] J. Yang, "An Introduction to the Theory of Piezoelectricity", vol. 9. New York: Sringer, [7] W. Zhang, Qiu, J., and Tani, J., "Robut Vibration Control of a Plate Uing Self-Sening Actuator of Piezoelectric Patche", Journal of Intelligent Material Sytem and Structure, vol. 15, , [8] G.J. Bala, J.C. Doyle, K. Glover, A. Packard and R. Smith, μ-analyi and Synthei Toolbox for ue with MATLAB, MATLAB Uer Guide Verion 3,.47, Natick, MA. June Ankara International Aeroace Conference