{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:22:32Z","timestamp":1785432152271,"version":"3.56.0"},"reference-count":77,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T00:00:00Z","timestamp":1659052800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A smart active vibration control (AVC) system containing piezoelectric (PZT) actuators, jointly with a linear quadratic regulator (LQR) controller, is proposed in this article to control transverse deflections of a wind turbine (WT) blade. In order to apply controlling rules to the WT blade, a state-of-the-art semi-analytical solution is developed to obtain WT blade lateral displacement under external loadings. The proposed method maps the WT blade to a Euler\u2013Bernoulli beam under the same conditions to find the blade\u2019s vibration and dynamic responses by solving analytical vibration solutions of the Euler\u2013Bernoulli beam. The governing equations of the beam with PZT patches are derived by integrating the PZT transducer vibration equations into the vibration equations of the Euler\u2013Bernoulli beam structure. A finite element model of the WT blade with PZT patches is developed. Next, a unique transfer function matrix is derived by exciting the structures and achieving responses. The beam structure is projected to the blade using the transfer function matrix. The results obtained from the mapping method are compared with the counter of the blade\u2019s finite element model. A satisfying agreement is observed between the results. The results showed that the method\u2019s accuracy decreased as the sensors\u2019 distance from the base of the wind turbine increased. In the designing process of the LQR controller, various weighting factors are used to tune control actions of the AVC system. LQR optimal control gain is obtained by using the state-feedback control law. The PZT actuators are located at the same distance from each other an this effort to prevent neutralizing their actuating effects. The LQR shows significant performance by diminishing the weights on the control input in the cost function. The obtained results indicate that the proposed smart control system efficiently suppresses the vibration peaks along the WT blade and the maximum flap-wise displacement belonging to the tip of the structure is successfully controlled.<\/jats:p>","DOI":"10.3390\/s22155691","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T23:49:27Z","timestamp":1659397767000},"page":"5691","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Smart Active Vibration Control System of a Rotary Structure Using Piezoelectric Materials"],"prefix":"10.3390","volume":"22","author":[{"given":"Ali","family":"Hashemi","sequence":"first","affiliation":[{"name":"Department of Civil, Environmental and Geomatics Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3657-698X","authenticated-orcid":false,"given":"Jinwoo","family":"Jang","sequence":"additional","affiliation":[{"name":"Department of Civil, Environmental and Geomatics Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shahrokh","family":"Hosseini-Hashemi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Iran University of Science and Technology, Tehran 13114-16846, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.compstruct.2018.11.060","article-title":"Semi-active nonlinear vibration control of a functionally graded material rotating beam with uncertainties, using a frequency estimator","volume":"210","author":"Salighe","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.jsv.2019.05.052","article-title":"Development of semi-active vibration control strategy for horizontal axis wind turbine tower using multiple magneto-rheological tuned liquid column dampers","volume":"457","author":"Sarkar","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"203003","DOI":"10.1109\/ACCESS.2020.3035611","article-title":"Utilizing nonlinear active vibration control to quench the nonlinear vibrations of helicopter blade flapping system","volume":"8","author":"Hamed","year":"2020","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"377","DOI":"10.2514\/1.C035607","article-title":"Experimental study on piezoelectric-stack-actuator-driven active vibration control of helicopter floor structure","volume":"57","author":"Meng","year":"2020","journal-title":"J. Aircr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"053001","DOI":"10.1088\/1361-665X\/ab7541","article-title":"Review on the use of piezoelectric materials for active vibration, noise, and flow control","volume":"29","author":"Shivashankar","year":"2020","journal-title":"Smart Mater. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Lang, K., Shang, L., Xia, P., and Song, L. (2022). An excellent harmonic feedforward-sliding mode output feedback hybrid algorithm for helicopter active vibration control. J. Vib. Control., 1\u201316.","DOI":"10.1177\/10775463221099350"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Martynowicz, P. (2021). Nonlinear optimal-based vibration control of a wind turbine tower using hybrid vs. magnetorheological tuned vibration absorber. Energies, 14.","DOI":"10.3390\/en14165145"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102938","DOI":"10.1016\/j.marstruc.2021.102938","article-title":"Passive control of jacket\u2013type offshore wind turbine vibrations by single and multiple tuned mass dampers","volume":"77","author":"Chen","year":"2021","journal-title":"Mar. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2784","DOI":"10.1177\/1077546319870933","article-title":"Active vibration control using piezoelectric actuators employing practical components","volume":"25","author":"Williams","year":"2019","journal-title":"J. Vib. Control."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Khan, A., and Kim, H.S. (2019). Active vibration control of a piezo-bonded laminated composite in the presence of sensor partial debonding and structural delaminations. Sensors, 19.","DOI":"10.3390\/s19030540"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wu, L., Huang, Y., and Li, D. (2021). Tilt active vibration isolation using vertical pendulum and piezoelectric transducer with parallel controller. Appl. Sci., 11.","DOI":"10.3390\/app11104526"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Huang, Z., Mao, Y., Dai, A., Han, M., Wang, X., and Chu, F. (2022). Active vibration control of piezoelectric sandwich plates. Materials, 15.","DOI":"10.3390\/ma15113907"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1177\/1077546320957533","article-title":"Active vibration control in human forearm model using paired piezoelectric sensor and actuator","volume":"27","author":"Hosseini","year":"2021","journal-title":"J. Vib. Control."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.rser.2015.05.078","article-title":"Performance enhancement of wind turbine systems with vibration control: A review","volume":"51","author":"Rahman","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mendoza, I., Hur, J., Thao, S., and Curtis, A. (2015). Power Performance Test Report for the Us Department of Energy 1.5-Megawatt wind Turbine, National Renewable Energy Lab. (NREL). Technical Report.","DOI":"10.2172\/1215120"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1016\/j.compstruc.2010.06.001","article-title":"Free vibration analysis of rotating Euler beams at high angular velocity","volume":"88","author":"Huang","year":"2010","journal-title":"Comput. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2997","DOI":"10.3390\/s130302997","article-title":"Vibration analysis of composite laminate plate excited by piezoelectric actuators","volume":"13","author":"Her","year":"2013","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1016\/j.ijnonlinmec.2011.03.017","article-title":"Non-linear modal analysis of a rotating beam","volume":"46","author":"Arvin","year":"2011","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/S0020-7683(97)00065-6","article-title":"A comprehensive analysis of the dynamics of a helicopter rotor blade","volume":"35","year":"1998","journal-title":"Int. J. Solids Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0022-460X(88)80024-5","article-title":"Flexural motion of a radially rotating beam attached to a rigid body","volume":"121","author":"Yigit","year":"1988","journal-title":"J. Sound Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"438","DOI":"10.2514\/3.20429","article-title":"Problem of the dynamics of a cantilevered beam attached to a moving base","volume":"12","author":"Hanagud","year":"1989","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"659","DOI":"10.2514\/3.20460","article-title":"Issues in the dynamics and control of flexible robot manipulators","volume":"12","author":"Baruh","year":"1989","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1115\/1.2896354","article-title":"On the modeling, and open-loop control of a rotating thin flexible beam","volume":"113","author":"Choura","year":"1991","journal-title":"J. Dyn. Syst. Meas. Control. Meas. Control"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Song, B., Jiang, Y., Huang, S., and He, W.-S. (2014, January 13\u201314). Study on the Wind-induced Dynamic Response of Wind Power Tower in Consideration of Fluid-structure Interaction. Proceedings of the International Conference on Mechanics and Civil Engineering (ICMCE-14), Wuhan, China.","DOI":"10.2991\/icmce-14.2014.57"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s11804-012-1139-9","article-title":"Numerical simulation of wind turbine blade-tower interaction","volume":"11","author":"Wang","year":"2012","journal-title":"J. Mar. Sci. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1007\/BF03184733","article-title":"Flapwise bending vibration analysis of rotating composite cantilever beams","volume":"18","author":"Lee","year":"2004","journal-title":"KSME Int. J."},{"key":"ref_27","first-page":"977","article-title":"Modal Behaviour of Vertical Axis Wind Turbine Comprising Prestressed Rotor Blades: A Finite Element Analysis","volume":"25","author":"Masoumi","year":"2017","journal-title":"Pertanika J. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1016\/j.renene.2019.07.131","article-title":"Dynamic modeling and free vibration analysis of horizontal axis wind turbine blades in the flap-wise direction","volume":"146","author":"Jokar","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Farsadi, T., \u015eener, \u00d6., and Kayran, A. (2017, January 3\u20139). Free vibration analysis of uniform and asymmetric composite pretwisted rotating thin walled beam. Proceedings of the ASME 2017 International Mechanical Engineering Congress and Exposition, Tampa, FL, USA.","DOI":"10.1115\/IMECE2017-70531"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Vurtur Badarinath, P., Chierichetti, M., and Davoudi Kakhki, F. (2021). A machine learning approach as a surrogate for a finite element analysis: Status of research and application to one dimensional systems. Sensors, 21.","DOI":"10.3390\/s21051654"},{"key":"ref_31","first-page":"V008T10A047","article-title":"Vibration analysis of vertical-axis wind-turbine blades","volume":"Volume 50206","author":"Afzali","year":"2016","journal-title":"Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1002\/we.2141","article-title":"Bend-bend-twist vibrations of a wind turbine blade","volume":"21","author":"Acar","year":"2018","journal-title":"Wind. Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s11803-019-0515-8","article-title":"Wind-induced instabilities and monitoring of wind turbine","volume":"18","author":"Wait","year":"2019","journal-title":"Earthq. Eng. Eng. Vib."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1017\/S000192400000960X","article-title":"Lagrangian formulation for the rapid estimation of helicopter rotor blade vibration characteristics","volume":"118","author":"Goulos","year":"2014","journal-title":"Aeronaut. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1177\/0954410016675891","article-title":"Modelling and analysis of coupled flap-lag-torsion vibration characteristics helicopter rotor blades","volume":"231","author":"Goulos","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part J. Aerosp. Eng."},{"key":"ref_36","first-page":"2523","article-title":"Modeling and Simulation of Nonlinear Dynamics of Helicopter Rotor Flapping Considering Offset, Blade Weight Moment and Frequency of Flapping","volume":"19","author":"Navabi","year":"2019","journal-title":"Modares Mech. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1177\/1099636217698443","article-title":"An analytical solution for bending, buckling and vibration responses of FGM sandwich plates","volume":"21","author":"Meksi","year":"2019","journal-title":"J. Sandw. Struct. Mater."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wang, B., Dai, X., Zhao, X., and Qian, Z. (2017). A semi-analytical solution for the thickness-vibration of centrally partially-electroded circular at-cut quartz resonators. Sensors, 17.","DOI":"10.3390\/s17081820"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1177\/0957456520901355","article-title":"Fundamental natural frequencies investigation for a typical 5-MW wind turbine blade","volume":"51","author":"Alsabagh","year":"2020","journal-title":"Noise Vib. Worldw."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.jsv.2018.10.011","article-title":"Dynamic analysis of rotating curved beams by using Absolute Nodal Coordinate Formulation based on radial point interpolation method","volume":"441","author":"Chen","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1177\/1077546315576431","article-title":"Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method","volume":"23","author":"Chen","year":"2017","journal-title":"J. Vib. Control."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.jsv.2017.03.026","article-title":"Investigations on bending-torsional vibrations of rotor during rotor-stator rub using Lagrange multiplier method","volume":"401","author":"Mokhtar","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"115204","DOI":"10.1016\/j.jsv.2020.115204","article-title":"Identification of blade operational mode shapes during wear of abradable coating","volume":"472","author":"Tang","year":"2020","journal-title":"J. Sound Vib."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"114961","DOI":"10.1016\/j.jsv.2019.114961","article-title":"Structural vibrations and acoustic radiation of blade\u2013shafting\u2013shell coupled system","volume":"463","author":"Liu","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1007\/s10483-019-2506-6","article-title":"Coupled flapwise-chordwise-axial-torsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation","volume":"40","author":"Zeng","year":"2019","journal-title":"Appl. Math. Mech."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2311","DOI":"10.1007\/s11012-020-01236-9","article-title":"Nonlinear vibrations of an extensional beam with tip mass in slewing motion","volume":"55","author":"Warminski","year":"2020","journal-title":"Meccanica"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/j.tws.2017.06.018","article-title":"Dynamics, vibration and control of rotating composite beams and blades: A critical review","volume":"119","author":"Rafiee","year":"2017","journal-title":"Thin-Walled Struct."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1088\/0964-1726\/9\/1\/311","article-title":"Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator","volume":"9","author":"Wang","year":"2000","journal-title":"Smart Mater. Struct."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1177\/1045389X14554134","article-title":"Analytical and experimental analysis of lamb wave generation in piezoelectrically driven timoshenko beam","volume":"26","author":"Shamshirsaz","year":"2015","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1007\/s00773-020-00705-w","article-title":"Investigation on semi-analytical solution of dynamic characteristics of an anti-pitching generating WEC (AG-WEC)","volume":"25","author":"Chen","year":"2020","journal-title":"J. Mar. Sci. Technol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1016\/j.mechmachtheory.2007.07.005","article-title":"High-order model and slide mode control for rotating flexible smart structure","volume":"43","author":"Huang","year":"2008","journal-title":"Mech. Mach. Theory"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jsv.2007.10.027","article-title":"PD control of a rotating smart beam with an elastic root","volume":"312","author":"Lin","year":"2008","journal-title":"J. Sound Vib."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1080\/15376494.2017.1387324","article-title":"Active vibration control of composite plate with optimal placement of piezoelectric patches","volume":"26","author":"Bendine","year":"2019","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.apacoust.2018.04.016","article-title":"Reduced order finite element formulations for vibration reduction using piezoelectric shunt damping","volume":"147","author":"Larbi","year":"2019","journal-title":"Appl. Acoust."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"04018049","DOI":"10.1061\/(ASCE)AS.1943-5525.0000853","article-title":"Active vibration control of an axially moving cantilever structure using PZT actuator","volume":"31","author":"Ma","year":"2018","journal-title":"J. Aerosp. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2721","DOI":"10.1177\/1077546319868883","article-title":"Active vibration control of a blade element with uncertainty modeling in PZT actuator force","volume":"25","author":"Sivrioglu","year":"2019","journal-title":"J. Vib. Control."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1177\/1045389X20917456","article-title":"Active vibration control of smart structure using poling tuned piezoelectric material","volume":"31","author":"Sharma","year":"2020","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Cui, M., Tang, W., Han, Y., and Li, Z. (2020, January 22\u201324). Smart Active Vibration Control System Using Piezoelectric Materials. Proceedings of the Chinese Control and Decision Conference (CCDC), Hefei, China.","DOI":"10.1109\/CCDC49329.2020.9164082"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Pu, Y., Yao, C., Li, X., and Liu, Z. (2020). Adaptive active vibration control for piezoelectric smart structure with online hysteresis identification and compensation. J. Vib. Control.","DOI":"10.1177\/1077546320980574"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Awada, A., Younes, R., and Ilinca, A. (2021). Review of vibration control methods for wind turbines. Energies, 14.","DOI":"10.3390\/en14113058"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1515\/secm-2021-0039","article-title":"Active vibration suppression of wind turbine blades integrated with piezoelectric sensors","volume":"28","author":"Lee","year":"2021","journal-title":"Sci. Eng. Compos. Mater."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1016\/j.renene.2020.12.009","article-title":"Vibration and power regulation control of a floating wind turbine with hydrostatic transmission","volume":"167","author":"Tong","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Malliotakis, G., Alevras, P., and Baniotopoulos, C. (2021). Recent advances in vibration control methods for wind turbine towers. Energies, 14.","DOI":"10.3390\/en14227536"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Bai, H., Aoues, Y., Cherfils, J.M., and Lemosse, D. (2021). Design of an active damping system for vibration control of wind turbine towers. Infrastructures, 6.","DOI":"10.3390\/infrastructures6110162"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"4233","DOI":"10.1016\/j.egyr.2022.03.083","article-title":"Simultaneous active control of tower lateral vibration and power control of wind turbine: A novel multivariable approach","volume":"8","author":"Golnary","year":"2022","journal-title":"Energy Rep."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1177\/0020294020983377","article-title":"Vibration control of cantilever blade based on trailing-edge flap by restricted control input","volume":"54","author":"Liu","year":"2021","journal-title":"Meas. Control."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"111474","DOI":"10.1016\/j.oceaneng.2022.111474","article-title":"Optimal model reference adaptive control of spar-type floating wind turbine based on simulated annealing algorithm","volume":"255","author":"Mu","year":"2022","journal-title":"Ocean. Eng."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1177\/1045389X20916804","article-title":"Active vibration control of a rotor bearing system using flexible piezoelectric patch actuators","volume":"31","author":"Brahem","year":"2020","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_69","first-page":"26","article-title":"Active vibration control analysis in smart composite structures using ANSYS","volume":"36","author":"Shakir","year":"2020","journal-title":"Rev. Int. M\u00e9todos Num\u00e9ricos Para C\u00e1lculo Dise\u00f1o Ing."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1177\/1045389X20948597","article-title":"Sliding mode predictive vibration control of a piezoelectric flexible plate","volume":"32","author":"Qiu","year":"2021","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Fu, Y., Li, S., Liu, J., and Zhao, B. (2021). Design and experimentation of a self-sensing actuator for active vibration isolation system with adjustable anti-resonance frequency controller. Sensors, 21.","DOI":"10.3390\/s21061941"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"e48","DOI":"10.1002\/adc2.48","article-title":"Smart vibration control of structures with unknown structural parameters using integrated virtual synchronization method\/linear-quadratic regulator approach","volume":"2","author":"Ghaderi","year":"2020","journal-title":"Adv. Control. Appl. Eng. Ind. Syst."},{"key":"ref_73","unstructured":"(2011). ANSYS CFX. User Manual Release 12.1, ANSYS Inc."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Dul, F., Lichota, P., and Rusowicz, A. (2020). Generalized linear quadratic control for a full tracking problem in aviation. Sensors, 20.","DOI":"10.3390\/s20102955"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"8356","DOI":"10.1109\/JIOT.2020.2990449","article-title":"Leveraging linear quadratic regulator cost and energy consumption for ultrareliable and low-latency iot control systems","volume":"7","author":"Yang","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1109\/TAC.1998.705000","article-title":"Linear-quadratic Control: An Introduction [Book Review]","volume":"43","author":"Hodel","year":"1998","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1687814020913782","DOI":"10.1177\/1687814020913782","article-title":"Condition monitoring and vibration analysis of wind turbine","volume":"12","author":"Xiao","year":"2020","journal-title":"Adv. Mech. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/15\/5691\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:59:18Z","timestamp":1760140758000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/15\/5691"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,29]]},"references-count":77,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22155691"],"URL":"https:\/\/doi.org\/10.3390\/s22155691","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,29]]}}}