Vol.:(0123456789) 1 3 Journal of Vibration Engineering & Technologies https://doi.org/10.1007/s42417-019-00133-0 ORIGINAL PAPER Determining the Parameters of Active Modal Control in a Composite Beam Using Multi‑objective Optimization Flower Pollination C. A. X. da Silva 1  · E. Taketa 1  · E. H. Koroishi 1  · F. A. Lara‑Molina 1  · A. W. Faria 2  · F. S. Lobato 3 Received: 27 December 2018 / Revised: 29 April 2019 / Accepted: 3 May 2019 © Krishtel eMaging Solutions Private Limited 2019 Abstract Purpose In this contribution, an active vibration control in a composite beam considering electromagnetic actuators is pro- posed. The control theory used was the linear quadratic regulator solved by linear matrix inequalities. Methodology The electromagnetic actuator was linearized using a methodology similar to that used in magnetic bearings. To reduce the displacement of the system and reduce the energy consumption by determining the parameters used in active control, a multi-objective optimization problem was formulated. To solve this problem, a new bio-inspired optimization strategy, Multi-objective Optimization Flower Pollination (MOFP) algorithm is presented. In general, this approach consists of extending the Flower Pollination algorithm to a multi-objective context considering two operators (non-dominated sort- ing strategy and crowding distance). The numerical results obtained by using the MOFP algorithm are compared with those obtained by using the compromise optimization approach. Conclusions From numerical simulations, the system’s response was obtained in the time domain, which demonstrated the efciency of the proposed technique in the active control of vibrations. Keywords Active vibration control · Multi-objective optimization · Flower pollination · Compromise optimization Introduction Composite materials are characterized by innovative arrangements formed by various layers with diferent fber orientation, characterized by lightness, mechanical resist- ance and the possibility of being optimized for a specifc working condition. Aircraft, aerospace and automotive industries are examples in which composite materials have been increasingly used [1]. These materials are the subject matter of many studies that involve modeling, characteriza- tion and applications such as [2–7]. In the context of countless demands of mechanical sys- tems with optimal performance, control has become of great importance in industrial and production processes, where these areas have been seeking ways to optimize the perfor- mance of mechanical systems. Among modern control tech- niques, active vibration control (AVC) can be cited, which in recent decades has shown great advances and new con- trol methodologies [8–10]. Engineering research aimed at developing these new methodologies is driven by the need to have light structures, as well as a high operating perfor- mance, generating lower operating costs and increasing com- petitiveness. As an example, a fnite element (FE) model of a clamped-free shell structure considering the coupling efect of actuators was proposed in [11]. As mentioned by these authors, the electromagnetic actuators were simpli- fed as models for concentrated parameters and the movable parts of the actuators were treated from the FE model of the shell. Thus, the optimal confguration of actuators and sen- sors was studied by harmonic response analysis and modal analysis. A multiple-source multiple-harmonic (MSMH) active vibration suppression algorithm with a feed-forward * E. H. Koroishi edsonh@utfpr.edu.br 1 Mechanical Engineering Department, Federal University of Technology of Paraná, Avenue Alberto Carazzai, 1640, Cornélio Procópio Campus, Paraná, Cornélio Procópio 86300-000, Brazil 2 Civil Engineering Department, Federal University of Triângulo Mineiro, ICTE, Avenue Dr. Randolfo Borges Junior, 1250, Unit I, Uberaba, Minas Gerais 38064-200, Brazil 3 Laboratory of Modeling, Simulation, Control and Optimization, School of Chemical Engineering, Federal University of Uberlândia, Avenue João Naves de Ávila, 2121, Campus Santa Mônica, Uberlândia, Minas Gerais 38400-902, Brazil