H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake

  • Michael Dowglas de Gois Silva Department of Mechanical Engineering, Faculty of Engineering of Ilha Solteira, UNESP-Paulista State University, Ilha Solteira, São Paulo 15385-000, Brasil
  • Fábio Roberto Chavarette Department of Engineering, Physics and Mathematics, Institute of Chemistry, UNESP-Paulista State Univerity, Araraquara, São Paulo 14800-060, Brasil
Ariticle ID: 451
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Keywords: shear building; earthquake; wind; H∞ control; MRD; hybrid controller


The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.


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How to Cite
de Gois Silva, M. D., & Chavarette, F. R. (2024). H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake. Journal of AppliedMath, 2(2), 451. https://doi.org/10.59400/jam.v2i2.451