A hybrid optimal-base fuzzy-proportional-integral-derivative controller for vibration mitigation of structural system against earthquake

Document Type : Research Article


Khorasan Institute of Higher Education


This paper proposes an experimental investigation of a four-story structure that is connected to a shaking table. The investigated shaking table is designed with a particular method to produce any kind of vibration amplitude. Also, the whale optimization algorithm is used for the identification of the experimental structure parameters such as mass, stiffness, and damping to show the adaptation of the results collected from the identified model on the results achieved from the linear model. The other idea of this paper is to suggest a novel control strategy that is established by combining proportional-integral-derivative and fuzzy logic control, using an optimization procedure called whale optimization algorithm for optimum tuning of controller coefficients, the hybrid control method is designed. The main objective of the hybrid optimal-based fuzzy-proportional-integral-derivative controller is to reduce the displacement of isolation system without allowing a significant increase in the acceleration of superstructure for both far-field and near-field earthquake excitations. The proposed control algorithm is designed and developed on a four-story shear frame, which contains an active tuned mass damper on each level. Numerical simulations show that the proposed controller which is a combination of two controllers better mitigates the seismic responses of a smart structure excited by a range of real-data earthquakes.


Main Subjects

Zadeh, L.A., Fuzzy sets. Information and control, 8(3) (1965) 338-353.
R.-E. Precup, H. Hellendoorn, A survey on industrial applications of fuzzy control, Computers in Industry, 62 (2011) 213-226.
E. Allam, H.F. Elbab, M.A. Hady, S. Abouel-Seoud, Vibration control of active vehicle suspension system using fuzzy logic algorithm, Fuzzy Information and Engineering, 2 (2010) 361-387.
A. Shehata, H. Metered, W.A. Oraby, Vibration control of active vehicle suspension system using fuzzy logic controller, in: Vibration Engineering and Technology of Machinery, Springer, (2015), 389-399.
D. Singh, M. Aggarwal, Passenger seat vibration control of a semi-active quarter car system with hybrid Fuzzy–PID approach, International Journal of Dynamics and Control, (2015) 1-10.
M. Marinaki, Y. Marinakis, G.E. Stavroulakis, Fuzzy control optimized by PSO for vibration suppression of beams, Control Engineering Practice, 18 (2010) 618-629.
A. Sagirli, C.O. Azeloglu, R. Guclu, H. Yazici, Self-tuning fuzzy logic control of crane structures against earthquake induced vibration, Nonlinear Dynamics, 64 (2011) 375-384.
J. Lin, Y. Zheng, Vibration suppression control of smart piezoelectric rotating truss structure by parallel neuro-fuzzy control with genetic algorithm tuning, Journal of Sound and Vibration, 331 (2012) 3677-3694.
M.E. Uz, M.N. Hadi, Optimal design of semi active control for adjacent buildings connected by MR damper based on integrated fuzzy logic and multi-objective genetic algorithm, Engineering Structures, 69 (2014) 135-148.
K. Dhanalakshmi, M. Umapathy, D. Ezhilarasi, Shape memory alloy actuated structural control with discrete time sliding mode control using multirate output feedback, Journal of Vibration and Control, 22 (2016) 1338-1357.
S.-B. Choi, Y.-M. Han, Vibration control of electrorheological seat suspension with human-body model using sliding mode control, Journal of Sound and Vibration, 303 (2007) 391-404.
Zhang D, Pan P, Zeng Y. An optimum model reference adaptive control algorithm for smart base-isolated structures. Bulletin of Earthquake Engineering, (2018) 1-24.
J. Fu, J. Lai, G. Liao, M. Yu and J. Bai, Genetic algorithm based nonlinear self-tuning fuzzy control for time-varying sinusoidal vibration of a magnetorheological elastomer vibration isolation system, Smart Materials and Structures, 27(8) (2018) 085010.
M. Miah, E. Chatzi and F. Weber, Semi-active control for vibration mitigation of structural systems incorporating uncertainties, Smart Materials and Structures, 24(5) (2015) 055016.
H. Ozer, Y. Hacioglu and N. Yagiz, Suppression of structural vibrations using PDPI + PI type fuzzy logic controlled active dynamic absorber, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(7) (2015) 2105-2115.
L. Xu, Y. Yu and Y. Cui, Active vibration control for seismic excited building structures under actuator saturation, measurement stochastic noise and quantisation, Engineering Structures, 156 (2018) 1-11.
K. Park, H. Koh and C. Seo, Independent modal space fuzzy control of earthquake-excited structures, Engineering Structures, 26(2) (2004) 279-289.
S. Pourzeynali, H. Lavasani and A. Modarayi, Active control of high rise building structures using fuzzy logic and genetic algorithms, Engineering Structures, 29(3) (2007) 346-357.
Y. Liu and S. Tong, Adaptive fuzzy control for a class of unknown nonlinear dynamical systems, Fuzzy Sets and Systems, 263 (2015) 49-70.
M. Awruch and H. Gomes, A fuzzy α-cut optimization analysis for vibration control of laminated composite smart structures under uncertainties, Applied Mathematical Modelling, 54 (2018) 551-566.
A. Bathaei, S. Zahrai and M. Ramezani, Semi-active seismic control of an 11-DOF building model with TMD+MR damper using type-1 and -2 fuzzy algorithms, Journal of Vibration and Control, 24(13) (2017) 2938-2953.
S. Etedali, N. Mollayi, Cuckoo search-based least squares support vector machine models for optimum tuning of tuned mass dampers, International Journal of Structural Stability and Dynamics. 18 (2) (2018) 1850028.
S. Etedali, S. Tavakoli, PD/PID controller design for seismic control of high-rise buildings using multi-objective optimization: a comparative study with LQR controller, Journal of Earthquake Tsunami 11 (3) (2016) 1750009.
N. Fisco, H. Adeli, Smart structures: part I—active and semi-active control, Scientia Iranica 18 (3) (2011) 275–284.
S. Golnargesi, H. Shariatmadar and H. Razavi, Seismic control of buildings with active tuned mass damper through interval type-2 fuzzy logic controller including soil–structure interaction, Asian Journal of Civil Engineering, 19(2) (2018) 177-188.
A. Zamani, S. Tavakoli and S. Etedali, Fractional order PID control design for semi-active control of smart base-isolated structures: A multi-objective cuckoo search approach, ISA Transactions, 67 (2017) 222-232.
S. Hadad Baygi and A. Karsaz, A hybrid optimal PID-LQR control of structural system: A case study of salp swarm optimization, in 2018 3rd Conference on Swarm Intelligence and Evolutionary Computation (CSIEC), kerman, (2018) 1-6.
S. Etedali, A. Zamani and S. Tavakoli, A GBMO-based PI λ D μ controller for vibration mitigation of seismic-excited structures, Automation in Construction, 87 (2018) 1-12.
Fukushima, I., Kobori, T., Sakamoto, M., Koshika, N.,Nishimura, I., Sasaki, K.: Vibration control of a tall building using active–passive composite tuned mass damper. In: Third International Conference on Motion and Vibration Control, Chiba, Japan, September, (1996) 1–6
Nishimura, H., Ohkubo, Y., Nonami, K.: Active isolation control for multi-degree-of-freedom structural system. In: Third International Conference on Motion and Vibration Control, Chiba, Japan, September, (1996) 82–87
C. Muresan, E. Dulf and O. Prodan, A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers, Journal of Vibration and Control, 22(8) (2014) 1980-1992.
S. Etedali, S. Tavakoli and M. Sohrabi, Design of a decoupled PID controller via MOCS for seismic control of smart structures, Earthquakes and Structures, 10(5) (2016) 1067-1087.
A. Heidari, S. Etedali and M. Javaheri-Tafti, A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD, Frontiers of Structural and Civil Engineering, 12(1) (2017) 44-57.
J. Cheong and S. Lee, Linear PID Composite Controller and its Tuning for Flexible Link Robots, Journal of Vibration and Control, 14(3) (2008) 291-318.
M.L. James, G.M. Smith, J.C. Wolford, and P.W.  Whaley, Vibration of mechanical and structural systems, 2nd ed., Harper  Collins  College Publishers, New  York, NY, (1994) 432-35
S. Mirjalili, A. Lewis, The whale optimization algorithm, Advances in engineering software, 95 (2016) 51-67