Active Vibration Control of a Nonlinear System with Optimizing The Controller Coefficients Using Metaheuristic Algorithms

Document Type : Research Article


1 Department of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran.

2 Department of Electrical and Robotics Engineering, Shahrood University of Technology, Shahrood, Iran


An active vibration absorber is utilized in this study for a nonlinear system with unknown multi-harmonic frequency disturbance. At first, a function for disturbance force and its first and second derivatives are estimated. Then the position of the main system is controlled by feedback linearization and sliding mode controllers. A magnetic actuator is designed, which is controlled by a sub-controller. Liunberger observer estimates disturbance function, and the feedback linearization and sliding mode controllers regulate the main system's position. Metaheuristic algorithms obtain the controller's coefficients to minimize settling time and errors. Four different techniques, namely, Genetic algorithm, Particle swarm optimization, Simulated annealing, and Teaching-learning-based optimization, are utilized for the optimization process. A magnetic actuator is designed using Faraday and Lorentz's law for applying the controlling force to the system. Simulation results of the observer have been compared to real value, and the results show the excellent effect of active vibration absorbers on vibration suppression. Moreover, optimizing the controller coefficient shows an improvement in settling time and error. Comparing the algorithms, particle swarm optimization has the best cost function, where Teaching-learning-based optimization has the best-averaged results.


Main Subjects

[1] P. Bonello, Adaptive tuned vibration absorbers: Design principles, concepts and physical implementation, in:  Vibration Analysis and Control-New Trends and Developments, InTech, 2011.
[2] E. Caetano, Á. Cunha, C. Moutinho, F. Magalhães, Studies for controlling human-induced vibration of the Pedro e Inês footbridge, Portugal. Part 2: Implementation of tuned mass dampers, Engineering Structures, 32(4) (2010) 1082-1091.
[3] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.
[4] T. Taniguchi, A. Der Kiureghian, M. Melkumyan, Effect of tuned mass damper on displacement demand of base-isolated structures, Engineering Structures, 30(12) (2008) 3478-3488.
[5] J. Ji, N. Zhang, Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber, Journal of Sound and Vibration, 329(11) (2010) 2044-2056.
[6] X. Chen, A. Kareem, Efficacy of tuned mass dampers for bridge flutter control, Journal of Structural Engineering, 129(10) (2003) 1291-1300.
[7] A. Baz, A neural observer for dynamic systems, Journal of sound and vibration, 152(2) (1992) 227-243.
[8] J.-S. Bae, J.-H. Hwang, J.-H. Roh, J.-H. Kim, M.-S. Yi, J.H. Lim, Vibration suppression of a cantilever beam using magnetically tuned-mass-damper, Journal of Sound and Vibration, 331(26) (2012) 5669-5684.
[9] E. El Behady, E. El-Zahar, Vibration reduction and stability study of a dynamical system under multi-excitation forces via active absorber, International Journal of Physical Sciences, 7(48) (2013) 6203-6209.
[10] F. Beltran-Carbajal, G. Silva-Navarro, Active vibration control in Duffing mechanical systems using dynamic vibration absorbers, Journal of sound and vibration, 333(14) (2014) 3019-3030.
[11] T. Bailey, J.E. Hubbard, Distributed piezoelectric-polymer active vibration control of a cantilever beam, Journal of Guidance, Control, and Dynamics, 8(5) (1985) 605-611.
[12] R. Zhang, C. Tong, Torsional vibration control of the main drive system of a rolling mill based on an extended state observer and linear quadratic control, Journal of Vibration and Control, 12(3) (2006) 313-327.
[13] F. Beltrán‐Carbajal, G. Silva‐Navarro, Adaptive‐Like Vibration Control in Mechanical Systems with Unknown Paramenters and Signals, Asian Journal of Control, 15(6) (2013) 1613-1626.
[14] N. Al-Holou, T. Lahdhiri, D.S. Joo, J. Weaver, F. Al-Abbas, Sliding mode neural network inference fuzzy logic control for active suspension systems, IEEE Transactions on Fuzzy Systems, 10(2) (2002) 234-246.
[15] Z. Xianmin, S. Changjian, A.G. Erdman, Active vibration controller design and comparison study of flexible linkage mechanism systems, Mechanism and Machine Theory, 37(9) (2002) 985-997.
[16] 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(1-2) (2007) 391-404.
[17] C. Hansen, S. Snyder, X. Qiu, L. Brooks, D. Moreau, Active control of noise and vibration, CRC press, 2012.
[18] M. McLaren, G. Slater, A disturbance model for control/structure optimization with output feedback control, Structural optimization, 6(2) (1993) 123-133.
[19] G. Zhao, B. Chen, Y. Gu, Control–structural design optimization for vibration of piezoelectric intelligent truss structures, Structural and Multidisciplinary Optimization, 37(5) (2009) 509.
[20] X. Zhang, A. Takezawa, Z. Kang, Topology optimization of piezoelectric smart structures for minimum energy consumption under active control, Structural and Multidisciplinary Optimization, 58(1) (2018) 185-199.
[21] P. Bisegna, G. Caruso, Optimization of a passive vibration control scheme acting on a bladed rotor using an homogenized model, Structural and Multidisciplinary Optimization, 39(6) (2009) 625.
[22] E. Boroson, S. Missoum, Stochastic optimization of nonlinear energy sinks, Structural and Multidisciplinary Optimization, 55(2) (2017) 633-646.
[23] I. Venanzi, Robust optimal design of tuned mass dampers for tall buildings with uncertain parameters, Structural and Multidisciplinary Optimization, 51(1) (2015) 239-250.
[24] D. Howe, Magnetic actuators, Sensors and Actuators A: Physical, 81(1-3) (2000) 268-274.
[25] S.-M. Jang, J.-Y. Choi, S.-H. Lee, H.-W. Cho, W.-B. Jang, Analysis and experimental verification of moving-magnet linear actuator with cylindrical Halbach array, IEEE transactions on magnetics, 40(4) (2004) 2068-2070.
[26] N. Mikhaeil-Boules, Design and analysis of linear actuator for active vibration cancellation, in:  Industry Applications Conference, 1995. Thirtieth IAS Annual Meeting, IAS'95., Conference Record of the 1995 IEEE, IEEE, 1995, pp. 469-475.
[27] S. Evans, I. Smith, J. Kettleborough, Permanent-magnet linear actuator for static and reciprocating short-stroke electromechanical systems, IEEE/ASME transactions on mechatronics, 6(1) (2001) 36-42.
[28] Q. Li, F. Ding, C. Wang, Novel bidirectional linear actuator for electrohydraulic valves, IEEE transactions on magnetics, 41(6) (2005) 2199-2201.
[29] J. Kim, J. Chang, A new electromagnetic linear actuator for quick latching, IEEE Transactions on Magnetics, 43(4) (2007) 1849-1852.
[30] A.E. Rundell, S.V. Drakunov, R.A. DeCarlo, A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing, IEEE Transactions on Control Systems Technology, 4(5) (1996) 598-608.
[31] C. Van Lierop, J. Jansen, A. Damen, E. Lomonova, P. Van den Bosch, A. Vandenput, Model-based commutation of a long-stroke magnetically levitated linear actuator, IEEE Transactions on Industry Applications, 45(6) (2009) 1982-1990.
[32] H. Guckel, T. Earles, J. Klein, J. Zook, T. Ohnstein, Electromagnetic linear actuators with inductive position sensing, Sensors and Actuators A: Physical, 53(1-3) (1996) 386-391.
[33] DK. Cheng, Field and wave electromagnetics, Pearson Education India, 1989.
[34] S. Mirjalili, A. Lewis, The whale optimization algorithm, Advances in engineering software, 95 (2016) 51-67.
[35] S. Sivanandam, S. Deepa, Genetic algorithms, in:  Introduction to genetic algorithms, Springer, 2008, pp. 15-37.
[36] J. Kennedy, R. Eberhart, Particle swarm optimization, in:  Proceedings of ICNN'95-international conference on neural networks, IEEE, 1995, pp. 1942-1948.
[37] M. Pincus, Letter to the editor—a monte carlo method for the approximate solution of certain types of constrained optimization problems, Operations research, 18(6) (1970) 1225-1228.