Some active vibration control methods are based on mathematical models. In these cases, parameter variations play an important role in the system performance. As it is not possible to know in advance the precise values for all parameters of the mechanical system, a possible alternative is to design robust controllers that take into account the uncertainties. In this context, this work presents a vibration active control technique devoted to rotating machinery by incorporating electromagnetic actuators, which considers uncertainties in the parameters of the system. the gains of the electromagnetic actuator are determined by using linear matrix inequalities, which consist in a powerful tool for the cases in which parameter uncertainties are taken into account. In addition, Kalman estimators are employed to deduce the modal states of the system. The model of the rotating system is obtained by using the finite element method and the potentiality of the methodology for applications in engineering was investigated through experimental tests.
Abdalla M, Zimmerman D and Grigoriadis K (2000) Reduce Optimal Parameter Update in Structural Systems Using LMIs. American Control Conference 991–995.
2.
Assunção E (2000) Redução H2 e H∞ de Modelos através de Desigualdades Matriciais Lineares: Otimização Local e Global. Phd thesis, State University of Campinas, Campinas-SP.
3.
Assunção E and Teixeira M (2001) Projeto de Sistema de Controle Via LMIs usando o MATLAB. Escola Brasileira de Aplicações em Dinâmica e Controle – APLICON USP. São Carlos – SP.
4.
Boyd S, Balakrishnan V, Feron E and El Ghaoui L (1994) Linear Matrix Inequalities in Systems and Control Theory. Vol. 15, Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), p. 193.
5.
Der HagopianJMahfoudJ (2010) Electromagnetic actuator design for the control of light structures. Smart Structures and Systems6: 29–38.
6.
ErkusBLeeYJ (2004) Linear Matrix Inequalities and Matlab LMI Toolbox, Los Angeles, California: University of Southern California Group Meeting Report.
7.
GuDWPetkovPKonstantinovMM (2013) Robust Control Design with Matlab, Springer: Springer Science & Business Media, pp. 468.
8.
HorstHGWölfelHP (2004) Active vibration control of a high speed rotor using PZT patches on the shaft surface. Journal of Intelligent Material Systems and Structures15: 721–728.
9.
Johnson EA and Erkus B (2002) Structural Control with Dissipative Camping Devices. Proceedings of the American Control Conference. Vol. 3, Anchorage, Alaska, pp. 2463–2468.
10.
KoroishiEHBorgesASCavaliniAAJrSteffenVJr (2014) Numerical and Experimental Modal Control of Flexible Rotor Using Electromagnetic Actuator. Mathematical Problems in Engineering2014: 1–14.
11.
Koroishi EH, Steffen V Jr and Mahfoud J (2012) Fuzzy Control of Rotor System Using an Electromagnetic Actuator. MATEC Web of Conferences: CSNDD 2012 – International Conference on Structural Nonlinear Dynamics and Diagnosis 1: 6.
12.
Kulesza Z (2013) Virtual Collocation Method for a flexible rotor supported by active bearings. Journal of Vibration and Control. Epub ahead of print, DOI: 10.1177/1077546313497246.
13.
KuleszaZSawickiJTGyekenyesiAL (2012) Robust fault detection filter using linear matrix inequalities’ approach for shaft crack diagnosis. Journal of Vibration and Control19: 1421–1440.
14.
LalanneMFerrarisG (1998) Rotordynamics Prediction in Engineering, John Wiley & Sons, INC: John Wiley and Sons.
15.
LyapunovAM (1992) The general problem of stability motion. International Journal of Control55: 531–534.
16.
Mahfoud J and Der Hagopian J (2011) Fuzzy Active Control of Flexible Structures by Using Electromagnetic Actuators. Journal of Aerospace Engineering 329–337.
17.
MoraisTSSteffenVJrMahfoudJ (2012) Control of the Breathing Mechanism of a cracked rotor by using electro-magnetic actuator: numerical study. Latin American Journal of Solids and Structures9: 581–596.
18.
OgataK (2010) Modern control engineering, New Jersey: Prentice Hall.
19.
PalazzoloABJogannathanSKascakAFMontagueGTKiralyLJ (1993) Hybrid Active Vibration control of Rotorbearing Systems Using Piezoelectric Actuators. Journal of Vibration and Acoustics115: 111–119.
20.
Palhares RM (1998) Filtragem Robusta: Uma Abordagem por Desigualdades Matriciais Lineares. Phd thesis, State University of Campinas, Campinas-SP.
21.
SawickiJTGawronskiW (1997) Balanced Model Reduction and Control of Rotor-Bearing Systems. ASME Journal of Engineering for Gas Turbines and Power119: 556–563.
22.
SawickiJTGentaG (2001) Modal Uncoupling of Damped Gyroscopic Systems. Journal of Sound and Vibration244: 431–451.
23.
SchweitzerGMaslenEH (2009) Magnetic Bearings: Theory, Design and Application to Rotating Machinery, Berlin: Springer-Verlag.
24.
SilvaSLopesVJrAssunçãoE (2004) Robust Control to Parametric Uncertainties in Smart Structures Using Linear Matrix Inequalities. Journal of the Brazilian Society of Mechanical Science and Engineering26: 430–437.
25.
SimõesRCDer HagopianJMahfoudJSteffenVJr (2007) Modal active vibration control of a rotor using piezoelectric stack actuators. Journal of Vibration and Control13: 45–64.
26.
Van AntwerpJGBraatzRD (2000) A Tutorial on Linear and Bilinear Matrix Inequalities. Journal of Process Control10: 363–385.
27.
WangHBWangJLLamJ (2007) Robust Fault Detection Observer Design: Iterative LMI Approaches. Journal of Dynamic Systems, Measurement, and Control129: 77–82.
28.
YuHCLinYHChuCL (2007) Robust Modal Vibration Suppression of a Flexible Rotor. Mechanical Systems and Signal Processing21: 334–347.
