FUZZY CONTROLLER FOR ELIMINATION OF THE NONLINEAR RESONANCE PHENOMENON Ognjen Kuljaca*, Ljubomir Kuljaca # , Zoran Vukic # , Bruno Strah † *Automation & Robotics Research Institute, The University of Texas at Arlington fax: +1 817 272 5989 e-mail: okuljaca@arri.uta.edu # Faculty of Electrical Engineering and Computing, University of Zagreb fax: +385 1 6129 809 e-mail: ljubomir.kuljaca@fer.hr e-mail: zoran.vukic@fer.hr † AVL List GmbH fax: +43 316 787 7766 e-mail: bruno.strah@avl.com Keywords: Nonlinear system, fuzzy control, nonlinear resonance, limit cycles, forced oscillations. Abstract The paper deals with the capability of the fuzzy controller to eliminate the frequency resonance jump of the nonlinear system. The simulation method is used for the analysis purposes. The nonlinear system operates in the forced oscillation mode, and the fuzzy regulator of the Mamdani type is used for elimination of the resonance jump. The proposed method of resonance jump elimination proved to be reliable and useful. 1 Introduction Resonance jump was investigated more in the theory of oscillation of mechanical systems [1, 11] than in the theory of control systems [2, 5, 9]. The term "resonance jump" is used in case of a sudden jump of the amplitude and/or phase and/or frequency of a periodic output signal of a nonlinear system. This happens due to non-unique relation that exists between periodic forcing input signal acting upon a nonlinear system and the output signal from that system. It is believed that resonance jump occurs in nonlinear control systems with small stability phase margin i.e. with small damping factor of the linear part of the system and with amplitudes of excitation signal that force the system into the operating modes where nonlinear laws are valid, particularly saturation. Higher performance indices such as: maximal speed of response with minimal stability degradation, high static and dynamic accuracy, minimal oscillatory dynamics and settling time as well as power efficiency and limitations (durability, resistivity, robustness, dimensions, weight, power), boils down to a higher bandwidth of the system. Thanks to that, input signals can have higher frequency content in them and in some situation can approach closer to the "natural" frequency of the system. As a consequence this favours the occurrence of the resonance jump. Namely, the fulfilments of the aforementioned conditions can bring the forced oscillation frequency (of the nonlinear system operating in the forced oscillations mode) closer to the limit cycle frequency of some subsystems, which together with the amplitude constraints creates conditions for establishing the nonlinear resonance. Resonance jump can occur in nonlinear systems operating in forced oscillations mode and is often not desirable state of the system. Resonance jump cannot be seen from the transient response of the system and cannot be defined by solving nonlinear differential equations. It is also Proceedings of the 10th Mediterranean Conference on Control and Automation - MED2002 Lisbon, Portugal, July 9-12, 2002.