Modeling, Identification and Compensation of Complex Hysteretic Nonlinearities: A Modified Prandtl-Ishlinskii Approach

Abstract

Undesired complex hysteretic nonlinearities are present to varying degree in virtually all smart material based sensors and actuators provided that they are driven with sufficiently high amplitudes. This necessitates the development of purely phenomenological models which characterize these nonlinearities in a way which is sufficiently accurate, robust, amenable to control design for nonlinearity compensation and efficient enough for use in real-time applications. To fulfill these demanding requirements, the present paper describes a new compensator design method for invertible complex hysteretic nonlinearities which is based on the so-called modified Prandtl-Ishlinskii hysteresis operator. The parameter identification of this model can be formulated as a quadratic optimization problem which produces the best L 2 2 -norm approximation for the measured input-output data of the real hysteretic nonlinearity. Special linear inequality and equality constraints for the parameters guarantee the unique solvability of the identification problem and the invertibility of the identified model. This leads to a robustness of the identification procedure against unknown measurement errors, unknown model errors and unknown model orders. The corresponding compensator can be directly calculated and thus efficiently implemented from the model by analytical transformation laws. Finally, the compensator design method is used to generate an inverse feedforward controller for a magnetostrictive actuator. In comparision to the conventional controlled magnetostrictive actuator the nonlinearity error of the inverse controlled magnetostrictive actuator is lowered from about 50% to about 3%.