Inverse feedforward controller for complex hysteretic nonlinearities in smart-material systems

Abstract

Undesired complex hysteretic nonlinearities are present to a varying degree in virtually all smart material-based sensors and actuators provided that they are driven with sufficiently high amplitudes. In motion and active vibration control applications, for example, these nonlinearities can excite unwanted dynamics which leads in the best case to reduced system performance and in the worst case to unstable system operation. This necessitates the development of purely phenomenological models which characterize these nonlinearities in a way which is sufficiently accurate, amenable to a compensator design for actuator linearization and efficient enough for use in real-time applications. To fulfil these demanding requirements the present paper describes a new compensator design method for invertible complex hysteretic nonlinearities which is based on the so-called Prandtl-Ishlinskii hysteresis operator. The parameter identification of this model 2can be formulated as a quadratic optimization problem which produces the best L2 2-norm approximation for the measured output-input data of the real hysteretic nonlinearity. Special linear inequality constraints for the parameters guarantee the unique solvability of the identification problem and the invertability 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 the linearization of a magnetostrictive actuator. In comparision to the conventionally controlled magnetostrictive actuator the nonlinearity error of the inverse controlled magnetostrictive actuator is lowered from about 30 % to about 3 %.