A simple fuzzy system for modelling of both rate-independent and rate-dependent hysteresis in piezoelectric actuators

In this paper, a novel fuzzy system based method for modelling both rate-independent and rate-dependent hysteresis in the piezoelectric actuator is proposed. First, the partial Takagi–Sugeno (T–S) fuzzy rule is designed. The antecedent structure of the fuzzy system is identified through uniform partition of its input variable. Then, the parameters of the consequent structure are optimized via the recursive least squares (RLS) algorithm. The modelling method is simple to implement and highly efficient to compute. Experimental results show that the proposed method is efficient to model both rate-independent and rate-dependent hysteresis. Based on the inverse of the developed model, feed-forward hysteresis compensation experiments at the frequencies of 50 Hz and 100 Hz are also conducted with the hysteresis effects being obviously reduced. The major contribution of this paper is that the inverse of the model can be analytically computed and the method can be applied to the case of real-time on-line modelling.

► The model is capable of characterizing both rate-independent and rate-dependent hysteresis.
► The model's inverse can be analytically obtained.
► The model can be applied on-line.
► The model needs little computation time or space.