To describe the rate-dependent hysteresis behavior of the piezoelectric actuators, a cascade block-based model is proposed in this paper, i.e., a rate-independent hysteresis block cascading with a rate-dependent block. For the approximation of the hysteresis block, a hysteresis operator is introduced into the input space to represent the changing tendency of the gradient with the hysteresis. Then a neural hysteresis sub-model is constructed based on a one-to-one mapping. Meanwhile, to describe the rate-dependent characteristics of the dynamic hysteresis, a NARX (nonlinear autoregressive model with exogenous inputs) model is adopted. And a recursive stochastic Newton approximation algorithm is derived for the optimization of the model. The validation results have shown the effectiveness of the proposed model for characterizing the dynamic hysteresis.

How to quickly control the main steam temperature to the setpoint is difficult problem in the field of fire power station control．
Considering the control problem of the main steam temperature of super critical boiler machine set，a neuro-fuzzy model based adaptive
PID cascade control for the main steam temperature of fire electrical engineering set is proposed in this paper． A neuro-fuzzy
model for main steam temperature is established by using the information of attemperation water flow，inlet temperature of high temperature
superheater，main steam flow and the main steam temperature． Then the adaptive PID cascade control of main steam temperature is
implemented． A PI controller is employed in the inner loop to overcome inner disturbance，which can decrease the influence of the leading
area＇s differential temperature． Then the single neuron PID controller ( SNAC) is implemented to control the called generalized
process，which includes PI closed loop and inert segment． This controller is adjusted to eliminate the error between the predicted value
and the output value． Finally，the effectiveness of this methodology is verified by simulation example．