A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator,which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result,the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach,the inverse model of the plant is identified to be the initial controller firstly. Then,the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.
The performance of smart structures in trajectory tracking under sub-micron level is hindered by the stress-dependent hysteresis generated by varying mechanical loads. In this paper,a stress-dependent Preisach operator is proposed for describing the hysteresis nonlinearity under both varying input current and compressive stress featured by introducing the dependence of the density function on the compressive stress. Subsequently,the properties together with the parameter identification scheme based on a fuzzy tree method of the presented operator are investigated to formulate an inverse compensator. Then,a feedback control scheme combined with a feed-forward compensator is implemented to a magnetostrictive smart structure (MSS) for real-time precise trajectory tracking. Compared with the classical operator,the proposed operator and corresponding control scheme experimentally demonstrate a dramatically improved performance for mitigating the effects of stress-dependent hysteresis.
