ANN and Non-Integer Order Modeling of ABS Solenoid Valves

This brief presents an electric model of an on/off solenoid valve used to regulate brake pressure in anti-lock braking control systems (ABS). The model has been derived with the purpose to test and validate some coil driver integrated circuits in a Hardware-in-the-loop approach. The valve model is composed by magneto-dynamic, mechanical and fluid dynamic subsystems. The global system is highly nonlinear and presents hysteresis phenomena due to the ferromagnetic effect. A non-integer order system has been adopted to simply represent the high order dynamics present into the system, while Duhem equations coupled with two different neural networks are used to model the hysteresis. Several experimental trials have been performed in order to validate the suitability of the proposed approach.