A New One-Dimensional Rate-Based Phenomenological Model to Describe the Non-Linear Behaviour of Piezoelectric Actuators for Real-Time Applications

Abstract

In this paper, a new rate-based phenomenological model of piezoelectric actuators for real-time applications is developed. This compact theoretical approach employs the Arrhenius equation for chemical reaction kinetics in order to describe the non-linear effect of domain switching. It needs only nine model parameters to account for the complete non-linearity of a piezoelectric actuator as well as the dependence of its non-linear effect on the electric field, the mechanical stress, and the temperature. This general validity for a wide range of operation conditions, which is based on a simplified description of the real behaviour, is the optimum prerequisite for a technically inexpensive control loop strategy for fast piezoelectric actuators as they are employed in state-of-the-art gasoline and diesel injectors for combustion engines. Moreover, other interfering physical effects, such as ageing, which may cause an injector's dosing function to deteriorate severely can be tackled by making use of this approach in electronic control units. All this is possible because the extremely compact theoretical formulation with a compact set of parameters does not need access to complex characteristic diagrams so that the most essential requirements of an automotive control unit such as a minimum computation time and a modest requirement of storage space can be fulfilled.