A distributed parameter Maxwell-Slip hysteresis model for piezoelectric actuators

Hysteresis is an important nonlinearity existing in piezoelectric actuators. Modeling and compensation is a common approach to handle it. This paper proposes a distributed parameter Maxwell-slip (DPMS) model. It is extended from the Maxwell-slip (MS) model. The DPMS model replaces the spring-slider elements in the MS model by a sliding cell and a elastic cell with distributed parameters. The properties of the elastic cell are described by two functions, i.e. the saturation deformation function and the stiffness function. These two functions also govern the hysteresis generated by the DPMS model and only require a few parameters. An approach to identify model parameters are proposed. Experiments demonstrate the effectiveness of the DPMS model. With a linear function describing the saturation deformation function, only two parameters (the character length and a coefficient) are required and the normalized mean squire error is 1.96%. The hysteresis nonlinearity is reduced from 13.8% to 2.55% by 81.5% if it is compensated by the inverse DPMS model.