Piezoelectric stack actuators are commonly used in a number of different position control applications due to their compactness, high resolution, speed and dynamic properties. For accurate position control, position feedback has traditionally been employed since the parameters of the constitutive equations change with temperature and age. In addition, the identification of constitutive parameters is complicated by the presence of hysteresis voltage that is not accounted for in the linear constitutive equations. Recently, there has been a push towards sensor less control. This approach requires an accurate identification technique of the constitutive parameters. For this purpose, the constitutive equations used to identify the piezoelectric parameters are usually considered linear under a low electric field. However, at larger driving voltages hysteresis effect become significant and the parameters identified at lower excitation levels are no longer valid. This is traditionally addressed by providing constitutive parameters as a function of applied voltage. However, this is usually done for the ascending hysteresis branch only. The changes due to the descending hysteresis branch are commonly ignored. As a result, it is often difficult to match the constitutive equations to experimental data. We propose a new identification procedure that is based on online capacitance measurements of the piezo actuators. These measurements indicate, that the piezo capacitance is not constant, but a linear function of linearized piezo voltage. Using this result, we are able to construct values for the remaining constitutive parameters that are largely independent of piezo voltage. The resulting constitutive equations match our experimental actuator performance well no matter where they are applied in the hysteresis loop. This new identification technique then provides more accurate piezo models that are very useful for developing sensor less control strategies for piezo actuators.

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