Non-parametric convex identification of extended generalized Prandtl-Ishlinskii models
Non-parametric convex identification of extended generalized Prandtl-Ishlinskii models
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DOI：
10.1016/j.automatica.2013.12.010
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
Marcus Hedegärd;T. Wik
中科院分区：
文献类型：
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作者：
Marcus Hedegärd;T. Wik
磁滞的广义Prandtl-Ishlinskii模型(GPI)具有广泛的适用性，部分原因是它能够模拟非对称磁滞。它的特点是有三个未知函数。如今，GPI模型通常是通过特殊方法通过试错法识别的，假定这些函数的参数表达式，然后使用非线性最小二乘来确定参数，同时存在收敛问题、对初始参数猜测的依赖和局部极小值。除了聚合滞后输入-输出拟合度外，结果没有给出关于所选函数是否合适的信息。在这里，我们提出了一种方法来绕过这些问题的更一般的一类滞后模型。首先，我们介绍了一个扩展的GPI模型(XGPI)，其中一个附加的无记忆函数与GPI模型并行放置。这进一步扩大了适用性，例如允许磁滞回线的任意取向。对于这类模型，证明了它的四个独立映射是如何通过凸优化来识别的。然后，适当的单值函数可以被单独地适配到所得到的映射，如果需要，可以使用输入输出数据的非线性最小二乘来微调所找到的函数参数。将该方法应用于磁弹性扭矩传感器的仿真数据和实验数据，其结果与另一种常用的磁滞模型的结果进行了比较。
The Generalized Prandtl–Ishlinskii model (GPI) of hysteresis has wide applicability, partly because of its capability to model asymmetric hysteresis. It is characterized by three unknown functions. Today, GPI models are typically identified through trial and error by ad hoc methods, presuming parameterized expressions for these functions and then using nonlinear least squares to determine the parameters, with concurrent problems of convergence, a dependence on the initial parameter guess, and local minima. Except for the aggregated hysteresis input–output fit the result gives no information as to whether the functions chosen are appropriate or not. Here we present a method to circumvent these problems for a more general class of hysteresis models. First, we introduce an extended GPI model (XGPI), where an additional memoryless function is placed in parallel to the GPI model. This further widens the applicability, allowing, for example, arbitrary orientation of the hysteresis loop. For such models it is shown how its four separate mappings can be identified by convex optimization. Appropriate single-valued functions can then be fitted individually to the resulting mappings and, if necessary, the function parameters found can be fine-tuned using nonlinear least squares on input–output data. The method is applied to simulated data and experimental data from a magnetoelastic torque sensor, and the results are favorably compared to the results of another commonly used hysteresis model.