Modeling, identification and compensation of complex hysteretic nonlinearities: A modified Prandti-Ishlinskii approach
Modeling, identification and compensation of complex hysteretic nonlinearities: A modified Prandti-Ishlinskii approach
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DOI：
10.3166/ejc.9.407-418
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发表时间：
2003-01-01
影响因子：
3.4
通讯作者：
Kuhnen, K
中科院分区：
文献类型：
--
作者：
Kuhnen, K
在几乎所有基于智能材料的传感器和执行器中都存在不同程度的复杂滞后非线性，只要它们以足够高的幅度驱动。这就需要开发纯粹的现象学模型，以足够准确、稳健、服从于非线性补偿的控制设计并且足够高效地用于实时应用的方式来表征这些非线性。为了满足这些要求，本文提出了一种基于改进的Prandtl-Ishlinskii滞环算子的可逆复滞后非线性补偿器的设计方法。该模型的参数辨识可归结为一个二次优化问题，该问题对实际滞后非线性的实测输入输出数据产生最佳的L-2(2)范数逼近。参数的特殊线性不等式和等式约束保证了辨识问题的唯一可解性和辨识模型的可逆性。这使得辨识过程对未知的测量误差、未知的模型误差和未知的模型阶数具有较强的鲁棒性。通过解析变换律，可以直接计算相应的补偿器，从而有效地从模型中实现补偿器。最后，将补偿器设计方法应用于磁致伸缩执行器的逆前馈控制器设计。与传统的可控磁致伸缩执行器相比，逆控磁致伸缩执行器的非线性误差从50%左右降低到3%左右。
Undesired complex hysteretic nonlinearities are present to varying degree in virtually all smart material based sensors and actuators provided that they are driven with sufficiently high amplitudes. This necessitates the development of purely phenomenological models which characterize these nonlinearities in a way which is sufficiently accurate, robust, amenable to control design for nonlinearity compensation and efficient enough for use in real-time applications. To fulfill these demanding requirements, the present paper describes a new compensator design method for invertible complex hysteretic nonlinearities which is based on the so-called modified Prandtl-Ishlinskii hysteresis operator. The parameter identification of this model can be formulated as a quadratic optimization problem which produces the best L-2(2)-norm approximation for the measured input-output data of the real hysteretic nonlinearity. Special linear inequality and equality constraints for the parameters guarantee the unique solvability of the identification problem and the invertibility of the identified model. This leads to a robustness of the identification procedure against unknown measurement errors, unknown model errors and unknown model orders. The corresponding compensator can be directly calculated and thus efficiently implemented from the model by analytical transformation laws. Finally, the compensator design method is used to generate an inverse feedforward controller for a magnetostrictive actuator. In comparision to the conventional controlled magnetostrictive actuator the nonlinearity error of the inverse controlled magnetostrictive actuator is lowered from about 50% to about 3%.