补偿设计中的NARX模型辨识
Identification of NARX Models for Compensation Design
摘要：
本报告介绍了三个系统的建模结果，两个数值和一个实验。在数值例子中，我们使用以前在文献中获得的数学模型作为待识别的系统。第一个数值例子是一个加热系统的多项式非线性描述的Hammerstein模型。第二个是一个Bouc-Wen模型，代表在压电致动器的滞后行为。最后，实验的例子是一个气动阀，提出了各种非线性，包括滞后。对于每个例子，一个非线性自回归模型与外源输入（NARX）确定使用两个行之有效的技术在一起，误差减少比（ERR）的方法，分层选择回归和赤池的信息准则（AIC）截断的条款的数量。使用这两种方法，实现结构选择。激励输入的设计基于保持感兴趣的频率并迫使系统实现不同的操作点。因此，具有先前用ERR和AIC选择的结构，我们使用扩展最小二乘（ELS）算法来估计参数。结果表明，它是可能的，以识别不超过五项的参考系统。这些模型将用于非线性补偿在未来的工作。
英文摘要：
This report presents the modeling results for three systems, two numerical and one experimental. In the numerical examples, we use mathematical models previously obtained in the literature as the systems to be identified. The first numerical example is a heating system with a polynomial nonlinearity that is described by a Hammerstein model. The second is a Bouc-Wen model that represents the hysteretic behavior in a piezoelectric actuator. Finally, the experimental example is a pneumatic valve that presents a variety of nonlinearities, including hysteresis. For each example, a Nonlinear AutoRegressive model with eXogenous inputs (NARX) is identified using two well-established techniques together, the Error Reduction Ratio (ERR) method to hierarchically select the regressors and the Akaike's Information Criterion (AIC) to truncate the number of terms. Using both approaches, the structure selection is achieved. The design of the excitation input is based on preserving the frequencies of interest and force the system to achieve different points of operation. Hence, having the structure previously selected with ERR and AIC, we use the Extended Least Squares (ELS) algorithm to estimate the parameters. The results show that it is possible to identify the referred systems with no more than five terms. These identified models will be used for nonlinearity compensation in future works.
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