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Mathematical models based on spline functions for industrial applications.

机译：用于工业应用的基于样条函数的数学模型。

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There are several instances where samples of the controlled variable are the only data available to describe a process. In order to determine the performance of a plant, digital techniques are used to analyze the data. Then, the set of samples conforms the plant model. The main disadvantage of this approach is the poor predictive properties that the model has when changes in the process occur.; Spline functions are the tool of choice for the analytical representation of a plant based on the sampled data from a process. Once a plant model is described in spline form, the spline coefficients become the model parameters. These parameters are used for the adaptation of sample-based models.; Two practical applications are considered in this study: non-parametric plant models and systems excited with non-sinusoidal waveforms. Classical adaptive control techniques, such as projection algorithm and least square, can be used when non-parametric plant models are approximated by spline functions. Additionally, the spline approximation techniques extend the applicability of the non-parametric models to the area of multirate sampling control. The spline approximation of voltage and current signals is used in this work to predict the behavior of a nonlinear circuit at a different operating point. Instantaneous phasors are used in combination with spline functions to create a hybrid technique that takes advantage of both classical methods and spline models. Sampled data from electric arc furnaces are used to test the spline-base signal approximation techniques.
机译：在某些情况下，受控变量的样本是唯一可用于描述过程的数据。为了确定植物的性能，使用数字技术来分析数据。然后，这组样本符合工厂模型。这种方法的主要缺点是，当过程发生变化时，模型的预测性能很差。样条函数是基于来自过程的采样数据来分析工厂的分析表示的首选工具。一旦以样条形式描述了工厂模型，样条系数就成为模型参数。这些参数用于调整基于样本的模型。在这项研究中考虑了两个实际应用：非参数工厂模型和由非正弦波形激励的系统。当样条函数近似非参数工厂模型时，可以使用经典的自适应控制技术，例如投影算法和最小二乘。此外，样条近似技术将非参数模型的适用性扩展到了多速率采样控制领域。在这项工作中，电压和电流信号的样条近似被用于预测非线性电路在不同工作点的行为。瞬时相量与样条函数结合使用以创建一种混合技术，该技术可以同时利用经典方法和样条模型。来自电弧炉的采样数据用于测试基于样条曲线的信号近似技术。

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