This paper presents the application of the tensor product (TP)-based model transformation approach to produce Tower CRrane (TCR) systems models. The modeling approach starts with a nonlinear model of TCR systems as representative multi-input–multi-output controlled processes. A linear parameter-varying model is next derived, and the modeling steps specific to TP–based model transformation are proceeded to obtain the TP model. The TP model is tested on TCR laboratory equipment in two open-loop scenarios considering chirp signals and pseudorandom binary step signals applied to the three model inputs (control inputs). The nonlinear and TP model outputs in the two scenarios are the payload position, the cart position, and the arm angular position. The nonlinear and TP model outputs are collected, measured, and compared. The simulation results prove that the derived TP model approximately mimics the behavior of the nonlinear model; both system responses and numerical approximation errors are illustrated.

中文翻译：

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基于张量积的塔式起重机系统建模模型转换方法

本文介绍了基于张量积 (TP) 的模型转换方法在生成塔式 CRrane (TCR) 系统模型中的应用。建模方法从 TCR 系统的非线性模型开始，作为代表性的多输入多输出受控过程。接下来导出线性参数变化模型，并进行特定于基于 TP 的模型转换的建模步骤以获得 TP 模型。考虑应用于三个模型输入（控制输入）的啁啾信号和伪随机二进制步进信号，在两个开环场景中的 TCR 实验室设备上测试了 TP 模型。两种场景下的非线性和 TP 模型输出是有效载荷位置、小车位置和臂角位置。收集、测量和比较非线性和 TP 模型输出。仿真结果证明，导出的TP模型近似地模拟了非线性模型的行为；说明了系统响应和数值近似误差。