Multiple-input multiple-output (MIMO) tests are used to replicate environmental conditions on dynamic systems in a lab setting. MIMO tests allow responses at multiple locations to be replicated far better than possible with normal single input tests. However, achieving a desired response at multiple response locations is affected by various factors. Specifying test tolerances based on multiple responses (vs. on just a single input) is challenging and of great interest. The dynamic relationships between the inputs and the outputs of the system, given by the frequency response functions (FRFs), may not be perfectly characterized. Given a desired output, the FRF matrix must be inverted to obtain an input. This process has inexact solutions because the FRF matrix is usually not square and is ill-conditioned. The realization of time histories from a frequency domain input is not perfect, and the spectral content of the actual input to the system does not match what was initially sought after. Previous work has established a framework for predicting error in MIMO tests, the approximate error prediction method (AEPM), but was limited in the types of error sources that could be accounted for and the tests it could be applied to. This paper improves that method by changing to a matrix-based formulation and accounting for inversion error, called the exact error prediction method (EEPM). The EEPM is applied to similar tests in the previous paper, specifically single-input single-output (SISO) and square MIMO tests, with significant improvements in error prediction over the AEPM. Additionally, a broader set of rectangular MIMO tests, where inversion is a large source of error, are conducted with similarly effective results.

中文翻译：

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MIMO 控制测试的精确误差预测方法


多输入多输出 (MIMO) 测试用于在实验室环境中复制动态系统的环境条件。 MIMO 测试可以比正常的单输入测试更好地复制多个位置的响应。然而，在多个响应位置实现期望的响应受到多种因素的影响。根据多个响应（相对于仅单个输入）指定测试容差具有挑战性且非常有趣。由频率响应函数 (FRF) 给出的系统输入和输出之间的动态关系可能无法完美表征。给定所需的输出，必须对 FRF 矩阵求逆以获得输入。该过程具有不精确的解，因为频响函数矩阵通常不是方阵并且是病态的。从频域输入实现时间历程并不完美，系统实际输入的频谱内容与最初寻求的不匹配。先前的工作已经建立了一个用于预测 MIMO 测试中的误差的框架，即近似误差预测方法 (AEPM)，但在可解释的误差源类型及其可应用的测试方面受到限制。本文通过更改为基于矩阵的公式并考虑反演误差来改进该方法，称为精确误差预测方法（EEPM）。 EEPM 应用于上一篇论文中的类似测试，特别是单输入单输出 (SISO) 和方形 MIMO 测试，与 AEPM 相比，在错误预测方面有显着改进。此外，更广泛的矩形 MIMO 测试（其中反演是一个很大的误差源）也得到了类似的有效结果。