This article presents a solution to the 2 × 2 multivariable tracking error problem. Current quantitative feedback theory methods commonly employ plant‐inverting splittings in order to arrive at an approximately decoupled design on the feedback control elements. This results in suitable design regions in the high‐gain, low‐frequency range, but can result in conservative design at and above the gain‐crossover frequency, resulting in overdesigned feedback controllers. Our method aims to reduce this conservatism by supplementing a plant‐inverting design with a non‐plant‐inverting design, which tends to perform well at higher frequencies. Decoupling the design of the controller elements is facilitated by making use of appropriate existence conditions. The union of the two resulting design regions then describes a larger solution space, and by enlarging the admissible design regions for the feedback controller, lower gain feedback controller design at all design frequencies of interest may be possible. A benchmarking example is presented, showing the viability of the proposed method.

中文翻译：

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2×2跟踪误差问题的互补定量反馈理论解决方案

本文提出了2×2的解决方案多变量跟踪误差问题。当前的定量反馈理论方法通常采用工厂求逆分裂，以便在反馈控制元件上实现近似解耦的设计。这会在高增益，低频范围内产生合适的设计区域，但会导致增益交叉频率及以上的设计保守，从而导致反馈控制器的设计过度。我们的方法旨在通过用非植物反相设计补充植物反相设计来减少这种保守性，非植物反相设计在较高频率下往往表现良好。通过使用适当的存在条件，可以使控制器元件的设计脱钩。然后，两个结果设计区域的并集描述了更大的解决方案空间，并且通过扩大反馈控制器的允许设计区域，可以在所有感兴趣的设计频率下实现较低增益的反馈控制器设计。给出了一个基准测试示例，显示了所提出方法的可行性。