In this study, we investigated the optimal tracking performance (OTP) of feedback control systems with limited bandwidth and colored noise in a fading channel. For the steady state of the feedback control systems, an equivalent average channel (EAC) model was developed by retaining the effects of the first and second moments of the multiplicative channel output, and on the basis of the coprime decomposition, all-pass factorization, and Youla parameterization of controllers, exact expressions for the OTP were derived by designing two compensators. The expressions quantitatively show the relationship between the OTP and inherent features of the plant. Specifically, the directions and locations of unstable poles (UPs) and nonminimum phase (NMP) zeros adversely affect the tracking performance. Furthermore, the bandwidth limitation and the presence of colored noise also degrade the tracking performance. Finally, our conclusions were verified by considering a numerical arithmetic example.

中文翻译：

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跟踪反馈系统在带宽有限的衰落信道上的性能


在本研究中，我们研究了衰落信道中具有有限带宽和有色噪声的反馈控制系统的最佳跟踪性能（OTP）。针对反馈控制系统的稳态，保留乘法通道输出的一阶矩和二阶矩的影响，在互素分解、全通分解的基础上，建立了等效平均通道（EAC）模型，和 Youla 控制器参数化，通过设计两个补偿器推导出 OTP 的精确表达式。这些表达式定量地显示了 OTP 与植物固有特征之间的关系。具体来说，不稳定极点（UP）和非最小相位（NMP）零点的方向和位置会对跟踪性能产生不利影响。此外，带宽限制和有色噪声的存在也会降低跟踪性能。最后，通过数值算例验证了我们的结论。