Departamento de Ingeniería Eléctrica, Universidad de Concepción, Chile.
ISA Trans. 2019 Dec;95:235-242. doi: 10.1016/j.isatra.2019.05.010. Epub 2019 May 15.
The explicit consideration of a communication channel model in a feedback control loop is known to be constrained by a fundamental limitation for stabilizability on the channel signal-to-noise ratio (SNR) when the linear time invariant (LTI) plant model is unstable. The LTI modelling approach for real, usually nonlinear, processes compromises accuracy versus complexity of the resulting model. This in turn introduces a gap between the proposed model and the real process, which is known as the model uncertainty. In this paper we then study SNR limitations by considering the continuous-time scenario and the case of an additive coloured Gaussian noise (ACGN) channel with bandwidth limitation, for which we then quantify the infimal SNR subject to the simultaneous presence of plant, channel and noise model uncertainties. We observe, for the special case of memoryless additive white Gaussian noise (AWGN) channels, that the obtained SNR limitation subject to plant model uncertainty can be redefined as a channel capacity limitation for stabilization.
在反馈控制回路中显式考虑通信信道模型时，已知当线性时不变 (LTI) 植物模型不稳定时，通道信噪比 (SNR) 的稳定性存在基本限制。对于实际的、通常是非线性的过程，LTI 建模方法在模型的准确性和复杂性之间进行权衡。这反过来又在提出的模型和实际过程之间引入了差距，这被称为模型不确定性。在本文中，我们通过考虑连续时间场景和具有带宽限制的加性色高斯噪声 (ACGN) 信道的情况来研究 SNR 限制，然后对同时存在的植物、信道和噪声模型不确定性的情况下，对最小 SNR 进行量化。我们观察到，对于无记忆加性白高斯噪声 (AWGN) 信道的特殊情况，在植物模型不确定性下获得的 SNR 限制可以重新定义为稳定的信道容量限制。
