Optimal noise shaping for networked control systems

In Networked Control Systems (NCS's) achievable performance is limited by the characteristics of the communication links used to transmit signals in the loop. In this paper we focus on ideal bit-rate limited channels, i.e., channels in which signals need to be quantized prior to transmission. We use noise shaping quantization ideas to develop a novel NCS architecture that takes quantization into account. Using linear time invariant system theoretical tools, we show how to design a noise shaping quantizer that minimizes the impact of quantization noise on loop performance, as measured by the variance of the tracking error component due to quantization. We provide explicit analytical expressions for both the optimal noise shaping quantizer parameters and the optimum achievable performance. It is also shown that the proposed NCS architecture outperforms other schemes recently proposed in the literature.