Remote Control Over Noisy Communication Channels: A First-Order Example

In this note, we consider a set up in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a noisy discrete channel. Our goal is to design codeword lengths of block source and channel encoders, and a controller to meet a model matching performance objective. Such design problems are difficult in general, as there is a strong interplay between control objectives and communication constraints, which forces the synthesis of controllers and encoder-decoder pairs to be done simultaneously. Current approaches typically fix one, while the other is designed to meet some objective. We first construct a model matching performance metric that captures the tradeoffs between coding the reference command to achieve more accuracy at the remote site and designing a controller to meet performance. We then simultaneously synthesize the controller and encoder codeword lengths that meet the specified objective for a first-order plant and model case. Finally, we illustrate performance sensitivity to the poles of the plant and model, and to the channel noise