Signal-to-noise ratio requirements subject to a PID controller design

In networked control a channel model is explicitly considered within the standard feedback loop configuration. It has been previously shown that an important communication channel parameter related to the stabilisability of the control feedback loop is the channel Signal-to-Noise Ratio (SNR). In this work we propose rules for the controller design for a given closed loop bandwidth that quantify the SNR requirement of a memoryless additive white Gaussian noise (AWGN) channel over the feedback path. The design is centered on a PID controller structure due to its simplicity and common use. We also consider reduced plant model complexity (first and second order models) in order to be compatible with the PID controller structure.