Signal-to-Noise Ratio Requirements for Discrete-time PID Controllers

Abstract In networked control a channel model is explicitly considered in discrete-time within the classic feedback loop scheme. It is well known by now that the channel model signal-to-noise ratio (SNR) happens to be an important parameter related to the overall stabilisability of the output feedback loop. In this paper we offer the rules for the design of discrete-time proportional-integral-derivative (PID) controllers for given closed loop bandwidth that quantifies the SNR requirement for the memoryless additive white Gaussian noise (AWGN) channel over the feedback path, which is a common used communication channel model. The design is centered on a PID controller structure due to its wide use in the industry. Since we focus on a PID controller structure, we then reduce the analysis to plant models of first and second order which are the structures more compatible with the PID controller design.