H2 Control through Wireless Sensor Network: A trade-off analysis between energy consumption and control performance based on distinct data rates

Abstract

This paper investigates the problem of control through a Wireless Sensor Network (WSN). Such communication channel is digital (the system to be controlled must be sampled and its mathematical model is discretized) and is also semi-reliable, since it admits the possibility of packet loss (that can be modeled by means of a Markov chain). The aim is to assure the stability of the closed-loop system and a good controller performance (measured in terms of the H2 norm) while trying to reduce the energy consumption of the network. For this purpose, an index that relates those conflicting criteria (H2 norm and energy consumption) is proposed, allowing the designer to choose the best WSN setup. The strategy adopted to develop the trade-off index consists in evaluating different network data rate settings, which implies: distinct sampling rates (better or worse digital representations of the continuous-time plant); distinct energy saving levels (due to higher or lower number of transmissions/receptions per seconds); and distinct probabilities of packet loss (due to, among others, increased network congestion). A numerical example based on the H2 state-feedback networked control of a Furuta’s inverted pendulum is presented to illustrate the employment of the proposed trade-off method. In this example, the statistical data used to model the communication channel are obtained from a WSN workbench.