Lp stability of networked control systems implemented on WirelessHART

Abstract

This paper provides results on input-output Lp stability of networked control systems (NCSs) implemented over WirelessHART (WH). WH is a communication protocol widely used in process instrumentation. It is mainly characterised by its multi-hop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We propose a non-linear hybrid model of WH-NCSs that is able to capture these network functionalities, and that it is more general than existing models in the literature. Particularly, the multi-hop nature of the network is translated into an interesting mathematical structure in our model. We then follow the emulation approach to stabilise the NCS. We first assume that we know a stabilising controller for the plant without the network. We subsequently show that, under reasonable assumptions on the scheduling protocol, stability is preserved when the controller is implemented over the network with sufficiently frequent data transmission. Specifically, we provide bounds on the maximum allowable transmission interval (MATI) under which all protocols that satisfy the property of being persistently exciting (PE) lead to Lp stable WH-NCSs. These bounds exploit the mathematical structure of our WH-NCS model, improving the existing bounds in the literature. Additionally, we explain how to schedule transmissions over the hops to satisfy the PE property. In particular, we show how simultaneous transmissions over different frequency channels can be exploited to further enlarge the MATI bound.

Observer Design for Nonlinear Networked Control Systems With Persistently Exciting Protocols

“…This property turns out to be more natural in the context of real networks. In particular, PE is verified by many network technologies [9], such as Ethernet, IEEE 802.11, and IEEE 802.15.4 standard, including WirelessHART (WH) networks [10] discussed further below. Under PE protocols and other reasonable conditions, we provide a bound on the MATI that guarantees an input-to-state stability property for the estimation error system.…”

“…where τ ∈ R >0 is the MATI and ε is the lower bound on the minimum achievable transmission interval given by the hardware constraints (see, e.g. [10], [15], [16]). Notice that the transmission intervals t i+1 − t i may be time-varying and uncertain.…”

“…A more detailed study of persistently exciting protocols is provided in [9], where more examples can be found. In physical networks such as WH, examples of P E T protocols can be found in [10].…”

“…NCSs implemented over WH, which we called WH-NCSs, have models that possess a very particular structure. In our previous work [10], we studied controller design of WH-NCSs over PE protocols. We showed that exploiting this WH network structure was key to obtaining less conservative MATI bounds in that context.…”

“…We showed that exploiting this WH network structure was key to obtaining less conservative MATI bounds in that context. In this current work, and inspired by [10], we use similar techniques in the context of observer design to show that exploitation of WH network structure yields less conservative MATI bounds guaranteeing an ISS property for the estimation error system. Moreover, we improve our previous results in [13], where we used UGES protocols and Lyapunov-based analysis in the observer design problem over WH-NCSs.…”