Gain-scheduling multi-bit Delta-Modulator for Networked Controlled System

Abstract

We analyze in this paper stabilization issues for a Networked Control System that uses a Delta-Modulator Scheme within the encoder/decoder structures. We also analyze the packet-loss issue, and determine a maximum allowable number of consecutive bits lost while keeping stability. We then design a compensation scheme for re-synchronizing the encoder and decoder, after a bit is lost in a network without acknowledgment signals. We finally present a compensation scheme that ensures stability after a pre-determined number of bits is lost. Examples and simulations are provided to demonstrate the results.

A brief introduction to the analysis and design of Networked Control Systems

“…These results emphasize the essential role that the available degrees of freedom play in NCS's (see [16][17][18] and also [19][20][21][22][23]). …”

“…Otherwise, if any of the more recent packets in (21) have been received by time k + τ (k), then U (k) is discarded. This guarantee that only fresh data is used at the plant side.…”

Analysis and design of networked control systems using the additive noise model methodology

“…For single-input single-output (SISO) linear time-invariant (LTI) plant models, we show how one can design coding schemes that, for a given initial nonnetworked controller design, allow one to minimize the impact of signal-to-noise ratio constraints on overall closed loop performance. These results emphasize the essential role that the available degrees of freedom play in NCSs (see [17,21,22] and also [23][24][25][26][27]).…”

“…By utilizing the previous results, it is immediate to design an iterative procedure that allows one to construct approximations to the optimal (A(z), F(z)) pair: In a first step, one fixes A(z) (or F(z)); trivial choices are F(z) = 0 and A(z) = 1. Then, one uses (25) to calculate the optimal F(z) for the initial choice of A(z) (or (24) to calculate the optimal A(z) for the initial choice of F(z)). This is repeated fixing A(z) or F(z) intermittently.…”

Stability analysis of optimally quantised LFT-feedback systems

“…So, many results on the dynamic quantiser design have been obtained so far. For example, for remote control over communication channels, the coarsest quantisers for stabilisation have been derived in Brockett and Liberzon (2000), Liberzon and Nesic (2007), and several results have been obtained as the characterisation of the minimum data rates (Nair and Evans 2003;Fagnani and Zampieri 2004;Tatikonda and Mitter 2004) and as the D-modulation (Canudasde-Wit, Rubio, Fornes, and Gomez-Estern 2006;Lopez and Canudas-de-Wit 2007;Canudas-de-Wit, Jaglin, and Crisanto Vega 2007). For control with command-driven actuators, various quantisers have been developed in Quevedo, Goodwin, and De Dona (2004), Minami, Azuma, and Sugie (2007), Azuma and Sugie (2008a) and have been given as hybrid/switching controllers (e.g.…”