Observable State Space Realization of Networked MIMO System for a Novel Virtual Observer-Based Delay Compensation

Abstract

With the ever increasing complexity of cyber-physical system, the coupling and interconnection between distributed nodes lead to a complicated description in mathematics. For example, time delays cannot be ignored in the cyber-physical system modeling. And delay compensation often requires the delayed Multi-Input-Multi-Output (MIMO) system to be presented in state space model and all time delays to be combined to sole side of input or output. The aim of this paper is to model the MIMO system with multiple delays in state space form and simultaneously combine both input and output delays into output channel only. In this paper, following up with the modeling of Networked MIMO System, an observable state-space realization of delayed transfer function matrix is developed, including the case with repeated poles. Meanwhile, multiple time delays are combined and allocated to the output side only. Based on the observable state space model, an observer can be designed and contributed to the delay compensation. Derivation and simulation results prove that the resulting model of Networked Control System (NCS) through the proposed modeling method is equivalent with the original networked MIMO system with both input and output delays in terms of input-output relationship, and thus it can be used in the prospective observer-based delay.