Markov Modeling of Delays in Networked Automation and Control Systems Using Colored Petri Net Models Simulation

This paper presents a two-step approach for modeling delays in Networked Automation and Control Systems (NAS/NCS). The approach combines the two well-known techniques: formal modeling using Colored Petri Nets (CPN) and mathematical modeling using Markov models to achieve this purpose. The first step is to build and simulate a structure-conserving hierarchical timed model for the whole NAS/NCS using (CPN). The step aims to generate extensive sampled time delay data records for detailed time analysis of delays. In the second step, Markov modeling is used to build compact mathematical models for network induced delays of NCS and response time of NAS. In addition, the second step introduces a new concept of mutual Markov modeling to analyze interaction between the two types of induced delays in NCS, namely, the sensor-to-controller time delay and the controller-to-actuator time delay. The proposed approach is new from two points of view: first using formal discrete event models for simulation in the modeling of NCS delays and their interaction, second using Markov models for modeling response time of NAS instead of estimating probability distributions of delays. In this paper a detailed procedure for the modeling steps will be provided in comparison to the overall concept presented in previous works. Finally, a numerical example is provided to demonstrate the applicability of the proposed mutual Markov modeling approach in the design of NCS state-feedback control.