Fault Diagnosis in Discrete Event Systems Using Interpreted Petri Nets
Jess Armburo-Lizrraga, Antonio Ramrez-Trevio, Ernesto Lpez-Mellado, E. Ruiz-Beltrán · InTech eBooks · 2008
Advances in Robotics, Automation and Control 70 locating the faults of the corresponding sub-model.(Arámburo-Lizárraga, et al., 2007) shows how to design low interaction distributed diagnosers reducing the communication among them and proposes a redundant distributed diagnoser scheme composed by a set of independent modules handling two kinds of redundancy (duplication or TMR).This work considers the system modeled as an interpreted PN (IPN) allowing describing the system with partially observable states and events; the model includes the possible faults it may occur.In order to build such a model, this work presents a bottom-up modeling methodology in which the behavior of the system elements is decomposed into state variables; a range for each state variable must be settled.These ranges represent the possible values of state variables.Afterwards, these rages are coded into IPN (modules), where each value is represented by a different place.Then two composition operators for joining modules are used; the first one is named synchronic composition, which merges transitions according to certain rules.It is similar to the synchronic product presented in (Giua & DiCesare, 1994); the second one is named permissive composition, which uses selfloops for enabling transitions among modules; this allows constraining the model behavior into the actual system behavior.This new operator avoids the use of tuning phases of other modeling methods used in supervisory control (Giua & DiCesare, 1994).Based on the derived IPN model with the proposed methodology, the diagnosability property for IPN models is introduced.Roughly speaking, this property says that an IPN is diagnosable if it is possible to know both, when a faulty place is marked and which faulty place is marked.This property is closely related to the observability property (Aguirre-Salas, et al., 2002) and (Ramírez-Treviño, et al., 2003) and polynomial algorithms to test when an IPN is diagnosable are derived, avoiding the reachability analysis of other approaches.Also, a distributed diagnoser is presented; every distributed diagnoser uses the local information or communication among diagnosers for detecting and locating a system fault.The diagnosability property is preserved in the distributed architecture.Redundancy techniques could be applied to the distributed diagnosers to detect and locate a malfunction in the distributed diagnosers set.The chapter is organized as follows: section 2 provides basic definitions of PN, IPN and the modeling methodology are presented.In section 3 the property of input-output diagnosability is defined and characterized, a diagnoser scheme devoted to detect and isolate failure states is also presented.Section 4 presents a procedure to build a reduced IPN model.Section 5 describes a method for model decomposition allowing interaction distributed diagnosers, also, it is presented a redundant scheme for reliable diagnosis applying redundancy to the distributed diagnosers.Finally, conclusions are given. Basic notations and system modeling Petri net basicsWe consider systems modeled by Petri Nets and Interpreted Petri Nets.A Petri Net structure is a graph G = (P, T, I, O) where: P = {p 1 , p 2 , ..., p n } and T = {t 1 , t 2 ,... ,t m } are finite sets of nodes called respectively places and transitions, I (O): P × T → ℤ + is a function representing the weighted arcs going from places to transitions (transitions to places), where ℤ + is the set of nonnegative integers.The symbol • t j (t j• ) denotes the set of all places p i such that I(p i ,t j )≠0 (O(p i ,t j )≠0).Analogously,denotes the set of all transitions t j such that O(p i ,t j )≠0 (I(p i ,t j )≠0) and the incidence matrix of G is C=[c ij ], where c ij = O(p i ,t j ) -I(p i ,t j ).www.intechopen.