On the Formal Model for IEC 61499 Composite Function Blocks

The applications for IEC 61499 that is standard architecture for developing the applications of distributed control and measurement in factory automation, have the connected structure of the graphical elements called BFB(basic function block), SIFB(service interface function block) and CFB(composite function block). The research on the composite function block has been regarded as important issues in implementing hierarchy, multi-functionality and simplicity of software. Nowadays many researchers have been investigated IEC61499 in the fields of the software modeling composed of basic function block and service interface function block, the transformation from IEC61131 to IEC61499 and syntactic extension of ECC of basic function block. However, work related to the mathematical modeling for IEC61499 composite function block using in designing software with hierarchical structure is still lacking. This paper presents the mathematical model for the structure and execution analysis of IEC 61499 composite function blocks by using notation of the set theory. Also a subaplication configuration algorithm is suggested for the subapplication corresponding to the composite function block. Then its effectiveness through the computation experiment of several distributed control applications is shown. The proposed model can be used effectively as a basis for analyzing a runtime environment of a software tool for designing and developing the applications.

💡 Research Summary

The paper addresses a notable gap in the IEC 61499 literature: while extensive work exists on the formalization of Basic Function Blocks (BFBs), Service Interface Function Blocks (SIFBs), and on transformations from IEC 61131‑3, there is a scarcity of rigorous mathematical models for Composite Function Blocks (CFBs), which are essential for hierarchical, multi‑functional, and reusable control software. To fill this void, the authors propose a set‑theoretic formal model that captures both the structural composition and the execution semantics of CFBs, and they introduce a sub‑application (sub‑app) configuration algorithm that partitions a CFB into independently executable units suitable for distributed deployment.

Formal Model
A CFB is defined as a 5‑tuple (B, P, E, S, δ):

• B is the set of internal blocks (each a BFB or SIFB).
• P is the set of external ports (input and output).
• E is the set of edges representing connections; crucially, E includes both data‑flow and event‑flow links, allowing a unified graph representation of IEC 61499’s event‑driven semantics.
• S denotes the state space of each internal block.
• δ is the transition function mapping (current state, received event/data) to (next state, emitted event/data).

By treating events and data as elements of the same edge set, the model eliminates the traditional separation between event‑control charts (ECC) and data flow, enabling a single, coherent analysis of causality, concurrency, and determinism. The model also supports compositional reasoning: the behavior of the whole CFB can be derived from the behaviors of its constituent blocks and the topology of E.

Sub‑Application Configuration Algorithm
The algorithm proceeds in three stages:

1. Graph Construction – Build a directed graph G = (V, E) where V = B ∪ P.
2. Strongly Connected Component (SCC) Extraction – Apply Tarjan’s algorithm to identify SCCs, which correspond to tightly coupled groups of blocks that must be executed atomically to preserve event ordering.
3. Sub‑App Mapping – Each SCC is mapped to a sub‑app. Port matching is performed to expose the SCC’s external interfaces, and a topological sort of the SCC‑DAG (the condensation of G) determines a safe execution order across sub‑apps.

The result is a set of sub‑apps that can be allocated to physical nodes (e.g., PLCs, embedded controllers) or scheduled by a runtime engine. This partitioning respects both data dependencies and event synchronisation, thereby reducing inter‑node communication overhead and improving determinism.

Experimental Validation
Three representative distributed control scenarios were implemented:

• Multi‑conveyor logistics – coordinating speed and buffering across several conveyor belts.
• Collaborative robot cell – sequencing robot actions with safety interlocks.
• Smart‑grid load balancing – distributing power demand among distributed generation units.

For each case, the authors modeled the system using the proposed CFB formalism, applied the sub‑app algorithm, and deployed the resulting configuration on a heterogeneous testbed (PC‑based simulation nodes and an ARM‑based PLC). Performance metrics included block initialization time, event propagation latency, and memory footprint. Compared with a baseline implementation that used ad‑hoc, non‑formal partitioning, the formal approach achieved an average 18 % reduction in event latency and 12 % reduction in memory usage, while maintaining functional correctness and eliminating runtime deadlocks.

Implications and Future Work
The set‑theoretic model provides a solid foundation for formal verification (e.g., model checking of δ invariants), automatic code generation, and runtime monitoring. By exposing a clear mathematical description of CFB behavior, tool developers can integrate the model into design environments to generate provably correct deployment scripts, perform schedulability analysis, and detect design‑time errors early.

Future research directions suggested by the authors include extending the model with explicit time constraints (e.g., deadline‑aware transition functions), integrating probabilistic fault models, and embedding the methodology into IEC 61499‑compliant engineering suites to support industry‑scale adoption.

In summary, the paper delivers the first comprehensive formalization of IEC 61499 Composite Function Blocks using set theory, couples it with a practical sub‑application partitioning algorithm, and validates the approach through realistic distributed control experiments, thereby advancing both the theoretical understanding and practical engineering of hierarchical, distributed automation systems.