# Application of Modeling and Simulation in a Self-Reprogrammable Prototype of a Manufacturing System
## 2 Digital Twin  
The DT can be defined as a virtual representation of products, processes, or services, enabling the replication of real-world characteristics in a simulated environment [16]. DT facilitates the modeling of real systems in a digital architecture, allowing interaction and data exchange among interconnected systems [29]. This interaction is typically established through real-time data exchange enabled by sensors [30; 31]. Digital models used for DT can be expressed in four dimensions: the Geometric Model, which represents geometry and physical connections; the Physical Model, which encompasses its properties and characteristics; the Behavioral Model, which represents its dynamism in response to external actions; and the Rule Model, which can explore tacit concepts, serving as a basis for building more intelligent models [32]. In essence, a DT is characterized by three fundamental elements: a physical component, a virtual representation, and the connection between them. This concept emerged in 2002 at the University of Michigan by [PERSON] et.al. [33]. Some researchers classify DT components into two categories: Elementary Components, these include the physical component, the virtual representation, and the connection linking the physical and virtual environments; Imperative Components, these encompass IoT devices, collected and stored data, machine learning models for prediction, response, and optimization, data and information flow security, and the performance evaluation of the virtual representation [16; 22]. The DT concept differentiates itself from Digital Models, Virtual Factory Models, and Product Lifecycle Management (PLM) systems through some key features: Data Flow Integration, seamless integration of data between the physical system and the digital model; Real-Time Synchronization, continuous synchronization of virtual factory models with real-time data; Component Information Management, comprehensive capture and management of information from product components; Smart Products Integration, interfacing with other advanced technologies; Model Clustering, enabling real-time data monitoring and processing [8; 16]. Additionally, the DT environment incorporates continuous learning and self-updating capabilities based on data collected through sensors or other external sources [30]. There are essentially three levels of integration between the real and digital environments: Digital Model, characterized by the manual exchange of data between the real and virtual environments; Digital Shadow, where data flows automatically from the real system to the virtual environment, but the exchange of data from the virtual system to the real one is performed manually; and DT, where data flows automatically in both directions between the virtual and real environments [33]. DT allows the convergence of simulation, prototyping, real-time monitoring, analytics structuring, and optimization technologies. However, implementing DT is intrinsically tied to other technologies, such as integrated devices, big data, and machine learning tools. These dependencies affect the understanding and application of DT models, as successful implementation requires a high level of technological maturity and seamless integration of complementary technologies [16]. DT relies on robust simulation models that rely on data received in real time, which in turn benefits from the results offered by the simulation [34]. Despite these challenges, DT presents several benefits, including: the capability to conduct complex testing without affecting the real environment; cost reduction by minimizing the need for physical prototypes; shortened project timelines; development of machine learning models to support decision-making processes. Through these capabilities, DT enables the representation of design, testing, production, and operational processes within a virtual environment [30].