## 1 Introduction  
Manufacturing systems are facing a new revolution based on the digitization of assets, processes, and computing capabilities imposed by new data-driven digital architectures. These initiatives emphasize their applications in the manufacturing industry to transform production systems into a new generation of systems that are equipped with CPS characterized by a strong interconnection between the physical and digital worlds. Among all of the enabling technologies of Industry 4.0, the DT is considered to lead the way for cyber-physical integration. With the constant and growing demand for products, several companies have driven forward and adapted to the industrial revolution to face the challenge of decreasing delivery times and having higher quality and product reliability. Therefore, the industry is facing a new revolution, based on the digitization of assets, processes, and computing capabilities imposed by the new data-driven digital architectures [1]. Industry 4.0 drives digital transformation, enabling better operational performance through disruptive technologies such as the Internet of Things (IoT), artificial intelligence (AI), cloud computing (CC), CPS, DT, and big data which have contributed to the rapid development of Industry 4.0 [2; 3]. Most initiatives emphasize applications in the manufacturing industry to transform production systems into a new generation of systems that incorporate CPS and are often referred to as cyber-physical production systems. Among all of the enabling technologies of Industry 4.0, the DT is considered to lead the way for cyber-physical integration [4]; this integration is an important prerequisite for smart manufacturing as well as being its core. CPSs and DTs are the preferred means for such integration and have gained considerable attention from academia, industry, and the government. However, there are open points in addressing cyber-physical convergence in traditional manufacturing enterprises to adapt the existing infrastructure to the growing business needs that demand high efficiency and at the same time the reduction of production costs [5]. This drives digital transformation, allowing greater agility and flexibility of production because it can connect the needs of consumers with the industry through automation systems linked to the planning level and enterprise resource planning (ERP) [6]. In addition, thanks to the ability to work with large amounts of data, using sensors and wireless technologies of connected devices in real-time offers promising digitized solutions in various fields of industry, including management, planning, and the control of production [7], allowing manufacturers to save time, increase productivity, reduce waste and costs. This change in the industry involves not only the digitization of processes but also the creation of smart factories, incorporating information and communication technologies (ICT) for the evolution of the supply chain and the production line [8]. However, it should be considered that the development of these systems in the industry involves high costs and requires the change of production systems in several parts of the production line. CPS are multidimensional and complex systems that integrate the cyber and dynamic physical world by adding new capabilities to physical systems through the integration of machine tools, manufacturing processes, computation, and communication, where processes and operations can be monitored and controlled in these computational spaces [3]. One concept of CPPS is the cyber-physical DT, which is a system that integrates digital models of cyberspace with physical manufacturing processes and resources. It has appeared in recent years with the advancement of new technologies and as sensors and IT infrastructure have become more cost effective and reliable [9]. However, it should be considered that CPS and DTs are not identical from many perspectives, including their origin, development, engineering practices, cyber-physical mapping, and core elements.