This paper presents a smart supervisory framework for a single process controller, designed for Industry 4.0 shop floors. This digitization of a full supervisory suite for a single process controller enables self-awareness, self-diagnosis, self-prognosis, and self-healing (by definition, these "self" elements are missing from other supervisory frameworks diagnosing numerous controllers in parallel). The proposed framework is aligned with the concept of a Cyber Physical System (CPS), since its implementation generates a rich cyber physical entity of the controlled process. This CPS entity can either be considered as the process digital twin, or can provide a solid basis for generating it. Finally, the framework includes the main characteristics of Industry 4.0, such as advanced use of Artificial Intelligence (AI) and big data analysis. The framework is based on four modules: (1) Control and Awareness module-performing both continuous process control and adjustments, as well as machine learning (ML) and statistical process control (SPC) for identifying abnormalities that require further diagnosis; (2) Process-diagnosis module-performing continual (recurrent) analysis of the process state and trends; (3) Prognosis and Healing module-performing prognosis and automated intervention via parameter changes, re-configurations, and automated maintenance; (4) External Interaction Platform-an interactive module for interfacing with experts, presenting them with the process analysis information and obtaining feedback from them as part of a learning process. Using an implementation showcase to illustrate the methodological framework's applicability, we demonstrate its real-world potential. The proposed framework could serve as a guide for implementing smart process control and maintenance systems in Industry 4.0 shop floors. It could also provide a firm basis for comparison with future suggested frameworks. Future research directions could include pursuing improvements to the proposed process control framework and validating the framework by case studies of its implementation.