The selection of an appropriate descriptive system and modeling framework to capture system dynamics and support process control applications is a fundamental problem in the operation of industrial processes. In this study, to account for the highly complex dynamics of industrial process and additional requirements imposed by smart and optimal manufacturing systems, an extended state space descriptive system, named comprehensive state space, is first designed. Then, based on the descriptive system, a hybrid first principles/machine learning modeling framework is proposed. The hybrid model is formulated as a combination of a nominal term and a deviation term. The nominal term covers the underlying physicochemical principles. The deviation term handles the effects of high-dimensional influence factors using regression of low-dimensional deep process features. To handle the multimodal and time-varying properties of process dynamics, the comprehensive state space is divided into subspaces indicating different operating conditions. The model parameters are identified and trained for each operating condition to form the sub-models. Then the system dynamics are formulated as a weighted sum of sub-models, with the weights being the probabilities that the current operating point belongs to different operating conditions. The weights update with the movement of the operating point in the comprehensive state space. Moreover, the descriptive system provides a platform for visualization, and can act as a digital twin of the physical process. A case study illustrates the feasibility and performance of the proposed descriptive system.