This paper presents a solution for the modelling, implementation and simulation of the fractional-order process of producing the enriched ¹³C isotope, through the chemical exchange between carbamate and carbon dioxide. To achieve the goal of implementation and simulation of the considered process, an original solution for the approximation of fractional-order systems at the variation of the system’s differentiation order is proposed, based on artificial intelligence methods. The separation process has the property of being strongly non-linear and also having fractional-order behaviour. Consequently, in the implementation of the mathematical model of the process, the theory associated with the fractional-order system’s domain has to be considered and applied. For learning the dynamics of the structure parameters of the fractional-order part of the model, neural networks, which are associated with the artificial intelligence domain, are used. Using these types of approximations, the simulation and the prediction of the produced ¹³C isotope concentration dynamics are made with high accuracy. In order to prove the efficiency of the proposed solutions, a comparation between the responses of the determined model and the experimental responses is made. The proposed model implementation is made based on using four trained neural networks. Moreover, in the final part of the paper, an original method for the online identification of the separation process model is proposed. This original method can identify the process of fractional differentiation order variation in relation to time, a phenomenon which is quite frequent in the operation of the real separation plant. In the last section of the paper, it is proven that artificial intelligence methods can successfully sustain the system model in all the scenarios, resulting in the feasible premise of designing an automatic control system for the ¹³C isotope concentration, a method which can be applied in the case of other industrial applications too.

This paper provides the modeling, implementation, and simulation of fractional-order processes associated with the production of the enriched ¹³C isotope due to chemical exchange processes between carbamate and CO₂. To demonstrate and simulate the process most effectively, an execution of a new approximating solution of fractional-order systems is required, which has become possible due to the utilization of advanced AI methods. As the separation process exhibits extremely strong nonlinearity and fractional-order-based performance, it was similarly necessary to utilize the fractional-order system theory to mathematically model the operation, which consists of the comparison of its output with an integrator function. The learning of the dynamic structure’s parameters of the derived fractional-order model is performed by neural networks, which are AI-based domain solutions. Thanks to the approximations executed, the concentration dynamics of the enriched ¹³C isotope can be simulated and predicted with a high level of precision. The solutions’ effectiveness is corroborated by the model’s response comparison with the reaction of the actual process. The current implementation uses neural networks trained specifically for this purpose. Furthermore, since the isotopic separation processes are long-settling-time processes, this paper proposes some control strategies that are developed for the ¹³C isotopic separation process, in order to improve the system performances and to avoid the loss of enriched product. The adaptive controllers were tuned by imposing them to follow the output of a first-order-type transfer function, using a PI or a PID controller. Finally, the paper confirms that AI solutions can successfully support the system throughout a range of responses, which paves the way for an efficient design of the automatic control for the ¹³C isotope concentration. Such systems can similarly be implemented in other industrial processes.