The mineral flotation process plays a pivotal role in the extraction and purification of nonferrous metal ores such as copper and silver. However, its inherent characteristics—strong nonlinearity, substantial disturbances, and frequent operating condition changes—pose major challenges to traditional control strategies, which often fail to achieve dynamic adaptability and global optimality. This research aims to develop an intelligent control framework capable of maintaining high concentrate grades and system stability under fluctuating production conditions.

To address process variability and model mismatch, a multimodel adaptive optimal control method based on adaptive dynamic programming (ADP) is proposed. First, a multicondition modeling framework is established using recurrent neural networks (RNNs), with the beluga whale optimization (BWO) algorithm employed to globally optimize RNN learning rates. This BWO-RNN modeling approach significantly enhances the generalization capability and fitting accuracy across different operating scenarios. In the control stage, a parallel ADP tracking controller within an augmented state-space framework is adopted, enabling real-time policy iteration to compute the optimal control law. Furthermore, a cumulative error–based model-switching mechanism is introduced to dynamically select the most suitable submodel and controller in response to changing process conditions, thereby ensuring robust system performance and seamless controller transitions.

The proposed framework was validated using simulation data from a copper–silver flotation plant. Compared to traditional model-based control and (particle swarm optimization) PSO-optimized RNNs, the BWO-RNN model achieved higher fitness values and shorter training times. In control experiments involving transitions among three typical operating conditions, the multimodel ADP controller demonstrated superior tracking accuracy for copper and silver concentrate grades, with lower overshoot and faster response times than baseline controllers. In addition, the model-switching strategy effectively suppressed oscillations and maintained stability even under abrupt changes in operating conditions, demonstrating strong robustness. The overall control cost was reduced by 4.3%, indicating improved reagent efficiency and operational economy.

This study presents a novel adaptive control framework integrating a multimodel structure, BWO-RNN–based data-driven modeling, ADP-based optimal tracking control, and a dynamic model-switching mechanism. The proposed method effectively addresses the nonlinear, time-varying, and disturbance-prone characteristics of the flotation process. Simulation results confirm its capability to achieve stable and accurate concentrate grade tracking across diverse operational scenarios, offering a promising approach for industrial deployment in mineral flotation systems. Future work will focus on extending the framework to real-time online identification and practical field implementation in industrial flotation plants.

Multimodel intelligent control technology provides an effective solution for managing complex systems. Traditional single-model control methods often struggle to achieve satisfactory performance when dealing with systems charactered by multimodal behaviors, strong nonlinearity, and uncertainty. In contrast, multimodel intelligent control describes different system states or behaviors by constructing a model set composed of multiple models, each representing a specific operating condition or mode. A dedicated controller is designed for each model, forming a corresponding controller set. A switching criterion based on the identification error between each model and the actual plant is designed. When the parameters of the controlled system change, the system switches to the model that best matches the current conditions and activates the corresponding controller. This approach significantly enhances adaptability and robustness, making it well-suited for complex, uncertain, stochastic, and nonlinear systems. Furthermore, with the continuous advancement of artificial intelligence, neural networks, and other emerging technologies, the application scope of multimodel intelligent control is expanding, which promotes the development of multimodel interaction fusion and multichannel applications.

In the area of model set optimization, various optimization strategies, such as genetic algorithms, particle swarm optimization, and other intelligent algorithms, have been proposed to enhance the accuracy and generalization capability of the model. This paper explores key challenges related to switch timing, target model selection, switching accuracy, and switching speed. Several indicator function designs are introduced to optimize the switch performance between models. With the integration of neural networks, fuzzy logic and other advanced technologies, the strategies underlying multimodel intelligent control have evolved considerably. The basic principle, design method, and stability of multimodel intelligent control have been extensively studied, and a variety of control strategies have emerged, such as neural network–based multimodel adaptive control and fuzzy logic–based multimodel control. From a practical standpoint, multimodel intelligent control has found wide application in industrial automation, intelligent manufacturing, and intelligent healthcare. These applications have demonstrated significant improvements in automation levels, production efficiency, and intelligent system optimization. In healthcare, for example, it has supported the automatic control of medical devices and the intelligent analysis of medical data.

Despite its advantages, multimodel intelligent control technology still faces several challenges. These include improving the accuracy and generalization ability of the model, optimizing the algorithm of the switching mechanism for greater efficiency, and integrating the approach with other advanced technologies to broaden its application range. Addressing these challenges requires further in-depth research and development. In the future, the continued advancement of artificial intelligence and machine learning is expected to drive multimodel intelligent control technology toward more intelligent, efficient, and precise control outcomes. Further research is likely to explore new application domains—such as speech, text, image, and video processing—within multimodal and cross-modal contexts.

The rapid advancement of artificial intelligence (AI) and digital technologies has necessitated the enhancement of the practical skills of graduate students, particularly in applying theoretical knowledge to real-world problems. However, traditional training models face several challenges, such as insufficient guidance, delayed feedback, inefficient supervision, and a lack of personalized learning experiences. This paper addresses these limitations by proposing an AI+ digitalization-based model designed to improve the practical ability of graduate students. This model integrates AI technologies with a digitalized experimental environment to provide a more personalized, efficient, and data-driven learning process.

The AI+ digitalization model is composed of three main layers: the data layer, the capability layer, and the application layer. The data layer gathers information on students, learning resources, experimental data, and equipment. In the capability layer, AI technologies such as deep learning and cloud computing are used to process the gathered information, providing insights that guide experimental decisions. The application layer presents these insights in the form of interactive learning tools, including virtual lab assistants and personalized learning services. Key features of the model include automated lab access, smart equipment management, and AI-driven real-time feedback on experimental progress. AI technologies allow for the continuous monitoring of students’ experiments, identifying issues, and delivering tailored feedback to enhance their learning experience. To evaluate the model, a case study was conducted using a signal amplification experiment. Students engaged in prelab activities, including reviewing digital learning materials, designing circuit diagrams, and simulating experimental setups. During the lab session, they worked in a digitally enabled environment where the system automatically recorded their progress, provided AI-assisted troubleshooting, and generated real-time analysis of their experimental data. After the experiment, the students received personalized feedback, and their instructors monitored their progress remotely, ensuring timely and data-informed evaluations.

The experimental results highlighted several key benefits of the AI+ digitalization model compared with traditional training methods. First, the model significantly improved lab management efficiency by automating routine tasks such as equipment distribution, lab access, and progress tracking. Second, students benefited from personalized learning experiences, with the system offering targeted feedback based on their performance and learning patterns. High-performing students were identified for more advanced experimental opportunities, whereas students requiring additional support were provided with extra resources and guidance. Third, the AI-driven system’s real-time tracking of experimental data allowed instructors to intervene promptly in cases of incorrect setups or safety concerns, improving the overall quality of the experimental process and helping students more deeply understand key concepts.

The AI+ digitalization-based model for practical ability training offers a transformative approach to graduate education. By integrating AI technologies into experimental designs and execution processes, the model enhances both the efficiency and effectiveness of teaching and learning. It equips students with the skills necessary to conduct independent research, troubleshoot complex problems, and apply theoretical knowledge to practical situations. The model also provides instructors with valuable data, enabling more informed decisions regarding curriculum development, student assessment, and resource management. Ultimately, the AI+ digitalization model can significantly improve the practical abilities of graduate students, fostering innovation and preparing them to meet the demands of an increasingly digital and technology-driven world.