The course “Nonlinear Control System” cultivates students' digital literacy path under the digital transformation of education

Introduction: With the development of modern information technologies, the deep integration of digital technology and teaching in educational settings has become an inevitable trend. This study utilizes the “Nonlinear Control System” course at Wuhan Institute of Technology, a public university in China, as a teaching experiment to explore and practice the pathway for enhancing the digital literacy of postgraduates in the context of educational digital transformation. In the context of the digital economy, the course faces three major challenges: (1) weak foundational support and a disordered digital environment; (2) outdated curriculum reform and the absence of a digital classroom; (3) lack of digital practices and weak skills literacy.

Methods: This study is mainly based on the Integrated Technology of Subject Teaching Knowledge (TPACK) framework, exploring and proposing paths to enhance the digital literacy of postgraduate students from four aspects: (1) build foundational digital tool application skills upon technological knowledge (TK); (2) construct a digital learning ecosystem oriented by pedagogical knowledge (PK); (3) achieve disciplinary transfer of digital literacy with content knowledge (CK) as the carrier; and (4) promote the advanced development of digital literacy with TPACK integration ability as the core. Adopting action research (March–July 2025), data were collected via questionnaires (57 distributed, 96.5% valid), semi-structured interviews (10 students), and learning artifacts.

Results: The questionnaire showed good reliability (Cronbach's α= 0.87) and validity (expert-reviewed). Results indicated 81.82% of students were “very satisfied” with digital teaching, 72.73% “proficient” in tools (e.g., MATLAB), and 78.18% found digital literacy “very useful” for learning.

Discussion: This study confirms the digital teaching model's effectiveness in improving postgraduates' literacy and provides references for educational digital transformation.

1 Introduction

In the wave of educational transformation in the 21st century, technology is reshaping the landscape of knowledge dissemination in unprecedented ways (Ryspayeva et al., 2025). Global education advocates are actively constructing strategic blueprints and providing policy guidance to facilitate the digitalization of education. Focusing on digital empowerment, The Outline of the Plan for Building an Education Powerhouse (2024–2035) advocates overall transformation of education—including concepts, teaching models and governance. It provides clear direction for China's higher education digitalization. Meanwhile, the global trend of digitalization in education has prompted countries to explore subject-specific paths for cultivating digital literacy. The integration of theoretical frameworks such as Technological Pedagogical Content Knowledge (TPACK) with engineering courses has become a common international research focus.

The “Nonlinear Control System” course is a compulsory core course for postgraduates in Control Science and Engineering at Wuhan Institute of Technology. It originally followed a traditional design: 60% of class hours were allocated to theoretical lectures, which focus on Lyapunov stability theory, sliding mode control, etc. The remaining 40% were for offline experiments, which rely on limited on-campus laboratory equipment. This model only required students to complete basic MATLAB simulation tasks (e.g., simple numerical calculations) rather than in-depth application of digital tools (such as complex nonlinear system modeling or AI-based controller optimization) or immersive virtual simulation practices. For instance, in the pre-reform assessment, only a very small number of students were able to independently use MATLAB/Simulink to optimize controller parameters, which neither met the industry's demand for digital literacy nor the practical needs of scientific research. This highlights the urgency of this research (Snyder and Prinsloo, 2007; Stenliden et al., 2019).

With the advent of the digital era, graduate students, who are the backbone of scientific research and innovation activities, must possess a wide range of digital literacy to meet the future demands of social development and the needs of scientific and technological progress (Ahmed and Roche, 2021; Lei et al., 2021). The aim of this study is to address the three key challenges faced by the “Nonlinear Control System” course—a core compulsory course for postgraduates in Control Science and Engineering at Wuhan Institute of Technology. Guided by the TPACK framework, this study intends to construct and validate an operable digital literacy cultivation system for engineering postgraduates, thereby enhancing their ability to apply digital technologies to solve complex professional problems and providing practical references for the digital transformation of similar specialized courses and the improvement of postgraduates' digital literacy.

2 Challenges faced by “Nonlinear Control System” course under the background of digital economy

Industry 4.0 promotes the rapid development of digital and intelligent economic and social fields (Hidayat-Ur-Rehman, 2024). This trend also has a profound impact on the field of graduate education and brings great opportunities for the future development of graduate students. However, this also poses challenges to the cultivation of digital literacy among graduate students. As a compulsory course for graduate students in the field of Control Science and Engineering, the teaching reform of “Nonlinear Control System” is urgently needed.

2.1 Weak foundational support and a disordered digital environment

The digital age provides a variety of ways for graduate students to overcome traditional learning and research problems, and at the same time, it also puts forward higher requirements for their digital skills (Regmi, 2024). Digital technology, digital space, and data information integration have been embedded in the whole process of graduate students' daily learning and research. With the deep integration of various emerging intelligent technologies and graduate education, a series of high-standard and high-quality smart teachers, smart classrooms, and digital twin platforms have emerged. Online learning platforms such as Blackboard and “Super Star Learning APP” have sprung up, prompting profound changes in students' learning environment, knowledge presentation, learning methods, and means. At the same time, Microsoft Office and other basic office software, as well as MATLAB/Simulink, LabView, and other basic research simulation software for graduate research have brought great convenience (Chen et al., 2012). With the emergence of network communication technologies, remote monitoring and control are possible, so that graduate students can do scientific research anytime and anywhere. However, the problem that the original course design lacks digital support is particularly prominent. For example, the original experimental sessions only allowed students to use MATLAB for basic programming, without access to advanced simulation platforms or cloud-based experimental resources. This made it impossible to conduct complex system simulations, which are crucial for understanding nonlinear control mechanisms. Moreover, the majority of graduate students lack a thorough understanding and practical application skills regarding digital tools and platforms, which results in difficulties when handling complex digital tasks or conducting research in digital environments.

2.2 Outdated curriculum reform and the absence of a digital classroom

The original course has remained unchanged for 5 years, focusing on classic control theory, but omitting content related to the digital age, such as the optimization of control algorithms based on artificial intelligence. The teaching syllabus strictly stipulates 16 weeks of lectures and 4 weeks of experiments, lacking the flexibility to integrate digital projects. This rigidity conflicts with the dynamic characteristics of the development of digital technology. With the deepening of digital transformation and the continuous maturation of cloud computing technology, the content and methods of postgraduate teaching also need to be changed accordingly (Paola Tramallino and Marize Zeni, 2024). As a result, the traditional curriculum does not adapt to the development of digital technology, and the graduate student's knowledge and skills in the digital field are lacking. In addition, colleges have insufficient investment in technical equipment and platform construction, which makes it difficult to support the implementation of digital classrooms for “Nonlinear Control System,” and college teachers have insufficient training and support in digital teaching, lack relevant experience and ability, and are often difficult to navigate the challenges of mathematical tools in the new era. Moreover, many institutions maintain a traditional approach to the course structure of a “Nonlinear Control System,” with rigid course content, syllabi, and assessment standards that lack flexibility and innovation. This fixed curriculum setup is unable to respond quickly to changes in teaching models, thus slowing down the pace of course reform.

2.3 Lack of digital practices and weak skills literacy

Digital economy with industrial digitalization and digital industrialization as its main characteristics has become the strategic point of China's future development (Dorfsman and Horenczyk, 2021; Pang and Yang, 2024). Strengthening the training of engineering talents and their practical abilities, and cultivating high-end talents with digital literacy for future industries are the key directions of graduate personnel training. Under the background of digital transformation, numerous emerging technologies are integrated into the field of graduate education.

However, the educational system and curriculum of the “Nonlinear Control System” remain relatively outdated, with a narrow disciplinary structure. The teaching content and cases fail to keep up with the digital trend and demand in time, and professional construction lags behind the development of emerging industries, which greatly affects the training of digital technology-skilled talents. Moreover, the “Nonlinear Control System” is heavily theoretical and lacks practical opportunities, leading to a weak foundation in digital technologies and skills among students. As a result, students are poorly equipped with the knowledge and ability to apply digital technologies in practice, and they are unable to flexibly utilize digital tools and skills in real-world scenarios.

3 Literature review

3.1 The era value of cultivating digital literacy

Digital technology, with its vast user base and data, is a globalized technology with minimal costs (Zhong et al., 2024). With the wide application of digital technology in all walks of life, improving digital literacy has become an important direction of talent development. As vital contributors to university research and innovation, graduate students require digital literacy as an essential skill for participating in research activities (Anthonysamy and Hew, 2020; Ciampa et al., 2023). Additionally, digital literacy education for graduate students can continually improve both individual and institutional research capabilities and efficiency, thereby enhancing the overall national research competitiveness. Cultivating graduate students with high digital literacy is both a logical necessity for education to adapt to external and internal developments and an unwavering pursuit of educational digital transformation (Hall et al., 2024; Pham et al., 2023; Rossiter et al., 2023). The aim is to “promote individual development” and “promote societal development.” Digital literacy supports comprehensive personal development, while high-quality talent drives coordinated social progress.

At the same time, digital literacy is also an essential skill for facing future societal challenges (Lee and Kim, 2019). With the continuous development and application of technology, digital technology will play an increasingly significant role in future society (Sharma et al., 2025). Existing research has confirmed the importance of digital literacy in higher education but also revealed critical gaps, particularly regarding engineering graduate students. Lu and Liang (2024) note that the digital technology-driven intelligent transformation of higher education presents both opportunities and challenges for university teachers, emphasizing that teachers' digital literacy—encompassing digital awareness, knowledge and skills, teaching capabilities, and learning innovation—has become a key indicator for future educators and a guarantee for high-quality higher education development. However, their research focuses exclusively on teachers and does not extend to the construction of digital literacy training systems for graduate students. Zeng-Hui et al. (2025) further expand on the challenges of digital transformation in higher education, pointing out that while the deep integration of digital intelligence technologies has reshaped the concepts and practices of university teaching services, it also gives rise to issues such as data security risks, limited technology implementation, suboptimal application effects, and insufficient digital literacy among teachers and students. To address these problems, they propose a four-dimensional empowerment solution for university teaching service systems and design a corresponding system architecture. Yet their study remains focused on the macro university level and lacks targeted discussions on graduate students in specialized engineering disciplines (e.g., Control Science and Engineering). Similarly, Zhang (2025) takes Wuhan University as an example to illustrate how universities promote digital reform through integrated teaching platforms and digital intelligence education evaluation systems, with the core goal of cultivating innovative talents. However, like prior research, Zhang's work centers on the macro integration of digital technologies in university management and general teaching, failing to explore the design of discipline-specific digital literacy cultivation paths for graduate students. Wang et al. (2025) analyze the mechanism of digital transformation in higher education, confirming that digital innovation improves educational quality by optimizing resource utilization and promoting knowledge equity, while interdisciplinary integration mediates this process. Their mixed-methods study (combining literature review, surveys, and interviews) also highlights that digital literacy enables students to better leverage digital innovations for interdisciplinary learning. Nevertheless, their research remains at the theoretical level of exploring the “relationship between digital transformation and educational quality” and does not provide operable digital literacy training programs for engineering graduate students. Even studies focusing on the intersection of AI and digital literacy have limitations for engineering education. Dalg et al. (2024) conduct empirical research on tourism education students and find that ChatGPT influences learning outcomes, with digital literacy playing a critical mediating role as a bridge between AI application and effective learning. However, their work does not involve the design of practical digital literacy paths for engineering courses. Complementing these findings (Jackson et al., 2022), argue that strong digital literacy helps individuals adapt to rapidly evolving technological environments, complete tasks more effectively, and develop a nuanced understanding of AI technologies' limitations and potential risks—enabling critical use of these tools by leveraging their strengths and mitigating weaknesses. This further reinforces the necessity of targeted digital literacy cultivation for engineering graduate students, who must apply such literacy to complex professional tasks.

3.2 TPACK model

The TPACK framework, proposed by American scholars Mishra and Koehler, is a theoretical model formed by the integration of technological knowledge (TK), pedagogical knowledge (PK), and content knowledge (CK; Mishra and Koehler, 2006). With the advent of the educational information technology era, teachers are required not only to master traditional CK and PK in their disciplines but also to be proficient in information TK, as well as to consider how to integrate technology into their subjects for better teaching. The TPACK framework integrates teachers' knowledge of using technology for effective instruction into the structure of professional expertise, representing a dynamic integration of CK, TK, and PK. Its specific block diagram is shown in Figure 1.

Figure 1

Figure 1. TPACK model.

Collectively, existing empirical studies based on the TPACK framework have further validated its application value in educational practice. Orozco-Rodríguez and Vera-Soria (2023) employed the TPACK model to find that when technology is deeply integrated into teaching practices, students not only demonstrate strong interest but also regard it as a vital opportunity to improve learning by analyzing and processing information for problem-solving. Teng and Xie (2024) focused on the field of teacher professional development, constructing a knowledge structure framework for teacher education based on TPACK theory, exploring pathways for the deep integration of digital technology into teacher education and instruction, and systematically demonstrating the necessity of this integration trend. However, their research is marked by a critical theoretical narrowness: they treat TPACK as a “teacher training tool” rather than a “student learning framework.” For Nonlinear Control System, this means the framework is not adapted to guide students in integrating TK, PK, and CK independently. Jing et al. (2025) analyzed the over 30-year practice of inclusive digital education in the European Union, noting that while such education has made remarkable contributions to eliminating educational exclusion, bridging the digital divide, and influencing global educational system reforms, it still faces challenges including insufficient external support, immature technical systems, mismatched learning designs, and weak digital literacy among teachers and students. To address these issues, the European Union has adopted governance strategies centered on the “integration of human, technology, and knowledge” under the I-TPACK framework, which involves strengthening top-level design, meso-level deployment, and micro-level reform, building a teacher digital literacy development system oriented to digital inclusion, and constructing a barrier-free and highly participatory inclusive digital knowledge system. Whether stimulating students' learning interests, optimizing teachers' professional knowledge structures, or improving curriculum design quality, the TPACK framework (and its extended I-TPACK form) has demonstrated remarkable adaptability to educational digital transformation. This not only provides an important theoretical reference for this study on digital literacy cultivation pathways in the “Nonlinear Control System” course but also highlights the practical necessity of systematically integrating technical knowledge, pedagogy, and disciplinary content in specialized course instruction.

Based on the above cutting-edge research, it can be seen that the core value of digital literacy has been widely confirmed. Whether in general scenarios, AI integration scenarios, or teacher development scenarios, it all indicates that digital literacy is a key ability for adapting to education in the digital age. Moreover, the application potential of the TPACK framework has been verified, providing theoretical support for the integration of technology, teaching methods and subject content. However, there is a clear gap in the existing research—a digital literacy cultivation system that deeply integrates “technology–teaching method–subject content” has not yet been constructed for the core courses of engineering postgraduates. It neither meets the professional needs of the postgraduate group nor breaks down the TPACK framework into an operational course practice path, nor does it involve the integrated digital teaching design of “theory–simulation–practice” that is unique to engineering courses. This research takes “Nonlinear Control System” as the carrier, materializes the TPACK framework into a four-dimensional practical path, fills the research gap in the cultivation of digital literacy in professional courses for engineering postgraduates, and at the same time provides a new practical paradigm for the application of the TPACK framework in the field of engineering education.

4 Digital literacy improvement path for graduate students

In the digital education of higher education institutions, the application of the modern teacher knowledge structure theory—TPACK framework plays a vital role (Zhang and Zhang, 2024; Ng and Chu, 2023). Based on the TPACK framework and targeting the three challenges of the “Nonlinear Control System” course, this study constructs a four-dimensional digital literacy cultivation path with clear logical progression. The system framework diagram is shown in Figure 2.

Figure 2

Figure 2. System framework.

4.1 Build foundational digital tool application skills upon TK

This design is rooted in Mishra and Koehler's TPACK framework, which emphasizes that TK is the basis for integrating technology into teaching. Specifically, Mancha and Shankaranarayanan (2020) verified that systematic training in discipline-specific tools (e.g., MATLAB for control engineering) significantly improves students' problem-solving efficiency. Thus, we selected CNKI, IEEE Xplore, and MATLAB/Simulink as core tools, as they are widely used in control science research.

Driven by the concept of “Internet + Education,” the course “Nonlinear Control System” is increasingly influenced by modern technologies such as artificial intelligence and virtual reality, enriching classroom teaching forms. In curriculum instruction, it is crucial to establish an integrated cultivation path of “Tool Adaptation-Situational Teaching-Ability Transfer.” First, focusing on the core content of the course, suitable tools are screened. As the main force of scientific research innovation, postgraduates must possess the core ability to retrieve, manage, and cite academic resources accurately and efficiently. The first four chapters of the course focus on the theoretical analysis and technological evolution of various nonlinear control methods. To help students deepen their understanding and broaden their academic horizons, scientific research papers are introduced as important learning carriers. For this purpose, in the early stage of “Nonlinear Control System” teaching, the course specially sets up a core module of information retrieval technology, systematically training students to proficiently use professional databases such as CNKI, IEEE Xplore, and SpringerLink. It also provides guidance on the correct use of literature management and citation tools (e.g., EndNote and Zotero), comprehensively cultivating students' scientific and standardized academic resource management capabilities. Second, each chapter of “Nonlinear Control System” ends with a “Frontier Interpretation” section, integrating ChatGPT-assisted research analysis to help students systematically deconstruct cutting-edge technologies, conduct critical analyses of typical cases, and recreate them for teaching purposes. The course content not only maintains the rigor of the theoretical system but also expands the boundaries of knowledge through dynamic technological practices that are continuously updated. Additionally, in the teaching of the last four chapters, focusing on practical ability cultivation, a systematic practical teaching module is set up. Using MATLAB/Simulink as the core tool platform, students are guided to carry out dynamic simulations of nonlinear systems and controller design practices, enabling them to master important research tools while deepening their understanding and application of theoretical knowledge.

4.2 Construct a digital learning ecosystem oriented by PK

In addition to the cultivation of tool skills, building a suitable digital learning ecosystem is the key to addressing the lack of digital classrooms in courses. In response to the current status of digital tool usage in higher education, this study takes the course “Nonlinear Control System” as a case to create a curricular ecosystem that integrates digital innovation with teaching practice, thereby enhancing students' digital thinking literacy. Based on the TPACK framework, this research conducts an in-depth innovative exploration of the teaching methods for the “Nonlinear Control System.” Our pre-class, in-class, and post-class design draws on Bieza (2020) definition of digital literacy as “contextualized technology application,” while the flipped classroom model is supported by Han and Krumsvik (2024) finding that interactive digital platforms improve learning initiative. The extensive application of artificial intelligence is redefining the spatial-temporal boundaries of traditional classrooms, while the rapid development of digital technologies continues to transform the educational ecosystem.

4.2.1 Pre-class stage

To address the shortage of digital resource construction in traditional teaching, a wealth of digital resources is screened and integrated into the “Super Star Learning APP” teaching platform. A systematic preview package is released via the “Super Star Learning APP,” covering MOOC-intensive lecture videos, preview courseware, inspiring thought-provoking questions, and micro-video resources. The package includes course objectives, syllabi, textbooks, reference materials, etc. In the PPT knowledge-point explanations, animated graphics examples are embedded to help students understand theoretical principles. Teaching videos uploaded to the platform are fragmented and streamlined into 10–20-min micro-videos, allowing students to repeatedly watch them during fragmented time for pre-class preview, or review and self-study at their own pace. Meanwhile, discussion topics are posted on the platform, requiring students to independently access online resources. Tutors provide comments on students' questions to guide pre-class thinking. Additionally, mentors guide students to correctly use generative AI tools for previewing “Nonlinear Control System” knowledge, leveraging AI to build knowledge frameworks. High-quality course-related articles can also be forwarded via QQ and WeChat platforms. Supported by digital technologies, this diverse teaching format promotes deep integration of digitization and instruction, helping students master nonlinear control theory while developing their digital skills and innovative thinking.

4.2.2 In-class teaching stage

The teaching of “Nonlinear Control System” has broken away from traditional models, no longer relying on one-size-fits-all approaches. Innovating the entire teaching process through new information technologies has become a central focus of educational research, leading to the development of a digital literacy curriculum system centered on the “Nonlinear Control System” course. In this curriculum, teachers not only impart basic knowledge and skills of “Nonlinear Control System” but also use the first electronic textbook “Nonlinear Control System,” compiled through the joint efforts of faculty members. Each chapter is equipped with dynamic links, enabling teachers to share real-time updated teaching documents, videos, case studies, and relevant resources, ensuring students are exposed to the latest technological trends and cutting-edge industry issues immediately. This approach enhances the textbook's timeliness, interactivity, and sharability, providing targeted learning support for students. During class, teachers deliver lectures by integrating PPT with the “Super Star Learning APP,” while classroom interaction is strengthened through functions such as attendance checking, in-class quizzes, and random calling via the “Super Star Learning APP.” Teaching content is adjusted in real-time based on classroom feedback. Additionally, the course adopts blended learning and flipped classroom models to enhance the dynamic and interactive nature of the learning environment.

4.2.3 Practical application and after-class expansion stage

The “Nonlinear Control System” course requires postgraduates to possess strong capabilities in integrating theory with practice. The course also integrates students' research directions with practical course content, guiding them to apply theoretical knowledge to real-world problems and enhance their initiative and acumen in the learning process. Digital practice should be supported by a digital environment to create simulated interactive virtual practice setups, enabling students to gain hands-on experience in the classroom. In the teaching of “Nonlinear Control System,” we have broken the traditional “digital resources-teacher-student” teaching model and integrated the “National Virtual Simulation Experimental Teaching Course Sharing Platform.” Resources from this platform are used for course design and implementation, providing various virtual experiment modules and simulation tools tailored for “Nonlinear Control System.” These tools integrate advanced technologies such as artificial intelligence, 5G, and virtual reality. Through this platform, students can conduct highly realistic experimental operations in a virtual environment, solve complex nonlinear control problems, and deepen their understanding of control theory and system behavior. This digital tool reconstructs experimental teaching scenarios through immersive virtual simulation technology, enabling cloud-based and repeatable operations for high-risk, high-cost, and high-loss experiments. This effectively expands the depth and practical dimension of classroom teaching. Additionally, based on traditional teaching methods, the course uses MATLAB/Simulink digital simulation software as an auxiliary teaching tool. As a common tool for control engineering students in scientific research, Simulink allows students to build models of nonlinear control systems using library modules, design different controllers and adjust parameters according to system performance requirements, set simulation parameters, and observe simulation results through the Scope module for performance analysis. Through this systematic approach, the “Nonlinear Control System” course effectively enhances postgraduates' digital literacy, laying a solid foundation for their professional development in the digital era.

Meanwhile, the “Nonlinear Control System” course provides online discussion and instant Q&A functions through the “Super Star Learning APP,” integrating highly interactive learning tools to enable teachers and students to exchange knowledge and ideas at any time. This promotes the deep integration of digital literacy and the “Nonlinear Control System” course, thereby enhancing students' learning initiative, participation, digital literacy, and information acquisition capabilities. The course also establishes the “Smart Chain Academy” digital learning community to support the implementation of a “Nonlinear Control System,” where students can share insights, exchange experiences, and strengthen their learning initiative and lifelong learning awareness. This open learning environment further promotes students' autonomous learning and the sustainable development of their digital skills, providing strong support for improving course quality. Additionally, personalized project cases are released on the “Super Star Learning APP” platform, combining theoretical knowledge learned in the course with operational methods of simulation software. Students complete practical tasks through information retrieval, literature review, and other means. During this process, mentors provide necessary guidance, and students discuss with each other to strengthen interaction and feedback between teachers and students, as well as among students, cultivating their innovative literacy. The results of the practice are displayed in the “Smart Chain Academy” digital learning community to enhance students' innovation capabilities and self-confidence.

4.3 Achieve disciplinary transfer of digital literacy with CK as the carrier

Under the premise of tool foundation and ecosystem construction, achieving the deep integration of digital literacy and subject content is the core of enhancing practical ability. The cultivation of postgraduates' digital literacy should not only focus on theoretical knowledge but also make breakthroughs in practice. Applied digital talent is the key to digital development, so cultivating postgraduates' digital application skills is crucial, especially in the course of “Nonlinear Control System.” It is necessary to construct a deep integration system of “knowledge-tool-ability,” drive the application of digital tools through disciplinary problems, and naturally generate digital literacy in the process of solving professional problems.

Build a “double-skilled” teaching staff, as shown in Figure 3. With the advent of the information age, the role of educators must continuously adjust to meet the educational needs of the new era. In the teaching of “Nonlinear Control System,” since the course content involves cutting-edge technologies in the field of control science and engineering, teachers should not only have profound theoretical knowledge but also rich practical experience. Therefore, the university provides various professional development opportunities for teachers. Regularly organizing “dual-skilled teacher” training programs and encouraging teachers to intern in enterprises, further enhances their industry knowledge and practical skills in addition to teaching. Through close cooperation with enterprises, teachers can more timely grasp the latest industry trends, while applying the innovative industry-university-research integration model to curriculum teaching, thereby improving students' practical abilities and employment competitiveness. Furthermore, the university regularly holds teaching competitions to systematically cultivate teachers' digital literacy and strengthen their capabilities in intelligent classroom management, digital teaching tool usage, and teaching design. These competitions not only promote teachers' growth but also provide students with more attractive and interactive teaching content. Through this comprehensive training system, teachers can better integrate the application of modern educational technologies, improve the effectiveness of classroom teaching, and ensure that students' learning experience in the “Nonlinear Control System” course remains at a high level.

Figure 3

Figure 3. Construction of “double-skilled” teaching team.

To further enhance the effectiveness of digital practice, we have also strengthened interdisciplinary collaboration and encouraged students to engage in project-based learning. This approach combines digital platforms with real-world engineering projects, cultivating students' ability to integrate knowledge from different disciplines and develop innovative thinking. In the “Nonlinear Control System,” students can not only learn through virtual experiments but also collaborate with experts in related fields to tackle real engineering challenges and solve practical problems together. This interdisciplinary collaboration, combined with virtual experiments and simulation tools on digital platforms, further enhances students' practical skills and innovative thinking.

4.4 Promote the advanced development of digital literacy with TPACK integration ability as the core

The digital era is an objective reality, and only by actively embracing it can we “survive.” As digital technologies continue to evolve in the future, digitization will inevitably take on new forms and characteristics. To meet the needs of digital transformation, it is essential to break down the barriers between technology, pedagogy, and disciplinary content, and construct a collaborative system for their deep integration. Teachers provide a methodological framework through TPACK integration demonstrations, students complete the transition from “imitative integration” to “independent innovation” in project practices, and a multi-dimensional evaluation system optimizes teaching strategies through data feedback, forming a closed loop of “demonstration–practice–evaluation–improvement.”

At the teacher level, teachers need to become demonstrators of TPACK integration, deeply integrating cutting-edge digital technologies with pedagogy and disciplinary content. In the “Nonlinear Control System” course, teachers can use MATLAB/Simulink to build virtual simulation experiment scenarios and combine project-based teaching methods to guide students in understanding the internal connections between technical tools and disciplinary knowledge while solving practical problems. Such demonstrations not only convey knowledge and skills but also show students how to organically integrate knowledge from different fields.

At the student level, a three-stage project training model of “basic level–advanced level–innovation level” is implemented. The basic level requires students to imitate teachers' operations to complete the design of the same cases. The “advanced level” requires students to complete similar cases. The “innovation level” requires students to participate in national postgraduate-level control competitions and related social practice activities. The course regularly organizes “Academic Salons on Nonlinear Control Theory,” inviting experts in the field to share the latest developments and technical applications, helping students broaden their academic horizons and stimulate their interest in the course. In addition, the course integrates students' research directions with practical course content, guiding them to apply theoretical knowledge to real-world problems and improve their initiative and acumen in the learning process. Through this systematic approach, the “Nonlinear Control System” course has effectively improved postgraduates' digital literacy, laying a solid foundation for their professional development in the digital age.

To ensure the effectiveness of cultivating TPACK integration capabilities, it is necessary to construct a compatible multi-dimensional teaching evaluation system. Establishing a multi-dimensional teaching evaluation system for the course is a complex but necessary process. The evaluation method has shifted from pure summative evaluation to comprehensive evaluation covering the entire learning process. A combination of process assessment and final assessment is adopted, with the improvement of students' disciplinary knowledge mastery and scientific research capabilities as the basis for evaluating the teaching process. The fundamental purpose is to inspire and promote the development of students' ideological and political core literacy and capabilities. To this end, we have adjusted the evaluation system: process assessment mainly includes the browsing of digital resources, online discussions, classroom attendance, and participation in in-class simulation experiments. The first three can be intuitively viewed for each student through the teacher backend system of the “U-learning” platform, while the latter requires mentors to give a subjective score based on students' enthusiasm in the teaching process. The outcome evaluation mainly starts from two aspects: the final exam and project reports. The final exam focuses on the assessment of theoretical knowledge mastery, and the project report focuses on the assessment of theoretical application and practical ability. Such an evaluation method not only conforms to the actual working environment but also can more comprehensively reflect students' comprehensive abilities and learning outcomes.

5 Research methods

5.1 Research design

This study adopts the method of action research and takes the core course “Nonlinear Control Systems” for postgraduate students majoring in Control Science and Engineering at Wuhan Institute of Technology as the carrier to verify the effectiveness of the four-dimensional digital literacy cultivation path based on the TPACK framework. Action research is a cyclical process of “planning–implementation–observation–reflection,” which is consistent with the dynamic nature of curriculum reform—constantly adjusting teaching strategies and optimizing the path of digital literacy cultivation based on practical feedback. The research period is from March 2025 to July 2025, covering the entire semester of the “Nonlinear Control System” course at Wuhan Institute of Technology.

(1) Sample selection and characteristics: the research subjects are 57 full-time postgraduate students (39 male and 18 female) from the 2023 and 2024 grades majoring in Control Science and Engineering, Communication Engineering, and Electrical Engineering, all of whom are taking the course “Nonlinear Control Systems” for the first time. The limitations of the sample lie in the fact that all the research subjects are within the Chinese higher education system. The homogeneity of cultural and educational backgrounds may make it difficult to directly extend the results to international or diverse educational scenarios. At the same time, failing to distinguish between student groups with and without engineering practice experience may overlook the impact of different practical foundations on the effectiveness of digital literacy cultivation.

(2) Potential bias explanation: the research relies on “self-reported data (questionnaires, interviews)” and “teacher assessment data (learning outcome scores),” and there are two types of bias risks: the first is self-reported bias, where students may overestimate their satisfaction with digital teaching or their mastery of digital tools due to “meeting teacher expectations;” the second is evaluator bias. Teachers' scoring of learning outcomes may be influenced by subjective impressions, and it is necessary to reduce this bias through standardized scoring criteria.

5.2 Data collection instruments

To comprehensively assess the effectiveness of the digital literacy improvement path, we integrated multiple data sources to ensure the validity and reliability of the results:

(1) Questionnaire survey: a structured questionnaire was designed based on the TPACK framework. It includes three core scales (with a total of 15 items), all of which adopt the 5-point Likert scale: students' satisfaction with digital teaching methods; Master digital tools (such as professional databases, MATLAB/Simulink); the perceptual role of digital literacy in learning. Before the official distribution, a pre-survey was conducted among 20 students to correct ambiguous items and ensure the validity of the content. This activity was conducted through a combination of anonymous online questionnaires and student interviews. Use the “Questionnaire Star” software to release questionnaires and analyze the results. Based on the TPACK knowledge framework, an investigation and analysis were conducted on the current status of digital literacy among students of the “Nonlinear Control System” course in the 2023 and 2024 grades at Wuhan Institute of Technology. A total of 57 questionnaires were distributed this time, 55 were retrieved, and 55 were valid, with an effective rate of 96.5%. Among them, there are 37 male postgraduate students and 18 female postgraduate students. Before starting to fill out the questionnaire, participants need to read a standardized ethical statement. They were also informed that participation was voluntary and their responses would be anonymized. To ensure the reliability of the questionnaire, this study selected 20 students for a pre-survey to ensure diversity in terms of comprehensive grades (15 students with scores above 75 and five students with scores below 75) and gender (13 males and seven females).

(2) Semi-structured interview: to supplement the quantitative data, ten students were selected for in-depth interviews. It contains six core issues, focusing on “the impact of digital teaching on the learning process,” “the difficulties in using digital tools,” and “the degree of integration between digital literacy and professional learning,” such as “What was the biggest difficulty you encountered when completing the controller design using MATLAB/Simulink?” Invite two experts in educational psychology to review the outline to ensure the relevance of the questions to the research objectives and avoid leading questions. Each interview lasts for 30–40 min. With permission, it was recorded and transcribed word for word.

(3) Learning artifacts: collect students' course assignments (such as MATLAB simulation reports, virtual experiment records, and project designs) to evaluate the practical application of digital skills and provide objective evidence for the improvement of reading and writing abilities.

5.3 Research procedure

The research will be conducted throughout the semester of the “Nonlinear Control Systems” course from March to July 2025, and will be implemented in four phases. The tasks and time nodes for each phase are clearly defined:

(1) Planning stage (March 1st–March 31st): determine the research objectives (verify the effectiveness of the four-dimensional training path) and the data collection schedule, complete the design and pre-validation of questionnaires and interview Outlines, and formulate the digital teaching implementation plan for the course.

(2) Implementation stage (April 1st–June 15th): implement the four-dimensional cultivation path Before class, a preview package (including 10–20 min micro-videos) is pushed through “Chaoxing Learning Pass.” During class, nonlinear system stability analysis experiments are conducted using the “National Virtual Simulation Experiment Platform.” After class, project tasks (such as “Robot Path Planning Simulation Based on ChatGPT Assistance”) are released through “Smart Chain Academy.”

(3) Collect data synchronously (June 1st–June 5th): questionnaires will be distributed within 1 week after the course ends. Interviews will be conducted from June 10th to June 20th (30–40 min per person, transcribed within 24 h after recording). The learning outcomes of the week will be collected every Friday.

(4) Observation stage (June 16th–June 30th): record students' participation data in digital teaching (such as the number of visits to “Chaoxing Learning Pass” resources and the completion rate of virtual experiments); organize the immediate feedback in class (such as the problems raised by students regarding the operation of digital tools).

(5) Reflection stage (July 1st–July 15th): analyze the preliminary results of the data, identify problems and propose suggestions for path optimization.

5.4 Analysis plan

To comprehensively verify the practical effect of the digital literacy cultivation path based on the TPACK framework in the course of “Nonlinear Control Systems,” this study adopts a mixed analysis strategy of “quantitative + qualitative,” and through the complementarity and verification of the two types of data, ensures the objectivity and richness of the research conclusion.

(1) Quantitative analysis takes questionnaire data as the core, focusing on three major dimensions: satisfaction with digital teaching, mastery of digital tools, and perception of the value of digital literacy learning. Descriptive statistics (mean, standard deviation, percentage) are used to process the data: by calculating the mean and standard deviation of scores in each dimension, the overall feedback level of students on the digital teaching model is reflected.

Scale 1: Digital Teaching Satisfaction Scale (five items, total score 5–25 points) corresponding to the core question of the questionnaire (Figure 4a): “How satisfied are you with the digital teaching method of the “Nonlinear Control System” course?” Item: (1) the integration degree of digital teaching and nonlinear control theory; (2) the assistance of digital resources for learning; (3) the effectiveness of digital teaching interaction forms; (4) the role of digital tools in assisting understanding knowledge points; and (5) the acceptance of the overall digital teaching model. Scoring rules: 1 = very dissatisfied, 2 = not very satisfied, 3 = Average, 4 = relatively satisfied, 5 = very satisfied.

Figure 4

Figure 4. The results of the questionnaire survey. (a) How satisfied are you with the digital teaching method of the “Nonlinear Control System” course? (b) What is the mastery level of professional databases, literature management and citation tools, ChatGPT auxiliary tools, and MATLAB/Simulink research tools? (c) What do you think is the role of digital literacy in daily learning?

Scale 2: Digital Tool Mastery Scale (six items, total score 6–30 points) corresponding to the core questions of the questionnaire (Figure 4b): “What is the mastery level of professional databases, literature management and citation tools, ChatGPT auxiliary tools, and MATLAB/Simulink research tools?” Item: (1) CNKI/IEEE Xplore retrieval; (2) EndNote/Zotero application; (3) ChatGPT academic assistance; (4) MATLAB programming; (5) Simulink modeling; and (6) virtual experiment operation. Scoring rules: 1 = unproficient, 2 = not very proficient, 3 = Average, 4 = relatively proficient, 5 = proficient.

Scale 3: Digital Literacy Perceived Value Scale (four items, total score 4–20 points) corresponds to the core question of the questionnaire (Figure 4c): “What do you think is the role of digital literacy in daily learning?” Item: (1) assistance in understanding abstract theories; (2) support for solving scientific research problems; (3) assistance for interdisciplinary learning; and (4) value for future career development. Scoring rules: 1 = useless, 2 = not very useful, 3 = Average, 4 = relatively useful, 5 = very useful.

In addition, Pearson correlation analysis was adopted to explore the relationship between the mastery of digital tools and learning satisfaction, as well as between the mastery of digital tools and the perceived value of digital literacy, to verify the intrinsic logical connection of the training effect.

(2) Qualitative analysis centers on the transcribed interview texts and learning outcomes: based on the interview data, through word-by-word transcription and topic coding (using the Braun and Clarke, 2006 six-step coding method), three core topic categories (digital tools reduce learning difficulty; virtual experiments make up for the shortage of offline equipment; personalized guidance is needed for digital tools) are extracted. Combined with typical interview quotes, the real experiences and potential needs of students in the digital learning process are explored. Based on learning outcomes such as MATLAB simulation reports, virtual experiment records, and course project designs, combined with evaluation indicators like “accuracy of simulation models” and “rationality of controller parameter optimization,” this paper analyzes the improvement trajectories of students in key abilities such as “simulation modeling” and “solving complex problems,” and selects typical cases to concretely present the actual improvement effects of digital literacy. Further supplement the depth information that quantitative data cannot cover.

5.5 Validity and reliability assurance of instruments

The questionnaire was reviewed by experts and pre-surveyed to ensure its content validity. Moreover, it was triangulated with three types of data—questionnaires, interviews, and learning outcomes—to reduce the limitations of a single data source. Moreover, Cronbach's α coefficient was used to test the internal consistency of the questionnaire.

5.6 Statistical methods

(1) Cronbach's α coefficient is a conventional means for the reliability test of scales. Cronbach's α coefficient was used to test the internal consistency of the questionnaire (as shown in Equation 1). The results showed that the overall Cronbach's α reliability coefficient of the questionnaire was 0.87, which was higher than the standard threshold of 0.7. This indicated that the questionnaire items were reasonably set, had good internal consistency, and could reliably reflect the characteristics of the measured variables. In terms of validity, this study specially invited three experts with relevant research backgrounds and more than 10 years of work experience in the field (covering education, psychology, and digital technology fields) to conduct a systematic evaluation of the questionnaire items, so as to ensure that each indicator accurately reflects the corresponding digital factors.

$\begin{array}{ll}\alpha \text{=}\frac{k}{k-1}(1-\frac{\sum {\displaystyle {\sigma }_{y_i}^2}}{{\sigma }_y^2})& (1)\end{array}$

where k represents the number of questions in the questionnaire design, $\sum {\sigma }_{y_i}^2$ denotes the total variance of all individual items, and ${\sigma }_y^2$ stands for the variance of the total scores of all individual items. In this test, the three values are 3, 63, and 150, respectively.

(2) The Pearson correlation coefficient is used to analyze the linear correlation between “mastery of digital tools” and “learning outcome scores.” It is applicable to the correlation analysis of double continuous variables. The calculation is simple and the result interpretation is intuitive, which meets the research's exploration needs for the “correlation between the use of digital tools and learning effects.” Pearson correlation analysis showed that the mastery of digital tools was significantly positively correlated with teaching satisfaction (r = 0.68, p < 0.01), and the mastery of digital tools was significantly positively correlated with the perceived value of digital literacy (r = 0.73, p < 0.01) (Table 1).

Table 1

Table 1. Pearson correlation analysis results of key variables.

5.7 Ethical statement

Before data collection, provide all student participants with detailed informed consent forms, clearly stating the research purpose, data collection methods, usage scope, confidentiality measures, and the right to withdraw from the research at any time without affecting course grades. All participants voluntarily signed the informed consent form. The questionnaire and interview data were anonymized by replacing personal information with codes to ensure the privacy and rights of the participants.

6 Results and discussions

6.1 Questionnaire results

The results of the questionnaire survey are shown in Figure 4. All data are calculated based on the total scores of the corresponding scale items. The specific explanations are as follows:

(1) How satisfied are you with the digital teaching method of the “Nonlinear Control System” course? This question is quantitatively evaluated through the Digital Teaching Satisfaction Scale (five items, each worth 1–5 points, with a total score of 5–25 points). The scoring rules correspond to the total score range as follows: a total score of ≥20 points is “very satisfied,” 17–19 points is “average,” and ≤ 16 points is “dissatisfied.” The survey shows that 81.82% of students are “very satisfied,” 14.55% are “relatively satisfied,” and 3.63% are “dissatisfied.” The average teaching satisfaction rate is 4.32 (standard deviation = 0.68). This high satisfaction result is not accidental but an inevitable outcome of the deep integration of technology and teaching. Consistent with the empirical research conclusion of Orozco-Rodríguez and Vera-Soria (2023) based on the TPACK framework, their research confirms that when technology is no longer an “add-on” to teaching but is deeply integrated with subject content and teaching methods, it can significantly enhance students' recognition of learning. This issue focuses on the integration effect of digital teaching methods with subject content and teaching methods, as well as students' acceptance and feedback on this integration model. Through follow-up interviews, it was found that most students showed strong interest in the course's digital teaching methods and highly recognized the positive role of this model in improving learning efficiency and knowledge comprehension. For instance, some students mentioned that they used MATLAB/Simulink dynamic simulation and the National Virtual Simulation Experiment platform to transform abstract core knowledge points such as Lyapunov's stability theory and sliding mode control into visual and operable practical scenarios, effectively reducing the learning difficulty of nonlinear system modeling and stability analysis. This is highly consistent with the view proposed by Stenliden et al. (2019) that digital tools can expand the boundaries of students' practice. However, the survey also revealed individual special cases. This special situation supplements the research limitations of Zeng-Hui et al. (2025) on “insufficient digital literacy among students.” Some postgraduates from cross-disciplinary backgrounds reported facing significant challenges in course learning and finding the content complex due to inconsistent undergraduate and graduate majors and a lack of prerequisite knowledge related to the “Nonlinear Control System.” In response to this issue, stratified teaching strategies will be adopted in subsequent teaching: on the one hand, more basic knowledge explanation videos, classic case analyses, and other preview materials will be uploaded to the “Super Star Learning APP” platform before class to help students with weak foundations build knowledge frameworks in advance; on the other hand, personalized tutoring will be provided to such students after class, including forming study mutual aid groups, arranging teacher Q&A sessions, and special exercise training, to help them make up for knowledge gaps. This ensures that students with different foundations can benefit from digital teaching and continuously optimize teaching effectiveness.

(2) What is the mastery level of professional databases, literature management and citation tools, ChatGPT auxiliary tools, and MATLAB/Simulink research tools? This question is quantitatively evaluated through the digital tool Mastery Scale (six items, each worth 1–5 points, with a total score of 6–30 points). The scoring rules correspond to the total score range as follows: a total score of ≥23 points is rated as “proficient,” 18–22 points is rated as “average,” and ≤ 17 points is rated as “unproficient.” Among them, 72.73% of students are “proficient,” 20% are “average,” and 7.27% are “unproficient.” The average tool mastery was 4.15 (standard deviation = 0.75). This result validates the core viewpoint of Mancha and Shankaranarayanan (2020)—that systematic training in subject-specific digital tools can significantly enhance students' problem-solving efficiency. The reason why this study can achieve a high level of tool mastery lies in the fact that when conducting operation teaching of tools such as MATLAB and EndNote, the application of the tools was effectively embedded into the course chapters, allowing students to naturally master the tools in the process of solving professional problems and avoiding the traditional training drawback of “disconnection between learning and application.” This subject mainly examines students' mastery and application ability of relevant technical tools in their professional fields. Through discussions, it was found that some students encountered obstacles in using MATLAB to write control algorithms or retrieving foreign literature through IEEE Xplore due to a lack of pre-training in programming and literature retrieval. This is consistent with the phenomenon observed by Regmi (2024) that graduate students tend to encounter obstacles in the application of complex digital tools. Although most students have good application capabilities of research tools, the needs of vulnerable groups still need to be paid attention to. Through dynamic and personalized teaching strategies, a “research tool mutual assistance community” should be established, with proficient students serving as team leaders to achieve experience transmission through online Q&A, code sharing, etc. Teachers regularly push typical error case analyses of tool usage to further strengthen the synergistic effect between tool application and professional learning, laying a solid foundation for students' future research and engineering practice.

(3) What do you think is the role of digital literacy in daily learning? This question is quantitatively evaluated through the Digital Literacy Perceived Value Scale (four items, each worth 1–5 points, with a total score of 4–20 points). The scoring rules correspond to the total score range as follows: a total score of ≥17 points is considered “very useful,” 12–16 points is “average,” and ≤ 11 points is “useless.” Among them, 78.18% of students believe it is “very useful.” This result is consistent with the research conclusion of Jackson et al. (2022). Strong digital literacy can help individuals better adapt to the technological iteration environment and efficiently complete complex tasks. In this study, students' high recognition of the value of digital literacy stems from the “disciplinary transfer ability” of digital literacy, which enables students to truly feel that digital literacy is not an abstract concept but a core ability that can be directly applied to solve professional research and engineering practice problem. However, 16.36% think it is “average,” and 5.46% consider it “useless.” The mean perceived value is 4.21 (standard deviation = 0.71). This issue emphasizes the role of digital literacy in the process of subject learning and how to enhance learning outcomes through the integration of digital technology and subject teaching. Through discussions, it was found that 55.56% of students who chose “average” admitted that they only stayed at the basic operation level of digital tools and failed to deeply integrate them with professional learning. For example, some students only use MATLAB to complete simple numerical calculations, but do not try to use it for system modeling and optimization; or only use ChatGPT for text polishing, but do not explore its application in high-order scenarios such as algorithm design idea generation and research problem decomposition. This finding fills the research gap of Wang et al. (2025) their study only confirmed that digital literacy can promote interdisciplinary learning, but did not point out the problem that the application of shallow tools cannot fully leverage the value of digital literacy. In the teaching process, more “digitally driven control projects” can be designed, requiring students to comprehensively use MATLAB to complete robot path planning tasks, etc., so as to force the improvement of digital literacy through practice and cultivate students' digital ability to solve complex engineering problems.

6.2 Interview results

Ten semi-structured interview texts were encoded by themes, and three core themes were extracted: “digital tools reduce learning difficulty,” “virtual experiments make up for the insufficiency of offline equipment,” and “digital tools require personalized guidance,” which mutually confirm and complement the results of the questionnaire. The frequency and typical citations are shown in Table 2. Students generally believe that digital tools and virtual experiments have addressed the pain points of traditional teaching, verifying the supplementary value of virtual experiments to traditional practical teaching, which is consistent with the conclusion of Pang and Yang (2024) that “Virtual simulation technology breaks through the limitations of traditional experiments.” It is worth noting that five students proposed that “targeted training is needed when retrieving foreign language literature using IEEE Xplore,” which echoes the result in the questionnaire that “7.27% of students are not proficient in the tools,” indicating that the individualized needs of vulnerable groups still need attention. This indicates that the path for cultivating digital literacy needs to be further optimized. Specialized training modules should be designed for the application difficulties of different tools. At the same time, regular communication channels should be established to promptly collect students' problems in tool usage and provide precise guidance, thereby enhancing the pertinence and effectiveness of the cultivation path.

Table 2

Table 2. Summary of interview thematic coding.

6.3 Learning artifact assessment results

The average score of the students' MATLAB simulation report was 82.3 (standard deviation = 6.5), which was significantly higher than 67.5 (standard deviation = 8.2) before the reform. The completion rate of virtual experiments reached 96.4, and 63.6% of the students' project designs integrated AI tools such as ChatGPT for algorithm optimization or problem decomposition. This series of results fully demonstrates the practical effectiveness of the training path. Consistent with the conclusion of Pang and Yang (2024)- virtual simulation technology can effectively break through the equipment limitations and risk constraints of traditional experiments and enhance students' practical operation abilities.

7 Conclusion

This study explores and practices the enhancement of digital literacy for graduate students from multiple perspectives. It creates an excellent environment for cultivating digital literacy and provides solutions to advance graduate students' digital skills. The effectiveness and general applicability of these enhancement pathways were validated using the specialized course “Nonlinear Control System” at the Wuhan Institute of Technology. These findings confirm the proposed methods' success and their potential for broader application in similar academic settings. Future research can expand the sample scope, conduct multi-center and interdisciplinary studies, and incorporate graduate student samples from universities in different regions and various engineering disciplines to verify the universality of the approach and the localization adjustment strategies.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

ZH: Conceptualization, Resources, Writing – review & editing. DZ: Conceptualization, Data curation, Investigation, Writing – review & editing. YZ: Investigation, Methodology, Writing – review & editing. ZL: Data curation, Methodology, Writing – original draft. HZ: Data curation, Funding acquisition, Investigation, Project administration, Supervision, Writing – review & editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Hubei Province Philosophy and Social Science Research Project (Special Task Project) (24Z328), 2024 Annual Theme Case Project-Healthy China (ZT-2410490004), National Research Project on Smart Course Teaching Reform in Universities (BLDXZHKCYJ007), 2024 New Engineering Discipline Construction Project (XGK02070), Wuhan University of Technology Undergraduate Teaching Research Project (X2024015), and Shandong Province Artificial Intelligence Empowered Education and Teaching Application Research Project for 2025 (WL-AIJ2504038).

Acknowledgments

The authors would like to thank the teaching and research team of Wuhan Institute of Technology for their support in the teaching experiment of “Nonlinear Control System” course. We also appreciate the valuable suggestions from colleagues during the research process.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

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