Preamble

Exploring Case-Based Teaching Reform in Fundamentals of Control Engineering
Li Xiang¹*
(1. School of Instrumentation Science and Optoelectronic Engineering, Beijing Information Science and Technology University, Haidian District, Beijing, 100192)

Abstract

To address the persistent challenges in traditional control engineering education—including the disconnection between theory and practice, fragmented learning scenarios, and insufficient cultivation of innovation capacity—this study constructs a "three-dimensional integrated" case-based teaching reform framework encompassing a multi-tiered case library, hybrid teaching model, and virtual simulation platform. By integrating industrial-grade real-world cases (e.g., heating furnace temperature control, UAV attitude control) with the "5E" (Engage-Explore-Explain-Elaborate-Evaluate) hybrid instructional approach, the reform achieves a profound fusion of knowledge transfer and competency development. Quantitative evaluations demonstrate significant improvements in students' system modeling accuracy, course design innovation, and excellence rates in theoretical examinations following the reform. Qualitative research further reveals transformative changes in students' engineering thinking, team collaboration, and lifelong learning capabilities. The study proposes establishing a four-dimensional "Theory-Case-Practice-Innovation" integrated teaching model, leveraging industry-academia collaboration to develop dynamic case libraries, digital twin technologies to construct virtual-real experimental platforms, and alumni tracking feedback mechanisms to form a demand-driven closed-loop talent cultivation system. This provides a replicable reform paradigm for nurturing talent in emerging engineering disciplines.

Keywords: Fundamentals of Control Engineering; Case-Based Teaching; Hybrid Learning; Multi-Tiered Case Library; Engineering Thinking

Project Funding: Beijing Information Science and Technology University Internal Teaching Reform Project "Visual Case Teaching of Fundamentals of Control Engineering Integrated with Simulation Technology"

Introduction

As a core curriculum for engineering majors such as automation and mechatronics engineering, Fundamentals of Control Engineering bears the critical responsibility of cultivating students' ability to analyze and design engineering control systems. However, with the rapid development of emerging technologies like intelligent manufacturing and industrial internet, traditional teaching models are facing unprecedented challenges. The widespread phenomenon of "emphasizing theoretical derivation while neglecting engineering application" has resulted in students who can proficiently perform Laplace transform calculations and plot root loci yet struggle to understand how these mathematical tools apply to practical scenarios such as temperature control systems or robotic motion control. Surveys reveal that over 65% of graduates report that engineering cases encountered during their studies were overly idealized, exhibiting significant discrepancies from the nonlinear, time-varying, and multi-disturbance characteristics of real industrial environments. This misalignment between knowledge acquisition and competency requirements directly leads to enterprises spending 6-12 months providing new hires with specialized training in control system debugging and anti-interference design, substantially increasing talent development costs.

Further analysis reveals three deep-seated contradictions in traditional teaching models. First, the high level of abstraction in control theory stands in stark contrast to the concreteness of engineering problems. Instruction on core topics such as frequency domain analysis and state-space methods often remains detached from specific physical systems, plunging students into a learning dilemma of "doing mathematics for mathematics' sake." Second, knowledge delivery exhibits fragmented characteristics, with classical control theory and modern control methods, continuous and discrete systems taught in isolation without engineering scenarios to connect them, preventing students from constructing a complete cognitive framework for control systems. Third, the one-way, lecture-based teaching approach stifles the stimulation of innovative potential, with teacher-dominated board derivations and software demonstrations occupying the central role while students passively receive knowledge without opportunities for active exploration. Consequently, students often demonstrate a lack of systematic thinking and insufficient innovation capacity when facing complex engineering problems.

In this context, the case-based teaching method, with its unique advantage of "using cases as carriers and problems as orientation," has gradually become an important direction for control engineering teaching reform. By introducing industrial-grade real-world cases, case-based teaching can situate core components such as control system modeling, controller design, and performance optimization within specific engineering contexts, enabling students to naturally grasp the engineering significance of control theory while solving practical problems. Assessment reports from the U.S. Accreditation Board for Engineering and Technology (ABET) demonstrate that graduates from control courses employing case-based teaching exhibit significantly superior system-level problem-solving and interdisciplinary collaboration abilities compared to those from traditional teaching models. China's "Emerging Engineering Education" construction guidelines also explicitly propose transforming engineering education from knowledge transmission to competency cultivation and building a deeply integrated "theory-practice-innovation" talent development system. Therefore, exploring case-based teaching reform in Fundamentals of Control Engineering represents not only a breakthrough innovation in traditional teaching models but also an inevitable choice for responding to national strategic needs and cultivating outstanding engineering talent.

2. Case-Based Teaching Reform Implementation Framework

Based on the above problem analysis, this study constructs a "three-dimensional integrated" case-based teaching reform implementation framework (as shown in Figure 1 [FIGURE:1]) centered on the core concept of "engineering problem orientation and progressive competency cultivation." This framework uses multi-level case library construction as its foundational support, achieves deep integration of theoretical teaching and engineering practice through a hybrid teaching model, and breaks through the temporal and spatial limitations of traditional experiments via a virtual simulation platform, forming a reform path of "case-driven, virtual-real combination, and competency advancement." Specific implementation strategies unfold across three dimensions—case resource development, teaching method innovation, and technology platform empowerment—to systematically address pain points such as case scarcity, scenario fragmentation, and single verification methods in traditional teaching.

2.1 Multi-Dimensional Case Library Construction

In exploring case-based teaching reform for Fundamentals of Control Engineering, constructing a multi-dimensional and hierarchically structured case library proves crucial for enhancing teaching quality and stimulating student interest and innovation capacity. The design of this case library emphasizes not only diversity and representativeness but also applicability and heuristic value in the teaching process, aiming to guide students from basic theory to practical application through rich and varied cases, thereby cultivating their ability to solve complex engineering problems. Specifically, the case library is carefully divided into three categories based on case complexity, application domain, and innovation level: basic verification type, comprehensive application type, and innovative research type, forming an organic whole that is both independent and interconnected.

Basic verification cases serve as the cornerstone of the case library, primarily selecting classic, easily understandable examples that intuitively reflect fundamental control theory principles, such as single pendulum systems and DC motor speed regulation. These cases typically feature simple structures and clear parameters, enabling students to personally experience control system construction, parameter adjustment, and performance analysis through experimental operations or simulation modeling, thereby deepening their understanding and mastery of basic control theory concepts, principles, and methods. Through such cases, students establish a solid theoretical foundation for subsequent study of more complex cases.

Comprehensive application cases focus on interdisciplinary knowledge integration and application, selecting complex systems involving multiple engineering domains as research objects, such as UAV attitude control and intelligent greenhouse environmental regulation. These cases require students not only to possess solid control theory foundations but also to master multidisciplinary knowledge in mechanics, electronics, and computer science, enabling them to comprehensively apply various technical means to solve practical problems. Through participation in comprehensive application case studies and project practices, students can cultivate interdisciplinary thinking and teamwork abilities in practice, learning how to design and implement efficient and stable control systems using system integration methods in complex and changing environments, thereby enhancing their comprehensive ability to solve actual engineering problems.

Innovative research cases represent the highlights and frontiers of the case library, focusing on cutting-edge fields such as industrial robot trajectory planning and intelligent manufacturing system optimization based on emerging technologies like digital twins and artificial intelligence. These cases often exhibit high innovation and challenge, requiring students to possess not only profound theoretical foundations but also keen research insight and innovation capacity. Through participation in innovative research case studies, students can keep pace with technological development, cultivate a scientific spirit of exploring the unknown and daring to innovate, and lay a solid foundation for becoming leading talents in the control engineering field.

2.2 Case Design Principles

In the reform practice of case-based teaching for Fundamentals of Control Engineering, case design constitutes the core element of the teaching system, with its quality directly determining students' ability to transfer theoretical knowledge and cultivate practical innovation literacy. To ensure that case teaching can both carry the systematic nature of control theory and stimulate student learning initiative, we follow the "authenticity-gradient-openness" trinity design principle to construct a case matrix with engineering depth.

Case authenticity serves as the key to breaking the barrier between theory and practice. Using a steel plant heating furnace temperature control system as a prototype, we completely transplanted multi-source heterogeneous data from actual production: including real-time furnace temperature curves measured by thermocouples (containing raw fluctuation data at 200Hz sampling frequency), PID control loop parameters for fuel flow and air flow (including implementation code for integral separation and anti-windup mechanisms), and temperature-time curves required by workpiece heat treatment processes (containing piecewise control strategies for phase transformation critical points). This data not only retains noise interference and nonlinear characteristics from industrial sites but also enables students to intuitively understand the quantitative relationship between control precision and product quality by reproducing real production accident scenarios such as "temperature overshoot causing steel plate grain coarsening." For instance, when analyzing the heating furnace regenerative chamber temperature control case, students must handle dynamic models containing 12 categories of disturbance factors including fuel calorific value fluctuations, reversing valve action delays, and flue gas waste heat recovery efficiency changes. This complexity far exceeds the simplified settings of "ideal sensors + linear objects" in traditional teaching cases, forcing students to apply advanced theories such as frequency domain analysis and robust control for system decoupling and compensation design.

Gradient design constructs a cognitive ladder from basic understanding to comprehensive innovation. The case system begins with single-input single-output (SISO) control systems, using typical cases such as heating furnace gas pressure control and cooling water flow regulation to help students master core skills like PID parameter tuning and stability criterion application. It then gradually introduces multi-input multi-output (MIMO) systems, such as heating furnace combustion control systems that require simultaneous coordination of gas/air flow ratios and furnace pressure. At this stage, students must apply relative gain matrix analysis to examine coupling relationships between variables and implement strategies like feedforward compensation and decoupling control to achieve multi-loop coordination. Finally, in the comprehensive case stage, using heating furnace full-process optimization as an example, students are required to integrate multiple subsystems including temperature, pressure, and flow, and design hierarchical control systems under multi-objective constraints considering energy consumption, equipment life, and production rhythm. This spiral case arrangement not only conforms to cognitive patterns but also forces students to transition from "parameter tuners" to "system architects" through exponential growth in problem complexity.

Open design provides flexible space for personalized learning. Each case reserves multi-dimensional parameter adjustment interfaces: at the model level, students can modify time constants and gain coefficients in the object transfer function to observe changes in system dynamic characteristics; at the algorithm level, they can replace PID controllers with intelligent algorithms such as fuzzy control or neural network control to verify the adaptability of different control strategies through comparative experiments; at the engineering constraint level, they can adjust hardware parameters such as sensor accuracy and actuator dead zone to analyze their impact on system robustness. For example, in the heating furnace temperature control case, students discovered that when thermocouple measurement delay increased from 5 seconds to 15 seconds, the overshoot of traditional PID control surged by 47%, while introducing a predictor could suppress overshoot to within 8%. This inquiry-based learning model of "parameter perturbation-phenomenon observation-theoretical verification" not only deepens students' understanding of control theory essence but also cultivates their ability to abstract and model engineering problems. Through open case design, the teaching team observed student-initiated innovative proposals such as "variable-parameter PID control based on furnace temperature prediction" and "adaptive compensation strategies considering fuel calorific value fluctuations," fully validating the stimulating effect of open architecture on innovative thinking.

2.3 Hybrid Case-Based Teaching Model

In the pre-class phase of the hybrid case-based teaching model, the teaching team constructed a multi-dimensional preview resource system relying on the smart teaching platform. The released digital case manual includes not only three-dimensional interactive models of inverted pendulum systems (such as the gyroscope model in inertial navigation systems shown in Figure 2 [FIGURE:2]), supporting students to observe mechanical structure details through multi-angle rotation and cross-sectional views, but also embedded dynamic simulation modules developed based on MATLAB/Simulink. Students can independently adjust PID parameter combinations and observe real-time changes in system response curves, intuitively experiencing the nonlinear relationship between key indicators such as overshoot and settling time and control parameters.

Accompanying the pre-research question chain pushed by the teaching platform, teachers set the core task of "analyzing influencing factors of slider-pendulum systems" (as shown in Figure 3 [FIGURE:3]), decomposing it layer by layer into sub-problems including mechanical parameters (such as pendulum rod length and moment of inertia), actuator characteristics (motor response bandwidth and output torque), and sensor precision (encoder resolution and sampling frequency). Each problem is equipped with theoretical hint cards to guide students in conducting preliminary analysis using tools such as Routh's criterion and root locus method, and submitting mind maps through the platform discussion area. The system automatically collects behavioral data such as model operation frequency and simulation parameter adjustment ranges, generating cognitive heatmaps to help teachers accurately identify common cognitive misconceptions and provide a basis for differentiated teaching during class.

The in-class phase adopts the "5E" teaching model to construct an immersive learning environment. For example, in the Engage phase, teachers play real vehicle test videos of Tesla's Autopilot system failing to maintain lane position under strong crosswind conditions, presenting engineering details such as sudden lateral displacement and control output saturation through first-person perspective footage to provoke deep thinking about "robust control boundaries." Subsequently, in the Explore phase, students operate physical inverted pendulum experimental platforms in groups, applying classical tuning strategies such as trial-and-error method and Ziegler-Nichols method for parameter optimization. Each group uploads experimental data in real-time to the central monitoring system via wireless sensors, with large screens dynamically displaying comparative curves of control effects from each group, creating a healthy competitive mechanism. In the Explain phase, teachers systematically explain the engineering significance of frequency domain analysis in control system design based on student experimental data: by plotting open-loop Bode diagrams, analyzing the quantitative relationship between phase margin, gain margin and system stability, and comparing the intrinsic correlation between time-domain indicators (such as overshoot) and frequency-domain indicators (such as resonant peak). The Elaborate phase introduces Model Predictive Control (MPC) for comparative analysis, with teachers demonstrating how MPC algorithms effectively overcome the sensitivity of traditional PID control to model errors through rolling optimization and multi-step prediction, and guiding students to compare the robustness differences between the two control strategies under parameter perturbations through simulation. Finally, in the Evaluate phase, students use smart terminals to log into a real-time voting system, quantitatively scoring each group's solution across three dimensions—stability, rapidity, and robustness—with the system automatically generating radar charts to display comprehensive solution performance. Teachers provide targeted comments based on voting results to reinforce students' engineering cognition of trade-offs between control performance indicators.

The post-class phase constructs a closed-loop improvement mechanism of "practice-feedback-iteration." Teachers assign engineering-open transformation tasks, such as adding anti-interference modules to existing inverted pendulum cases, requiring students to comprehensively apply advanced control strategies like feedforward compensation and disturbance observers for system upgrades. Students can upload multimedia materials including solution documents, simulation model files, and experimental videos. Teachers regularly organize online defense sessions, awarding honors such as "Best Innovation Award" and "Most Engineering Value Award," with outstanding works being included in the case library and credited to creators, forming a continuously motivating innovation ecosystem.

This three-stage progressive model of "pre-class precise preview—in-class deep exploration—post-class iterative optimization" effectively addresses core issues in traditional case teaching such as "theory divorced from engineering practice, insufficient student engagement, and discontinuous innovation capacity cultivation," providing a replicable hybrid teaching paradigm for control engineering talent development.

3. Analysis of Teaching Reform Effectiveness

3.1 Quantitative Assessment Data

To systematically verify the actual effectiveness of the hybrid case-based teaching model, the research team conducted comparative experiments with four consecutive cohorts of control engineering students from 2019 to 2022, with the 2019-2020 cohorts serving as the traditional teaching control group (using classroom lectures + verification experiment mode) and the 2021-2022 cohorts as the case teaching reform experimental group (implementing the "three-dimensional case library + 5E hybrid teaching" system). Through constructing a multi-dimensional evaluation index system, quantitative comparative analysis was performed across three dimensions: knowledge mastery, competency enhancement, and innovation literacy.

Table 1 [TABLE:1]. Quantitative Data for 2019-2022 Cohorts

In system modeling competency assessment, the experimental group achieved a correctness rate of 89.7% in mathematical modeling of complex systems, representing a 32% improvement over the control group's 68%. Specifically, in inverted pendulum system modeling tasks, experimental group students more accurately identified nonlinear elements (such as friction dead zones and motor saturation characteristics) and reasonably applied small-disturbance linearization methods for simplification. In heating furnace temperature control cases, experimental group students' dynamic models incorporated 12 categories of actual disturbance factors including fuel calorific value fluctuations and reversing valve action delays, while control group models averaged only 4 simplified disturbances. This difference directly reflected in course design quality—the experimental group's course design innovation score averaged 3.8 points (out of 5), an 81% improvement over the control group's 2.1 points, with numerous innovative achievements emerging in university innovation programs and competitions.

Theoretical examination score comparisons further confirmed the deep effects of the teaching model reform. The experimental group's excellence rate (≥85 points) in theoretical exams increased from 15% in the control group to 28%, a growth of 87%. More notably, the score distribution pattern changed significantly: the control group exhibited a typical normal distribution with 62% of students in the middle range, while the experimental group showed a "left-skewed heavy-tail" characteristic, with 54% of students scoring above 80 points and a 41% reduction in low-scoring (<60 points) students. This change stemmed from the case teaching's cultivation of higher-order thinking skills—in frequency domain analysis assessments, experimental group students more flexibly applied Nyquist criteria to analyze system stability with delay elements, calculating phase margin errors within ±3° (compared to ±8° average error in the control group). In optimal control theory application problems, 37% of experimental group students considered actuator saturation constraints in their solutions, while only 8% of control group solutions addressed such engineering constraints.

The data reflects a profound paradigm shift: the experimental group students developed a "problem-driven—theoretical verification—engineering iteration" cognitive model through case discussions, enabling them to more actively transform control theory into tools for solving practical problems. For example, in UAV attitude control cases, experimental group students spontaneously proposed upgrading traditional PID control to adaptive fuzzy-PID composite control by introducing air density sensors for real-time parameter correction. This transformation from "passive acceptance" to "active creation" represents the core educational achievement attained by the hybrid case-based teaching model through reconstruction of authentic engineering scenarios and construction of multi-dimensional cognitive scaffolds.

3.2 Student Interview Analysis

To further reveal the deep educational value behind the quantitative data, the research team conducted in-depth interviews with 28 students from the experimental group using stratified sampling, covering different academic levels (top 25%, middle 50%, bottom 25%) and gender ratios. Interview content focused on three dimensions: "knowledge transfer ability," "engineering thinking development," and "learning motivation changes."

1. Knowledge Structure Transition from Fragmented to Systematic

The majority of students (21/28) mentioned that the dynamic simulation models and physical experimental platforms in the three-dimensional case library formed a "virtual-real combination" cognitive closed loop. For example, when analyzing inverted pendulum system stability, one student noted: "Routh's criterion that I used to memorize by rote now comes to life when I adjust the pendulum rod length parameters in the 3D model and can visually see the trajectory of characteristic roots moving in the complex plane." This cognitive transformation becomes particularly significant when solving complex engineering problems—when asked how to design a boiler liquid level control system, experimental group students could proactively construct complete models containing 8 subsystems including steam flow disturbances and water supply valve nonlinear characteristics, while control group students mostly remained at the simplified analysis level of single-input single-output systems.

2. Engineering Thinking Transformation from "Problem-Solving" to "Problem Resolution"

Interviews revealed that the "5E" inquiry segments in case teaching effectively cultivated students' systematic engineering thinking. After discussing the "Tesla Autopilot failure case," 75% of students spontaneously attempted to apply "fault tree analysis" to deconstruct problems: deriving layer by layer from sensor noise (root node) to insufficient control algorithm robustness (intermediate node), ultimately proposing composite solutions. More notably, when asked "what if parameter tuning fails," experimental group students demonstrated stronger engineering fault tolerance awareness—19 students proposed adopting a "gradual parameter debugging method" that first ensures system stability before optimizing dynamic performance, while only 5 students in the control group could offer similar strategies, with most others falling into a trial-and-error cycle of "tuning-crash-retuning."

3. Learning Motivation Shift from External Drive to Intrinsic Value Recognition

Online case community interaction data and interview results form strong corroboration: experimental group students logged into the community an average of 3.2 times per week, with 63% actively sharing technical documents, far exceeding the control group students' passive downloading of materials at 0.8 times per week. When discussing "why they are willing to invest extra time optimizing cases," students commonly mentioned: "When I saw that my improved PID algorithm reduced the inverted pendulum swing amplitude by 40%, that sense of achievement was more lasting than high exam scores," and "When I received improvement suggestions from students at other schools in the community, I suddenly realized that control engineering is not isolated formulas but technology that can truly change reality." This value recognition directly translates into sustained learning motivation—experimental group students' autonomous post-class learning content covered frontier areas such as reinforcement learning control (14 students) and industrial network communication (9 students), while control group students' post-class learning remained focused on textbook chapter review.

4. Conclusion

Control engineering case teaching reform effectively promotes the transformation from knowledge to competency through immersive experiences in authentic engineering contexts. This transformation is manifested not only in students' deep understanding and flexible application of core theories such as system modeling and frequency domain analysis but more significantly in the migration of their engineering thinking from a "textbook paradigm" to a "field paradigm"—students begin to actively focus on practical engineering details such as sensor noise suppression and actuator saturation constraints, and can apply the engineering methodology of "problem decomposition—theoretical mapping—solution iteration" to solve complex control problems. Simultaneously, the hybrid teaching model reconstructs the learning ecology from "teacher-dominated" to "student-centered," with the continuous operation of online case communities and cross-institutional collaboration mechanisms fostering a new learning culture of "self-organized learning—collective wisdom co-creation," systematically enhancing students' teamwork and technical communication abilities.

Future efforts must continuously improve the case ecosystem and construct a four-dimensional "Theory-Case-Practice-Innovation" integrated teaching model. On one hand, we must deepen industry-academia integration, jointly developing "living cases" with leading enterprises to incorporate new technologies such as 5G communication and industrial internet into the case library, ensuring teaching content resonates with industry needs. On the other hand, we must strengthen digital technology empowerment, utilizing digital twin technology to construct virtual-real fused experimental platforms that enable full-process digitization of "case design—simulation verification—physical debugging," lowering the technical threshold for student exploration and innovation. Additionally, we should establish long-term feedback mechanisms to dynamically optimize case design through graduate tracking surveys and enterprise satisfaction evaluations, ultimately forming a demand-driven, case-supported, competency-oriented closed-loop talent cultivation system that provides a replicable and scalable reform paradigm for emerging engineering talent development.

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