Green Industrial Engineering for Sustainable Development

Course Program – Mechatronics in Green Industrial Applications The course provides an integrated framework of multiphysics dynamics, optimal control theory, and mechatronic system design applied to green and energy-efficient technologies. It is organized into three main modules, each combining theoretical lectures, numerical examples, and practical sessions using MATLAB/Simulink/Simscape. Module 1 – Principles of Multiphysics Dynamics and Variational Formulations Introduction to variational principles and their application to mechatronic systems. Fundamentals of the calculus of variations and examples of shape optimization. Hamiltonian formulation of mechanics and its equivalence with the Newtonian approach. Applications of Hamilton’s principle to structural dynamics: vibrations of discrete and continuous systems. Euler–Bernoulli, Rayleigh–Bernoulli, and Timoshenko beam equations. Axial and coupled (axial–bending) vibrations and structural instability phenomena. Hamiltonian formulation of electromagnetic and circuital systems. General equations of mechatronic systems with constant, time-varying, or state-dependent coefficients. Linearization of equations of motion and modal analysis. General architecture of controlled mechatronic systems and numerical examples in Simulink. Module 2 – Principles of Optimal Control Overview and classification of control systems. Variational control and derivation of Euler–Lagrange equations for control design. Linear Quadratic Regulator (LQR) control for single- and multi-degree-of-freedom systems. Practical examples of LQR application to mechanical and mechatronic systems. Generalization of the LQR method and introduction to the Kalman filter. Deterministic Min–Max approach and formulation of the Linear Quadratic Gaussian (LQG) control problem. Variational controllers for nonlinear and nonhomogeneous systems (e.g., cruise control). Applications of optimal control to pneumatic and electromechanical actuator systems. Design of LQR/LQG controllers for vehicle and ship roll stabilization. Introduction to predictive control and integral feedback in the LQR framework. Module 3 – Mechatronic System Design and Synthesis Architecture of a mechatronic system: definition of subsystems and performance indicators (KPIs). Modeling of the plant, sensors, actuators, and control algorithms. Controller synthesis through optimal control methods. System validation via simulation in Simulink/Simscape. Application examples: electronically controlled suspension systems for vehicles; attitude stabilization for drones; vibration control of flexible structures. Laboratory sessions. Introduction to patent databases (EPO, USPTO) and patent analysis in the field of mechatronics.

To successfully attend the course, students are expected to have a solid background in the following areas: Rational mechanics and rigid body dynamics, with particular reference to Lagrange’s and Hamilton’s principles and to the equations of motion for single- and multi-degree-of-freedom systems. Mathematical analysis and linear algebra, including partial derivatives, ordinary differential equations, and linearization methods. General physics and electromagnetism, to understand the principles of electromechanical coupling. Basics of vibration mechanics, including modal models and frequency-domain analysis. Fundamentals of control theory, especially stability, feedback, and state-space representations. Basic knowledge of numerical programming and simulation in MATLAB/Simulink. These prerequisites are typically covered in a Bachelor’s degree program in Mechanical, Automation, or Mechatronic Engineering (or equivalent).

Main Teaching Material Lecture notes prepared by the instructor (Prof. Nicola Roveri), including: Full Lecture Notes – Mechatronics in Green Industrial Applications (updated version). Supplementary materials provided via Google Classroom: numerical examples, MATLAB/Simulink/Simscape models, and exam guidelines. Guidelines for the Exam and additional operational instructions for report preparation. Recommended Reference Books H. Goldstein, C. Poole, J. Safko, Classical Mechanics, Addison-Wesley. D. G. Luenberger, Optimization by Vector Space Methods, Wiley. F. L. Lewis, D. L. Vrabie, V. L. Syrmos, Optimal Control, Wiley. D. Kirk, Optimal Control Theory: An Introduction, Dover. W. J. Terrell, Feedback Control Theory, Princeton University Press. R. C. Dorf, R. H. Bishop, Modern Control Systems, Pearson. P. C. Hughes, Spacecraft Attitude Dynamics, Dover. J. J. Craig, Introduction to Robotics: Mechanics and Control, Pearson. S. Skogestad, I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, Wiley. K. M. Lynch, F. C. Park, Modern Robotics: Mechanics, Planning, and Control, Cambridge University Press. Supplementary Material Official MathWorks documentation for Simulink and Simscape, including sample mechatronic systems. Technical papers and supporting notes provided during lectures or as exam resources.

Attendance is not compulsory but strongly recommended. Regular participation in lectures and computer-based exercises allows students to fully understand the modeling and control methods of mechatronic systems and to gain practical familiarity with the software tools (MATLAB/Simulink/Simscape) used throughout the course.

Guidelines for the Written Part of the Exam The Mechatronics in Green Industrial Applications course exam is divided into two parts: 1. A report on a mechanical control program implemented in Simulink/Matlab. 2. A written test lasting approximately one hour, covering the topics presented in the shared course notes. 1. Report The report should document a virtual experiment conducted using MATLAB, Simulink, or Simscape, focusing on implementing a mechanical control program in Simulink/Matlab. You may refer to the course content for guidance on constructing such a program. MATLAB/Simulink Resources for the Exam Report For the preparation of the report, students may refer to models already developed and made available by MathWorks. These examples provide a solid starting point for designing, simulating, and customizing mechatronic systems within the Simulink and Simscape environments. Students are encouraged to begin with an existing model, gain a thorough understanding of its structure, and subsequently may introduce modifications or extensions (for example, parameter variations, implementation of PID/LQR control, or the addition of external disturbances). The evaluation will primarily focus on the ability to customize the experiment, critically analyze the results, and derive meaningful engineering conclusions. The following examples are recommended for their clarity and educational value. Nevertheless, students are free to explore alternative models or to design their own systems if they feel confident in doing so. • Modeling a Two-Link Robotic Manipulator – MathWorks • Model and Control a Manipulator Arm with Robotics and Simscape – MathWorks • Inverted Pendulum with Animation – MathWorks • Control of an Inverted Pendulum on a Cart – MathWorks • Control DC Motor with PWM Voltage Source and H-Bridge Driver – MathWorks • Permanent Magnet DC Motor – MathWorks • Mass-Spring-Damper in Simulink and Simscape – MathWorks Guidelines for the Report The report must be at least 5 pages long and organized into three main sections: • General Description of the Experiment: A concise overview of the experiment's objective and purpose. • Procedure in the MATLAB Environment: Details on how the experiment was configured and executed using MATLAB. • Analysis of the Results: Discussion and interpretation of the results obtained from the virtual experiments. Customization of the experiment is encouraged. Evaluations will focus on the scientific maturity of the experiment, originality, and accuracy of the results, reflecting the topics covered in the course. Mature analysis and the ability to synthesize results suitable for a future engineer are essential. The following materials must accompany the report: • The MATLAB/Simulink/Simscape code (do not convert the code to PDF format). • A video presentation (approximately 15 minutes) explaining the analysis of the results, similar to a thesis defense. The presentation can be a narrated PowerPoint or a recording of the author discussing the results. The work can be written and presented in either Italian or English, at the student's discretion. All materials—PDF report, MATLAB code, and video presentation—must be sent via email to: nicola.roveri@uniroma1.it before attending the written part of the exam. 2. Written Test The written exam will consist of 1–2 main questions, requiring approximately one hour to complete. The questions will pertain to the course content, as covered in the lecture materials shared on Google Classroom by Prof. N. Roveri. The exact number, duration, and type of questions will be determined by the professor to ensure a uniform level of difficulty for the exam. Use of Computers During the Exam Students are permitted to use their computers during the exam exclusively for the computational part to simplify laborious calculations with the aid of software. The following rules strictly apply: • Permission: Computer use must be pre-authorized by the professor; students must request explicit permission before turning it on. • Monitoring: During computer use, students will be monitored closely to prevent cheating. The professor may require a change of seating to better observe the screen. • Software Restriction: Only the MATLAB environment may be open on the computer. Any violation of this rule will result in immediate cancellation of the exam. • File Access: Students may use exercise files shared by the professor or write new scripts during the exam. Previously prepared files can be consulted only if they have been reviewed and approved by the professor in advance. Embedded lecture notes or text notes within MATLAB scripts are strictly prohibited and will result in exam cancellation. • Limited Usage Time: The computer may be used only for the computational portion of the exam. Once this part is complete, the computer must be turned off. Example Exam Questions Here are illustrative examples of the types of questions or exercises that may appear on the written test: 1. Explain the role of variational dynamics and Hamiltonian principles in the modeling of mechatronic systems. Discuss how these principles are applied to derive equations of motion and analyze system behavior in green industrial applications. Provide examples from structural dynamics or electromagnetic systems. 2. Describe the key methods of optimal control (e.g., LQR, Kalman Filter, and LQG) and their applications in mechatronic systems. Compare their advantages and limitations and illustrate their implementation in green industrial scenarios, such as cruise control or vibration suppression. 3. Discuss the design process of a mechatronic system for a green industrial application. Outline the key steps from system architecture definition and KPI identification to controller synthesis and simulation-based verification. Include considerations for energy efficiency and sustainability.

The course combines frontal lectures, numerical exercises, and computer-based simulation activities, with the aim of integrating theoretical understanding with practical skills in modeling and controlling complex mechatronic systems. Frontal lectures focus on the physical, mathematical, and control principles governing mechatronic systems, as well as on the variational formulation of the equations of motion. During the laboratory sessions, students develop numerical models and optimal controllers in MATLAB/Simulink/Simscape, applying the multiphysics modeling and control techniques introduced in the course. The teaching activity also includes: discussion of case studies involving real-world systems (electromechanical actuators, active suspension systems, drones, smart structures); development of a technical report based on virtual experiments performed in MATLAB; thematic seminars and possible educational visits to laboratories or industrial facilities. All activities are conducted in presence, in a highly interactive environment oriented toward design and experimental simulation, combining theoretical rigor with practical application.