PORTALE DELLA DIDATTICA

### Modelling and simulation of mechatronic systems

02PCYQW

A.A. 2023/24

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Mechatronic Engineering (Ingegneria Meccatronica) - Torino

Course structure
Teaching Hours
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Teaching assistant
Context
SSD CFU Activities Area context
ING-IND/14
ING-INF/04
5
5
C - Affini o integrative
B - Caratterizzanti
Attivit� formative affini o integrative
Ingegneria dell'automazione
2022/23
The course is taught in English. The course provides the students with the basic skills required for model building and simulation of electromechanical systems. This means the theoretical and practical capabilities that will be used in order to model mechatronic components, equipment, and systems. The student will acquire the capability to understand the interactions between electromechanical structures and their actuations of various nature (such as magnetic, capacitive, piezoelectric. Unifying methodologies (state coordinates, work, potential and kinetic energy and co-energy, dissipation) and modeling approaches (Lagrange equations, Bond-Graph approach) constitute the core topics of the course.
To predict when the engine of our car needs maintenance, to design an algorithm that will land a spacecraft on the Moon, and to build a realistic digital twin of a smart factory we need a computer model of the system. The heart of every computer model is a mathematical model, that is, a system of mathematical equations (state equations) that governs the system's dynamics. Modern mechatronic systems are very complex and comprise components of different nature (mechanical, electromagnetic, hydraulic etc.) However, general methods exist that allow to derive mathematical models. This course introduces two approaches to complex systems modeling. The first one is based on Lagrangian formalism (generalized coordinates, energy functions, Lagrangian equations of motion), and the second one is based on bond graph diagrams (components, ports, effort and flow variables).
The student acquires the following knowledge - How to describe the structure of a system; various types of analytical representation (linear, non-linear, time invariant, time-varying, etc.) and their representations based on physical principles - Vectors, matrices, reference systems: how to use this concepts to represent motions of solid bodies in space - Rigid displacements in space: translations and rotation matrices , homogeneous representation of the body pose - Kinetic and potential energy: the building block for modeling approaches based on Lagrange equations. - The concept of state variables. - From Lagrange equations to state variable equations. - The concepts of flows and efforts; power and the bond-graph methodology; The student develops the following abilities - Ability to describe a rigid body in space and its motion using vectors and matrices (rotation and homogeneous) - Ability to compute analytically and numerically the kinetic and potential energy of a system that includes many bodies (multi-body analysis) - Ability to write the Lagrange equation, to transform in state variable equations and use for model simulation - Ability to write the Bond-Graph model, to transform in state variable equations and use for model simulation - Ability to use the above methods for modeling mechanical, electromagnetic and electromechanical systems such that actuators and transducer (electromagnets, capacitive, moving-coil transducers, piezoelectric material, etc.).
The student acquires the following knowledge: -- How to describe motion of a rigid body in the space and related mathematical tools: vectors, matrices, fixed and mobile reference systems, translation and rotation matrices, Euler angles, quaternions; -- How to introduce generalized coordinates and compute positions, attitudes, linear and angular velocities of rigid bodies as functions of generalized coordinates (direct/inverse kinematics); -- Lagrangian approach to dynamics: kinetic and potential energy, Rayley dissipation function, virual work; -- How to transform dynamical equations into the state-space form and linearize them; -- How to describe the structure of a system; various types of analytical representation (linear, non-linear, time invariant, time-varying, etc.) and their representations based on physical principles; - The concepts of flows and efforts; power and the bond-graph methodology; The student develops the following abilities: - Ability to describe a rigid body in space and its motion using vectors and matrices (rotation and homogeneous); - Ability to compute analytically and numerically the kinetic and potential energy of a system that includes many bodies (multi-body analysis); - Ability to write the Lagrange equation, to transform in state variable equations and use for model simulation; - Ability to write the Bond-Graph model, to transform in state variable equations and use for model simulation; - Ability to use the above methods for modeling mechanical, electromagnetic and electromechanical systems such that actuators and transducer (electromagnets, capacitive, moving-coil transducers, piezoelectric material, etc.).
The course requires the knowledge of the basic elements of physics, in particular mechanics and electromagnetism, and the capacity to compute with vectors and matrices; elements of system theory (states, inputs, outputs, transfer functions) elements of automatic control (simple PID control networks) are not mandatory, but beneficial.
The course requires the knowledge of 1) basic elements of physics, in particular mechanics and electromagnetism; 2) operations with vectors and matrices (product of two matrices, inverse matrix, determinant, eigenvalues); 3) basics of differential calculus (derivatives of a composite function, partial derivatives). Elements of system theory and automatic control (states, inputs, outputs, transfer functions) are not mandatory, but beneficial.
1. Introduction, examples of mechanical, electrical, hydraulic, electromechanical equipment, definition of power, energy and co-energy. (8 hours) 2. Analytical models: understanding of the system structure, of the analytical representation (linear, nonlinear, time invariant, time varying, etc.) and its representation based on physical principles. (10 hours) 3. Definition of the effort and flux variables in mechanical, electrical and hydraulic systems. (8 hours) 4. State functions: kinetic co-energy and potential energy. (10 hours) 5. Mathematical language needed in the course: vectors and matrices, rigid body kinematics and dynamics, generalized variables, degrees of freedom, constraints, holonomicity. Roto-translations of rigid bodies. general properties of the body dynamics: inertia, dissipation, elasticity. (8 hours) 6. Lagrange Equations. (8 hours) 7. Bond-graph modelling based on power exchange between subsystems. Power variables, reversibility, construction rules, relation between bond-graphs and block diagrams. (12 hours) 8. Configuration space and state equations. The dynamic system as a unifying mathematical representation. Linear and nonlinear models, Fundamental properties: stability and passivity. (8 hours) 9. How to write the equations that describe the interactions inside electromechanical actuators and transducer, as electromagnets, capacitive transducers, moving coil transducers, piezoelectric materials, synchronous motors. (10 hours) 10. Mechanical models of the rigid body, finite elements models. Finite elements models of lumped parameters electrical and electronic systems. Modal reduction techniques and bond-graph representation. (10 hours) 11. Examples and implementation of simulated systems. (8 hours)
1. Introduction, examples of mechanical, electrical, hydraulic, electromechanical equipment, definition of power, energy and co-energy. (8 hours) 2. Analytical models: understanding of the system structure, of the analytical representation (linear, nonlinear, time invariant, time varying, etc.) and its representation based on physical principles. (10 hours) 3. Definition of the effort and flux variables in mechanical, electrical and hydraulic systems. (8 hours) 4. State functions: kinetic co-energy and potential energy. (10 hours) 5. Mathematical language needed in the course: vectors and matrices, rigid body kinematics and dynamics, generalized variables, degrees of freedom, constraints, holonomicity. Roto-translations of rigid bodies. general properties of the body dynamics: inertia, dissipation, elasticity. (8 hours) 6. Lagrange Equations. (8 hours) 7. Bond-graph modelling based on power exchange between subsystems. Power variables, reversibility, construction rules, relation between bond-graphs and block diagrams. (12 hours) 8. Configuration space and state equations. The dynamic system as a unifying mathematical representation. Linear and nonlinear models, Fundamental properties: stability and passivity. (8 hours) 9. How to write the equations that describe the interactions inside electromechanical actuators and transducer, as electromagnets, capacitive transducers, moving coil transducers, piezoelectric materials, synchronous motors. (10 hours) 10. Mechanical models of the rigid body, finite elements models. Finite elements models of lumped parameters electrical and electronic systems. Modal reduction techniques and bond-graph representation. (10 hours) 11. Examples and implementation of simulated systems. (8 hours) Practical exercises in class will be devoted to analytically model several simple systems, using the different approaches introduced in the course.
The course consists of two parts: Lagrange equations (primarily focused on mechanical systems and Lagrange approach to dynamics) and Bond Graph diagrams. Practical exercises in class will be devoted to analytically model several simple systems, using the different approaches introduced in the course.
For the Lagrange approach: B. Bona, "Dynamic Modelling of mechatronic Systems", CELID, 2013 For the Bond-graph approach : Dean C. Karnopp, Donald L. Margolis, Ronald C. Rosenberg, "System dynamics: modeling and simulation of mechatronic systems", New York, Wiley, 2000. Slides, notes and other written material is available through the course web page
For the Lagrange approach: B. Bona, "Dynamic Modelling of mechatronic Systems", CELID, 2013 For the Bond-graph approach : Dean C. Karnopp, Donald L. Margolis, Ronald C. Rosenberg, "System dynamics: modeling and simulation of mechatronic systems", New York, Wiley, 2000. Slides, notes and other written material is available through the course web page
Modalit� di esame: Prova scritta in aula tramite PC con l'utilizzo della piattaforma di ateneo;
Exam: Computer-based written test in class using POLITO platform;
... The exam is constituted by a written test (no oral exam), and it is aimed at evaluating the competencies of the candidate with reference to all the topics of the course program. It consists of two parts: Part 1 � (LAG approach): one to three exercises (usually two); the exam lasts approximately 1 hour and 10 min; books and notes CAN be used. Examples are given during the course. Part 2 � (BG approach): one to three exercises (usually two); the exam lasts approximately 1 hour and 10 min; books and notes CAN be used. Examples are given during the course. The two parts can be taken together in the same exam session or separately at different times during the year. Each part is evaluated with a separate mark, computed as the weighted mean of the scores of the proposed questions, and expressed in 1/30. The final mark is unique and is the arithmetical mean of the marks of the two parts. Each part must get at least a mark > 9/30; if the mark is lower, that part must be repeated.
Gli studenti e le studentesse con disabilit� o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unit� Special Needs, al fine di permettere al/la docente la declinazione pi� idonea in riferimento alla specifica tipologia di esame.
Exam: Computer-based written test in class using POLITO platform;
The duration of exam is 2hours 20minutes. The exam includes 8 problems (which may be concerned with knowledge of theory, numerical computations, drawing of Bond graph diagrams, deriving of state-space equations etc.) -- 3 multiple-choice problems related to Lagrange equations (3 points in each problem, no penalty for wrong answers); -- 3 multiple-choice problem related to bond graph diagrams (3 points in each problem, no penalty for wrong answers); -- 1 open question, Lagrange equations (up to 7 points, partial grading may apply); -- 1 open question, bond graph diagrams (up to 7 points, partial grading may apply). The maximal mark is 3*3+3*3+7+7=32 (marks 31 and 32 are registered as 30 e lode). Books, printed or handwritten materials are welcome during the exam. The exam is computer-based, students should bring their own computers for the exam. Other electronic devices are not allowed. Open questions can, depending on their structure, be written on a paper, which is either collected by examiners or scanned and uploaded to Elaborati folder.
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.