02PCYQW

A.A. 2021/22

2021/22

Modelling and simulation of mechatronic systems

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.

Modelling and simulation of mechatronic systems

The course is taught in English. The course provides the students with the basic skills required for model building and simulation of mechanical, 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.

Modelling and simulation of mechatronic systems

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.).

Modelling and simulation of mechatronic systems

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.).

Modelling and simulation of mechatronic systems

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.

Modelling and simulation of mechatronic systems

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); 3) basics of differential calculus; 4) complex numbers. Elements of system theory and automatic control (states, inputs, outputs, transfer functions) are not mandatory, but beneficial.

Modelling and simulation of mechatronic systems

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)

Modelling and simulation of mechatronic systems

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)

Modelling and simulation of mechatronic systems

Modelling and simulation of mechatronic systems

Modelling and simulation of mechatronic systems

Practical exercises in class will be devoted to analytically model several simple systems, using the different approaches introduced in the course.

Modelling and simulation of mechatronic systems

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.

Modelling and simulation of mechatronic systems

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

Modelling and simulation of mechatronic systems

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

Modelling and simulation of mechatronic systems

**Modalità di esame:** Prova scritta (in aula);

Modelling and simulation of mechatronic systems

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.

Modelling and simulation of mechatronic systems

**Exam:** Written test;

Modelling and simulation of mechatronic systems

The exam will consist of two different tests (Lagrange and Bond Graph parts). Both tests can contain multiple-choice and open questions. The examples of problems will be given during the course. Some examples are available on are available the Exercise platform (exercise.polito.it) The length of each test is 1h 10 min. Two parts can be passed at different days (not necessarily in the same exam session) and graded separately. The minimal grade needed to pass each part is 18/30. The final mark can be registered only when the both parts are passed and is computed as the average of two marks (rounded up if non-integer). For instance, 18/30 for Lagrange equations and 21/30 for Bond Graph will give 20/30.

Modelling and simulation of mechatronic systems

**Modalità di esame:** Prova scritta a risposta aperta o chiusa tramite PC con l'utilizzo della piattaforma di ateneo Exam integrata con strumenti di proctoring (Respondus);

Modelling and simulation of mechatronic systems

The online exam will consist of two different tests (Lagrange and Bond Graph parts) in Quiz format, with open and multiple-choice questions. The examples of problems are available on exercise.polito.it and will be given during the course. The length of each test is 1h 10 min. Books and other printed materials can be used. Calculator is usually not needed, although it is enabled by the Exam platform. The two parts can be taken together in the same exam session or separately at different times during the year and are graded in separate. The minimal grade needed to pass each part is 18/30. The final grade can be registered only when the both parts are passed and is computed as the average of two grades. For instance, 18/30 for Lagrange equations and 22/30 for Bond Graph will give 20/30.

Modelling and simulation of mechatronic systems

**Exam:** Computer-based written test with open-ended questions or multiple-choice questions using the Exam platform and proctoring tools (Respondus);

Modelling and simulation of mechatronic systems

The online exam will consist of two different tests (Lagrange and Bond Graph parts). Both tests can contain multiple-choice and open questions. The examples of problems are available on the Exercise platform (exercise.polito.it) and will be given during the course. Depending on the number of students, the exam can be fully computerized and solved on the Exam platform or be written under the video-surveillance. The length of each test is 1h 10 min. Two parts can be passed at different days (not necessarily in the same exam session) and graded separately. The minimal grade needed to pass each part is 18/30. The final mark can be registered only when the both parts are passed and is computed as the average of two marks (rounded up if non-integer). For instance, 18/30 for Lagrange equations and 21/30 for Bond Graph will give 20/30.

Modelling and simulation of mechatronic systems

**Modalità di esame:** Prova scritta a risposta aperta o chiusa tramite PC con l'utilizzo della piattaforma di ateneo Exam integrata con strumenti di proctoring (Respondus);

Modelling and simulation of mechatronic systems

The online exam will consist of two different tests (Lagrange and Bond Graph parts) in Quiz format, with open and multiple-choice questions. The examples of problems are available on exercise.polito.it and will be given during the course. The length of each test is 1h 10 min. Books and other printed materials can be used. Calculator is usually not needed, however, it is enabled by the Exam platform. The two parts can be taken together in the same exam session or separately at different times during the year and are graded in separate. The minimal grade needed to pass each part is 18/30. The final grade can be registered only when the both parts are passed and is computed as the average of two grades. For instance, 18/30 for Lagrange equations and 22/30 for Bond Graph will give 20/30.

Modelling and simulation of mechatronic systems

**Exam:** Computer-based written test with open-ended questions or multiple-choice questions using the Exam platform and proctoring tools (Respondus);

Modelling and simulation of mechatronic systems

The online exam will consist of two different tests (Lagrange and Bond Graph parts). Both tests can contain multiple-choice and open questions. The examples of problems are available on the Exercise platform (exercise.polito.it) and will be given during the course. Depending on the number of students, the exam can be fully computerized and solved on the Exam platform or be written under the video-surveillance. The length of each test is 1h 10 min. Two parts can be passed at different days (not necessarily in the same exam session) and graded separately. The minimal grade needed to pass each part is 18/30. The final mark can be registered only when the both parts are passed and is computed as the average of two marks (rounded up if non-integer). For instance, 18/30 for Lagrange equations and 21/30 for Bond Graph will give 20/30.

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Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY