MSMS (01PCYQW) 2014-2015 Organization: the course is divided into - - PowerPoint PPT Presentation

MSMS (01PCYQW) 2014-2015

• Organization: the course is divided into two parts: the first

devoted to the Lagrange (LAG) approach, the second devoted to the Bond-Graph (BG) approach.

• Each part lasts approximately 50 hours distributed in 7 weeks.

– LAG: 29/09/2014 – 12/11/2014 – LAG: 29/09/2014 – 12/11/2014 – BG: 13/11/2014 – 20/01/2015

• Instructors:

– prof. Basilio Bona (LAG) – DAUIN – prof. Andrea Tonoli (BG) – DIMEAS

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MSMS (01PCYQW) 2014-2015

• Exam Rules: the exam is written. It consists of two parts:

– LAG part: one to three exercises (usually two); the exam lasts 1 h, 15 min; books and notes CAN be used.

Examples will be given during the course.

– BG part: one to three exercises (usually two); the exam lasts 1 h, 15 min; books and notes CANNOT be used.

Examples will be given during the course.

• The two parts can be taken together in the same exam

session or separately in different sessions during the year.

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MSMS (01PCYQW) 2014-2015

• Lessons schedule

Mon 13:00-14:30 room 1T Wed 08:30-11:30 room 2D Thu 14:30-17:30 room 10

• No Labs during the course
• Textbook for the LAG part
• Textbook for the LAG part
• B. Bona “Dynamic Modelling of Mechatronic Systems”
• B. Bona “Dynamic Modelling of Mechatronic Systems”

CELID, 2013 (available at CELID, 2013 (available at CELID Bookstore) CELID Bookstore)

• Web page for the LAG part

http://www.ladispe.polito.it/corsi/meccatronica/01PCYQW/2014-15/

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Examples

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Examples

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Why Modelling is necessary

• Modeling = USA English – Modelling = GB English
• Models are required for

– simulation, to predict future behaviour of systems – identification and parameter estimation, to find numerical values of unknown system parameters – control design, to write algorithms that enhance the system performance

• Models can be developed as

– Hardware models ... very rare today – Software models ... the most common type (MATLAB is the common choice)

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Necessary prerequisites

• Vectors: what they are and why they are important
• Matrix calculus: is the basic tool for representing physical

concepts and for algorithms development

• Physics: mainly basic concepts related to kinematics and

dynamics (forces and torques) dynamics (forces and torques)

• Basic notions of electrical circuits
• MATLAB/SIMULINK not required for the exam but useful for

the rest of the curriculum

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Other textbooks

• LAG

LAG: Fundamentals of Applied Dynamics J.H. Williams, Jr. Wiley 1996 available at the Electronic Department Library

• BG

BG: System Dynamics: A Unified Approach

• BG

BG: System Dynamics: A Unified Approach D.C. Karnopp, D.L. Margolis, R.C. Rosenberg Wiley Interscience 1990 available at the PoliTo Central Library

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Topics – Lagrange method

• Reference Frames and Roto-translations
• Rigid Body Kinematics
• Rigid Body Dynamics

– Point Mass and Distributed Mass System – Mathematical Formulation

• Rotation of the reference frame
• Principal inertia matrix
• Parallel axes theorem
• Parallel axes theorem

– Angular momentum and Euler Equation – Virtual Work Principle – Lagrange Equations in Mechanical Systems

• Kinetic energy and co-energy
• Potential energy
• Generalized forces in holonomic systems
• Lagrange equations with holonomic constraints
• Lagrange equations with non holonomic constraints
• Characterization of the Lagrange equations

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Topics – Lagrange method

• Electrical Systems Dynamics – Lagrange method
• Electromechanical Systems Dynamics – Lagrange method
• State variables and state equations

To test your initial state, please follow this link http://www.ladispe.polito.it/corsi/meccatronica/01PCYQW/201 4-15/Slides/01PCYQW%20Initial%20Test%202014-2015.pdf and try to answer to the questions inside

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Lagrange function Kinetic (co-)energy Potential energy Virtual works

Scalars

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Forces Velocities

Linear Angular Linear Angular

Positions = coordinates

Linear Angular Vectors

• Lagrange function
• Energies

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• Virtual works
• Velocities
• Positions