02pcyqw 2016 presentation - polito.it€¦ · msms (02pcyqw) 2016-2017 • exam rules: the exam is...

MSMS (02PCYQW) 2016-2017

• Organization: the course is composed of two parts:

– the first part is devoted to the Lagrange (LAG) approach

– the second part is devoted to the Bond-Graph (BG) approach

• Each part takes approximately 50 hours distributed in 7

weeks.

– LAG: 29/09/2016 – 12/11/2016

– BG: 13/11/2016 – 20/01/2016

• Instructors:

– prof. Basilio Bona (LAG) – DAUIN

– prof. Andrea Tonoli (BG) – DIMEAS

Basilio Bona MSMS - 02PCYQW 1

MSMS (02PCYQW) 2016-2017

• Exam Rules: the exam is written. It is unique, but consists of

two parts:

– LAG part: 1-3 exercises (usually 2); the exam lasts approx. 1h 15m;

books and notes CAN be used.

Examples will be given during the course.

– BG part: 1-3 exercises (usually 2); the exam lasts approx. 1h 15m;

books and notes CANNOT be used.

Examples will be given during the course.

– The final mark is the arithmetic mean between the two marks.

• Read the rules herehttp://www.ladispe.polito.it/corsi/meccatronica/02PCYQW/2016-17/exams.html

MSMS - 02PCYQW 2Basilio Bona

MSMS (02PCYQW) 2016-2017

• Lessons schedule

Mon 13:00 – 16:00 room 1B

Wed 08:30 – 10:00 room 11T

Thu 13:00 – 16:00 room 1B

• No Labs during the course

• Web page for the LAG part

http://www.ladispe.polito.it/corsi/meccatronica/02PCYQW/2016-17/

• Textbook for the LAG part

B. Bona “Dynamic Modelling of Mechatronic Systems” CELID, 2013

Available at CLUT bookstore


Other textbooks

• LAG: Fundamentals of Applied Dynamics

J.H. Williams, Jr.

Wiley 1996

available at the Electronic Department Library

• BG: System Dynamics: A Unified Approach

D.C. Karnopp, D.L. Margolis, R.C. Rosenberg

Wiley Interscience 1990

available at the PoliTo Central Library


Motivations

• Mechatronic systems often consist of a complex interaction of

moving structures, controlled by electronic circuits and by

software programs.


• In order to be able to write good

algorithms for control or simulation, it is

necessary to know how the various

mechanical + electrical parts interact.

• This means that one must be able to produce a

consistent mathematical description (= model) of

the overall mechanical + electrical system.

• The scope of MSMS is precisely to teach how to

produce mathematical equations modelling the

system.

Why Modelling is necessary

• Models are useful for

– simulation, to predict future behaviour of systems,

– identification and parameter estimation, to find the numerical

values of the unknown system parameters (masses, friction

coefficients, elastic modes, etc.)

– control design, to write control algorithms to improve the system

performances.

• Models can be implemented as

– Hardware models ... very rare

– Software models ... very common (MATLAB language is a popular

choice for models description and analysis.)


Models = Differential Equations

• Models are described using the language of physics, i.e., the

laws of mechanics and/or electromagnetism.

• These laws are expressed as differential equations, i.e., they

include first and second order time derivatives of some

physical quantity.

• Example: the Newton law of linear motion

• This is an equation relating the second order time-derivative

of the position x of a body having mass m, with the applied

external force f


fmx f x

m= ⇔ =ɺɺ ɺɺ

What is required

• To find the correct model equations it is necessary to

understand how the motion is mathematically represented in

3D space

• Motion includes translations and rotations

– first, it is necessary to describe bodies with reference frames,

– then it is necessary to describe motion of reference frames and their

representations

• The mathematical tools required are essentially vectors and

matrices: vector and matrix analysis is a topic that a student

must know in details


Necessary prerequisites

• Physics: concepts related to kinematics and dynamics (forces

and torques), and notions of electrical circuits.

• Vectors: used to represent many physical quantities.

• Matrices: matrix calculus is used to represent rotations,

transformations and other important physical equivalents.

• Basic MATLAB/SIMULINK: this software environment is not

required for the exam, but it is useful for the rest of the

Mechatronics curriculum (and will be extensively used in the

Robotics course at Semester 2).


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

– 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


Topics – Lagrange method

• Electrical Systems Dynamics – Lagrange method

• Electromechanical Systems Dynamics – Lagrange method

• State variables and state equations



Lagrange function

Kinetic (co-)energy Potential energy

Virtual works

Forces Velocities

Linear

Angular

Linear

Angular

Positions = coordinates

Linear

Angular

Vectors

Scalars


• Lagrange function

• Energies

• Virtual works

• Velocities

• Positions

Examples


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