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# Embedded Systems - Review on continuous processes

Contents:
- Modeling with differential equations;
- Taxonomy of systems;
- Solution to linear ODE;
- General solution concept;
- Simulation and numerical methods;
- State space representation;
- Stability.

Esame di Sistemi embedded docente Prof. L. Pomante

Anteprima

### ESTRATTO DOCUMENTO

Physical systems Capacitor

Inductor

Resistor

Damper Spring

Mass

Embedded Systems

Electric circuits I(t)

I(t) 1

+ L

V t

V(t)

## L

0 t

Embedded Systems

A pendulum r

Mg

Embedded Systems

Contents

Modeling with differential equations

 Taxonomy of systems

 Solution to linear ODEs

 General solution concept

 Simulation and numerical methods

 State space representation

 Stability

Embedded Systems

Linear versus nonlinear systems

Linear systems: if the set of solutions is closed under

 linear operation, i.e. scaling and addition

All the examples are linear systems, except for the

 pendulum

Embedded Systems

Time invariant versus time varying

Time invariant: the set of solutions is closed under time

 shifting

Time varying: the set of solutions is not closed under

 time shifting

Embedded Systems

Autonomous versus non-autonomous

Autonomous systems: given the past of the signals, the

 future is fixed

Non-autonomous systems: there is possibility for input,

 non-determinism

Embedded Systems

Contents

Modeling with differential equations

 Taxonomy of systems

 Solution to linear ODEs

 General solution concept

 Simulation and numerical methods

 State space representation

 Stability

Embedded Systems

Techniques for autonomous systems

Embedded Systems

Techniques for non-autonomous systems

Embedded Systems

Techniques for non-autonomous systems

Example:

u(t) y(t)

1 1

t t

Embedded Systems

Contents

Modeling with differential equations

 Taxonomy of systems

 Solution to linear ODEs

 General solution concept

 Simulation and numerical methods

 State space representation

 Stability

Embedded Systems

Solution concepts

Embedded Systems

Example of weak solution

Embedded Systems

Contents

Modeling with differential equations

 Taxonomy of systems

 Solution to linear ODEs

 General solution concept

 Simulation and numerical methods

 State space representation

 Stability

Embedded Systems

Simulation methods

x[1] x[2] x(t)

x[3]

## I

m

p

o

Embedded Systems

Simulation methods

Embedded Systems

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PESO

838.66 KB

AUTORE

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DETTAGLI
Corso di laurea: Corso di laurea magistrale in ingegneria delle telecomunicazioni
SSD:
Università: L'Aquila - Univaq
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Sistemi embedded e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università L'Aquila - Univaq o del prof Pomante Luigi.

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