Azionamenti elettrici - parte 2 esame

Name: Azionamenti elettrici - parte 2 esame
Rating: 4.0 (2 reviews)
Author: Alberto Luzzeri

Revisionato il 29/06/2026

di Alberto Luzzeri

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Vota 4,0/5 (2)

Contenuto verificato e approvato dal Team di Esperti di Skuola.net

Breve introduzione sulla trasformata di Laplace, funzione di trasferimento, classificazione dei poli, esempio di risoluzione circuito RC con Laplace, diagrammi di Bode e relativa …

Esame Macchine e azionamenti elettrici

Facoltà Ingegneria

Dal corso del Prof. Barater Davide

Università Università degli Studi di Modena e Reggio Emilia

A.A. 2021-2022

83 pagine

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Electric Drive control: a brief review

Using LT for solving differential equations

t=0 null Initial Conditions

R

i i

c V = +

E C = +

= =

= + → ℒ = ℒ + → = +

= → lim + lim +

1 1

+ 1

→0 + +

→−

− − −

= − = 1− = , ℎ: = 1 −

ℎ ℎ

Electric Drive control: a brief review

Using LT for solving differential equations

t=0 Initial Conditions = 0

R

i − +

0 = 0 = 0

c V

C = +

E C

= +

= =

= + → ℒ = ℒ + → = − 0 +

+ 0 + 0 1 + 0

= → lim + lim +

1 1

+ 1

→0 + +

→−

−

= − − 0

Electric Drive control: a brief review

Constant:

= = > 0

Consider a constant term:

Magnitude

Clearly the magnitude is constant:

Phase

The phase is also constant.

• If K is positive, the phase is 0°

(or any even multiple of 180°).

• If K is negative the phase is -180° (or any

odd multiple of 180°). We will use the unwrapped phase (0 or 180°).

In radians we can say that if is positive the phase is 0, if is negative -π rad.

Electric Drive control: a brief review

Constant: = = < 0

Consider a constant negative term:

Magnitude

Clearly the magnitude is constant (and

positive…) =

Phase

The phase is also constant.

• Since K is negative the phase is 180° (or

any odd multiple of 180°).

Electric Drive control: a brief review

A Real Pole

Consider a simple real pole: The frequency ω is called the break frequency, the corner

1 1 0

= → = frequency or the 3 dB frequency (more on this last name

1+ 1+ later).

0 0

Magnitude 1 1 1

= ; = log ; = 20 log

It is given by: 10 10

2 2 2

1 + 1 + 1 +

0 0 0

≪ ≫ =

0 0 0

2 2 2

1 + ≅1 1 + ≅ 1 + = 2

0 0 0 0

= −0.15

= −log

= ≅0 0

= −3

= −20log

10 0

Electric Drive control: a brief review

A Real Pole

Phase 1

= = − 1 + = −

The phase of a single real pole is given by:

1+ 0 0

≪ → − 0

if =0

≫ → − +∞ = −90°

if 0

= = − 1 = −45°

if 0 Electric Drive control: a brief review

A Real Zero

=1+ → = 1 +

Consider a simple real zero:

0 0

Magnitude 2

= 1 +

The magnitude is given by: 0

≪ ≫ =

0 0 0

2 2 2

1 + ≅1 1 + ≅ 1 + = 2

0 0 0 0

= 0.15

= log

= ≅0 0

= 3

= 20log

10 0

Electric Drive control: a brief review

A Real Zero

Phase

The phase of a single real zero is given by: = 1 + = + 1 + = +

0 0 0

≪ → + 0

if =0

≫ → + +∞ = +90°

if 0

= = + 1 = +45°

if 0 Electric Drive control: a brief review

A Pole at the Origin 1 1

A pole at the origin is easily drawn exactly. Consider: = → = −j

Magnitude In this case there is no need for approximate functions and asymptotes, we can

The magnitude is given by: plot the exact function. The function is represented by a straight line on a Bode

plot with a slope of -20 dB per decade and going through 0 dB at 1 rad/ sec.

1 Since there are no parameters (i.e., ω ) associated, it is always drawn in exactly

= 0

the same manner.

Phase 1

= − =−

The phase of a single real pole is given by: 2

Electric Drive control: a brief review

A Zero at the Origin = → = j

A zero at the origin is easily drawn exactly. Consider:

In this case there is no need for approximate functions and asymptotes, we can

Magnitude plot the exact function. The function is represented by a straight line on a Bode

The magnitude is given by: plot with a slope of +20 dB per decade and going through 0 dB at 1 rad/ sec.

Since there are no parameters

Anteprima

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