CriticalDamping

Output the input signal filtered with an n-th order filter with critical damping

    CriticalDamping

Library

Modelica/Blocks/Continuous

Description

This block defines the transfer function between theinput u and the output yas an n-th order filter with critical dampingcharacteristics and cut-off frequency f. It isimplemented as a series of first order filters.This filter type is especially useful to filter the input of aninverse model, since the filter does not introduce any transients.

If parameter normalized = true (default), the filteris normalized such that the amplitude of the filter transfer functionat the cut-off frequency f is 1/sqrt(2) (= 3 dB). Otherwise, the filteris not normalized, i.e., it is unmodified. A normalized filter is usuallymuch better for applications, since filters of different orders are"comparable", whereas non-normalized filters usually require to adapt thecut-off frequency, when the order of the filter is changed.Figures of the filter step responses are shown below.Note, in versions before version 3.0 of the Modelica Standard library,the CriticalDamping filter was provided only in non-normalized form.

If transients at the simulation start shall be avoided, the filtershould be initialized in steady state (e.g., using optioninitType=Modelica.Blocks.Types.Init.SteadyState).

The critical damping filter is defined as

    α = if normalized then sqrt(2^(1/n) - 1) else 1 // frequency correction factor    ω = 2*π*f/α              1    y = ------------- * u         (s/w + 1)^n

CriticalDampingNormalized.png

CriticalDampingNonNormalized.png

Parameters

CriticalDamping_0

NameLabelDescriptionData TypeValid Values

mo_n

n

Order of filter

Scalar

mo_f

f

Cut-off frequency

Scalar

mo_normalized

normalized

= true, if amplitude at f_cut is 3 dB, otherwise unmodified filter

Scalar

true
false

mo_alpha

alpha

Frequency correction factor for normalized filter

Scalar

mo_w

w

Scalar

mo_initType

initType

Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)

Structure

mo_initType/choice1

No initialization (start values are used as guess values with fixed=false)

Number

0
1

mo_initType/choice2

Steady state initialization (derivatives of states are zero)

Number

0
1

mo_initType/choice3

Initialization with initial states

Number

0
1

mo_initType/choice4

Initialization with initial outputs (and steady state of the states if possible)

Number

0
1

mo_x_start

x_start

Initial or guess values of states

Vector

mo_y_start

y_start

Initial value of output (remaining states are in steady state)

Scalar

mo_x

x

x

Structure

mo_x/fixed

fixed

Cell of vectors

true
false

mo_x/start

start

Cell of vectors

CriticalDamping_1

NameLabelDescriptionData TypeValid Values

mo__nmodifiers

Number of Modifiers

Specifies the number of modifiers

Number

mo__modifiers

Modifiers

Add new modifier

Structure

mo__modifiers/varname

Variable name

Cell of strings

mo__modifiers/attribute

Attribute

Cell of strings

'start'
'fixed'

mo__modifiers/value

Value

Ports

NameTypeDescriptionIO TypeNumber

u

implicit

Connector of Real input signal

input

1

y

implicit

Connector of Real output signal

output

1