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 the input u and the output y as an n-th order filter with critical damping characteristics and cut-off frequency f. It is implemented as a series of first order filters. This filter type is especially useful to filter the input of an inverse model, since the filter does not introduce any transients.

If parameter normalized = true (default), the filter is normalized such that the amplitude of the filter transfer function at the cut-off frequency f is 1/sqrt(2) (= 3 dB). Otherwise, the filter is not normalized, i.e., it is unmodified. A normalized filter is usually much better for applications, since filters of different orders are "comparable", whereas non-normalized filters usually require to adapt the cut-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 filter should be initialized in steady state (e.g., using option initType=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_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_alpha

alpha

Frequency correction factor for normalized filter

Scalar

mo_w

w

Scalar

CriticalDamping_1

NameLabelDescriptionData TypeValid Values

mo_u

u

u

Structure

mo_u/fixed

fixed

Cell of scalars

true
false

mo_u/start

start

Cell of scalars

mo_y

y

y

Structure

mo_y/fixed

fixed

Cell of scalars

true
false

mo_y/start

start

Cell of scalars

mo_x

x

x

Structure

mo_x/fixed

fixed

Cell of vectors

true
false

mo_x/start

start

Cell of vectors

Ports

NameTypeDescriptionIO TypeNumber

u

implicit

Connector of Real input signal

input

1

y

implicit

Connector of Real output signal

output

1