secondderivative

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secondderivative

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Library

Signal\Block Diagram

Implementations

SO

Pure

Use

Domains: Continuous. Size: 1-D. Kind: Block Diagrams.

Description - Pure

This model calculates the second derivative of an input signal. The initial value of the output is equal to the parameter initial. The rate of the output at the start is equal to the parameter initial_ddt.

 

rate = ddt(input, initial_ddt);

output = ddt(rate,initial);

 

A pure derivative requires special integration methods like the BDF method (default in 20-sim). Therefore 20-sim will try solve pure derivatives during compilation. If symbolic solving of a derivative fails, the Process Tab will show that the model contains 1 or more dependent state. To prevent dependent states, it is better to use the second order (SO) approximation of the second derivative.

Interface - Pure

Inputs

Description

input

 

Outputs

 

output

 

Parameters

 

initial

initial_ddt

The initial value of the output.

The initial derivative of the output.

Description - FO

This model is a second order (FO) approximation of a second derivative. For low frequency signals, the model gives a good approximation of  a pure second derivative. The transfer function is:

SecondDerivative-SO

The parameter fh is the derivative bandwidth. This is the maximum frequency or which this model gives a good approximation of a pure derivative. The parameter d gives the damping of the approximation. A value of 1 will in most cases be sufficient.

Interface - FO

Inputs

Description

input

 

Outputs

 

output

 

Parameters

 

fh

d

Differentiation bandwidth [Hz]

Damping, underdamped = between 0 and 1, overdamped = between 1 and inf

Initial Values

 

initial

initial_ddt

The initial value of the output.

The initial derivative of the output.