Integrator

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Integrator

Numerical integration of a signal

Category: Dynamics

Description:

The signal received in the input port is numerically integrated and returned as the result in the output port. The numerical integration uses the Simulation Step as its integration step. It uses Euler’s backward rectangular method for fixed-step integration:

y_k=\begin{cases}y_0 &,& k=0 \\ y_{k-1}+Tu_k &,&k>0\end{cases}

Where:

$u$
: Input signal received in the input port.
$y$
: Output signal with the integrated result.
$k$
: Integer discrete-time index used in the representation of internal state recurrence.
$T$
: Integration time step in seconds.

Dialog

In the Integrator Properties window shown in Figure 1, there are some configuration options which may change the behavior of the block.

Figure 1 - Default configuration

Parameters:

This option creates an input port named as IC when set to enable. The value of the signal received by this port works as an initial condition. The block icon in this situation looks like this:

Defines a constant initial condition

y_0

of the integrator.

Note

If the parameter External Initial Condition is set to Enable, this value will be neglected and only get updated based on the input signal.

In some applications, it is necessary to reset the integrator during the execution. When the block detects a rising edge in the reset port, the integration state is restarted to the initial condition.

If this parameter is set to enable, it will create a new input port and the block shall look like this:

Once this parameter is enabled, it is possible to saturate the output signal without a Saturation Block. Furthermore, the Limit Output saturates the internal integration value.

In case the parameter "Limit Output" is enabled, this parameter shall be used to limit the maximum output signal.

In case the parameter "Limit Output" is enabled, this parameter shall be used to limit the minimum output signal.

Ports:

Input

The input signal to be numerically integrated.

Data Types:

The value of the signal received in this port works as initial condition for the numerical integration.

Dependencies

In order to enable this port, select External Initial Condition in the configuration dialog.

Data Types:

Resets the states of the integration when the signal received has a rising edge.

Dependencies

In order to enable this port, select External Reset in the configuration dialog.

Data Types:

Output

The result of the numerical integration of the input signal.

Data Types:

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MWF Learn

Integrator

Description:

Dialog

Parameters:

External Initial ConditionDefines the initial condition using an external signalDefault value: DisablePossible value:Disable|Enable

External Initial Condition

Defines the initial condition using an external signal

Default value: Disable

Possible value:

Initial Condition ValueDefines the initial condition using a constante valueDefault value: 0Possible value:Double

Initial Condition Value

Defines the initial condition using a constante value

Default value: 0

Possible value:

External Reset Allows reset of the integration operation using an external signal as a triggerDefault value: DisablePossible value:Disable|Enable

External Reset

Allows reset of the integration operation using an external signal as a trigger

Default value: Disable

Possible value:

Limit OutputSaturates the output signalDefault value: DisablePossible value:Disable|Enable

Limit Output

Saturates the output signal

Default value: Disable

Possible value:

Upper Saturation LimitUpper bound of the internal state saturationDefault value: 1Possible value:Double

Upper Saturation Limit

Upper bound of the internal state saturation

Default value: 1

Possible value:

Lower Saturation LimitLower bound of the internal state saturationDefault value: -1Possible value:Double

Lower Saturation Limit

Lower bound of the internal state saturation

Default value: -1

Possible value:

Ports:

Input

IN Input Signalscalar

IN

Input Signal

Data Types:

ICExternal Initial Conditionscalar

IC

External Initial Condition

Data Types:

RSTExternal Resetscalar

RST

External Reset

Data Types:

Output

OUTOutput Signalscalar

OUT

Output Signal

Data Types: