Integrator

You can define the initial states as a parameter in the dialog box of the block or enter them from an external signal.:

To ensure that the output data does not exceed the specified levels, check the box Limit output and enter the restrictions in the appropriate parameter fields. This action results in the block functioning as a limited integrator. When the output reaches the limit values, the integrator operation ends.

During the simulation, you can change the constraints, but you cannot turn on or off the integrator constraints. The block defines the output data as follows:

To generate a signal indicating when the state is limited, check the box Show saturation port. The saturation port appears under the block output port.

The signal takes one of three values:

When this check box is selected, the block has three zero crossings.:

Some physical phenomena are cyclical, periodic, or rotational in nature. Modeling of these phenomena involves integrating the rate of change of periodic or cyclic signals to obtain a state variable.

The disadvantage of this approach is that over long periods of simulation time, states representing periodic or cyclic signals are integrated to very large values. In addition, the calculation of the sine or cosine of these signals takes more and more time. Large signal values also negatively affect the solver’s performance and accuracy.

One approach to overcome this disadvantage is to reset the angular state to 0 when it reaches (or before When it reaches , for numerical symmetry) using additional algorithms in the model. This approach improves the accuracy of the sine and cosine calculations. But keep in mind that this resets the solver, which slows down the simulation for a variable-pitch solver, especially in large models.

To avoid resetting the solver at the time of resetting the output value, block Integrator It contains a built-in state reset mechanism that you can enable by checking the box. Wrap state in the block parameters dialog box.

When you enable the parameter Wrap state, the block icon changes, indicating that cyclic state reset is enabled for the block.

If cyclic state reset is enabled, the state value is determined by the following expressions:

where:

Resetting cyclic states has the following advantages:

The block resets its state to the initial state on an external signal. The type of reset trigger is determined by the parameter External reset. When selecting a value other than none the unit has a reset port, next to which the type of reset trigger is indicated.

The External reset parameter allows you to define the reset signal attribute that is the reset trigger. The following triggers are possible:

The reset port has a direct input. If the output signal of the block is sent back to this port, either directly or through a series of direct transmission blocks, an algebraic loop is obtained. Use the block status port Integrator for feedback on block output without creating an algebraic loop.

Check the box Show state port in the block parameters dialog box Integrator This results in an additional output port, the status port, at the top of the integrator unit.

The output data of the status port is the same as the output data of the standard output port of the block, except in the following case. If the block is reset at the current time step, the status port output represents the value that would have appeared on the standard block output if the block had not been reset.

The output data of the status port appears earlier in the time step than the output data of the output port of the integrator unit. Use the status port to open algebraic circuits in these simulation scenarios.:

The block status port Integrator helps you avoid an algebraic loop when creating an integrator that resets itself based on the value of its output. Consider the following model.

This model attempts to create a self-aligning integrator by feeding the integrator’s output signal, subtracted from `1', back to the integrator’s reset port. However, the model creates an algebraic loop. To calculate the output of the integrator unit, the software must know the value of the unit reset signal, and vice versa. Since these two values are interdependent, the software cannot determine either of them. Therefore, an error message appears when trying to simulate or update this model.

The following model uses the integrator’s state port to avoid the occurrence of an algebraic loop.

In this version, the value of the reset signal depends on the value of the status port. The value of the status port is available earlier in the current time step than the value of the output port of the integrator unit. Therefore, it can determine whether to reset the block before calculating the block output, thereby avoiding an algebraic loop.

The status port helps to avoid the occurrence of an algebraic loop when transferring state between two enabled subsystems. Consider, for example, the following model.

The enabled subsystems A and B contain the following blocks:

In this model, a constant input signal drives two included subsystems that integrate the signal. The pulse generator generates a resolution signal that alternates execution between subsystems. The Enabled port of each subsystem is set to reset, which causes the subsystem to reset its integrator when it becomes active. Resetting the integrator causes the integrator to read the value of its initial state port. The initial state port of the integrator in each subsystem is connected to the output port of the integrator in the other subsystem.

This connection is designed to provide continuous integration of the input signal while alternating execution between the two subsystems. However, the connection creates an algebraic loop. To calculate the output of A', you need to know the output of `B, and vice versa. Because the output data is interdependent, it is not possible to calculate the output values. Therefore, an error message appears when trying to simulate or update this model.

This version of the same model uses the integrator’s state port to avoid creating an algebraic loop during state transfer.

The enabled subsystems A and B contain the following blocks:

In this model, the initial state of the integrator in A depends on the value of the port state of the integrator in B, and vice versa. The status port values are updated earlier in the simulation time step than the values of the integrator output ports. Therefore, it is possible to calculate the initial state of any integrator without knowing the final output value of another integrator.