Integrator

You can define the initial states as parameters in the block dialogue box or enter them from an external signal:

To ensure that the output does not exceed specified levels, select the Limit output check box and enter limits in the appropriate parameters fields. This action causes the block to function as a limited integrator. When the output reaches the limits, the integrator action is terminated.

You can change the limits during simulation, but you cannot turn the integrator limits on or off. The block defines the output as follows:

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

The signal takes one of three values:

When this checkbox is selected, the block has three zero crossings:

Some physical phenomena are cyclic, periodic, or rotational in nature. Modelling 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 simulation times, the states representing periodic or cyclic signals are integrated to very large values. In addition, calculating the sine or cosine of these signals takes increasingly longer time. Large values of the signals also negatively affect the performance and accuracy of the solver.

One approach to overcome this drawback is to reset the angular state to 0 when it reaches 2π (or to -π when it reaches π, for numerical symmetry) using additional algorithms in the model. This approach improves the accuracy of the sine and cosine calculations. But note that it leads to resetting the solver, which slows down the modelling for a variable step solver, especially in large models.

To prevent the solver from resetting when the output value is reset, the Integrator block contains a built-in state reset mechanism, which you can enable by checking the Wrap state checkbox in the block parameters dialogue box.

When you enable the Wrap state parameters , the block icon changes to indicate that cyclic state reset is enabled for the block.

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

,

where:

Resetting cyclic states has the following advantages:

The unit resets its state to the initial state by an external signal. The reset trigger type is determined by the parameters External reset. If a value other than none, the unit has a reset port with the reset trigger type labelled next to it.

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

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

Checking Show state port in the block parameters dialogue box Integrator results in an additional output port, the status port, at the top of the integrator block.

The output of the status port is the same as the standard block output port, 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 of the status port appears earlier in the time step than the output of the integrator block output port. Use the status port to open algebraic circuits in these simulation scenarios:

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

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

The following model uses the integrator 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 state port. The value of the state port is available earlier in the current time step than the value of the output port of the integrator block. Consequently, can determine whether the block should be reset before calculating the block output, thus avoiding an algebraic loop.

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

Enabled subsystems A and B contain the following blocks:

In this model, a constant input signal drives two enabled subsystems that integrate the signal. A pulse generator generates an enable signal that alternates execution between the 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 interconnection is intended to provide continuous integration of the input signal while alternating execution between the two subsystems. However, the connection creates an algebraic loop. To compute the output data A, one must know the output data B, and vice versa. Since the outputs are interdependent, it is not possible to compute the output values. Therefore, an error message appears when trying to model or update this model.

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

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 state port of the integrator in B, and vice versa. The values of the state ports are updated earlier in the time step of the simulation than the values of the output ports of the integrator. Hence, it is possible to calculate the initial state of any integrator without knowing the final output value of another integrator.