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Continuous
The Integrator block outputs the integral of its input at the current time step. The following equation represents the output of the block y as a function of its input u and an initial condition y0, where y and u are vector functions of the current simulation time t.
Simulink software can use a number of different numerical integration methods to compute the Integrator block's output, each with advantages in particular applications. Use the Solver pane of the Configuration Parameters dialog box (see Solver Pane) to select the technique best suited to your application.
Simulink software treats the Integrator block as a dynamic system with one state, its output. The Integrator block's input is the state's time derivative.
The selected solver computes the output of the Integrator block at the current time step, using the current input value and the value of the state at the previous time step. To support this computational model, the Integrator block saves its output at the current time step for use by the solver to compute its output at the next time step. The block also provides the solver with an initial condition for use in computing the block's initial state at the beginning of a simulation run. The default value of the initial condition is 0. The block's parameter dialog box allows you to specify another value for the initial condition or create an initial value input port on the block.
Use the parameter dialog box to:
Define upper and lower limits on the integral
Create an input that resets the block's output (state) to its initial value, depending on how the input changes
Create an optional state output so that the value of the block's output can trigger a block reset
Use the Discrete-Time Integrator block to create a purely discrete system.
You can define the initial conditions as a parameter on the block dialog box or input them from an external signal:
To define the initial conditions as a block parameter, specify the Initial condition source parameter as internal and enter the value in the Initial condition field.
To provide the initial conditions from an external source, specify the Initial condition source parameter as external. An additional input port appears under the block input.
Note If the integrator limits its output (see Limiting the Integral), the initial condition must fall inside the integrator's saturation limits. If the initial condition is outside the block saturation limits, the block displays an error message. |
To prevent the output from exceeding specifiable levels, select the Limit output check box and enter the limits in the appropriate parameter fields. This action causes the block to function as a limited integrator. When the output reaches the limits, the integral action is turned off to prevent integral wind up. During a simulation, you can change the limits but you cannot change whether the output is limited. The block determines output as follows:
When the integral is less than or equal to the Lower saturation limit, the output is held at the Lower saturation limit.
When the integral is between the Lower saturation limit and the Upper saturation limit, the output is the integral.
When the integral is greater than or equal to the Upper saturation limit, the output is held at the Upper saturation limit.
To generate a signal that indicates when the state is being limited, select the Show saturation port check box. A saturation port appears below the block output port.
The signal has one of three values:
1 indicates that the upper limit is being applied.
0 indicates that the integral is not limited.
-1 indicates that the lower limit is being applied.
When you select this check box, the block has three zero crossings: one to detect when it enters the upper saturation limit, one to detect when it enters the lower saturation limit, and one to detect when it leaves saturation.
The block can reset its state to the specified initial condition based on an external signal. To cause the block to reset its state, select one of the External reset choices. A trigger port appears below the block's input port and indicates the trigger type.
Select rising to reset the state when the reset signal rises from a zero to a positive value or from a negative to a positive value.
Select falling to reset the state when the reset signal falls from a positive value to zero or from a positive to a negative value.
Select either to reset the state when the reset signal changes from a zero to a nonzero value or changes sign.
Select level to reset the state when the reset signal is nonzero at the current time step or changes from nonzero at the previous time step to zero at the current time step.
Select level hold to reset the state when the reset signal is nonzero at the current time step.
The reset port has direct feedthrough. If the block output feeds back into this port, either directly or through a series of blocks with direct feedthrough, an algebraic loop results (see Algebraic Loops). Use the Integrator block's state port to feed back the block's output without creating an algebraic loop.
Note To be compliant with the Motor Industry Software Reliability Association (MISRA®) software standard, your model must use Boolean signals to drive the external reset ports of Integrator blocks. |
Selecting the Show state port check box on the Integrator block's parameter dialog box causes an additional output port, the state port, to appear at the top of the Integrator block.
The output of the state port is the same as the output of the block's standard output port except for the following case. If the block is reset in the current time step, the output of the state port is the value that would have appeared at the block's standard output if the block had not been reset. The state port's output appears earlier in the time step than the output of the Integrator block's output port. Use the state port to avoid creating algebraic loops in these modeling scenarios:
Self-resetting integrators (see Creating Self-Resetting Integrators)
Handing off a state from one enabled subsystem to another (see Handing Off States Between Enabled Subsystems)
Note When updating a model, Simulink software checks that the state port applies to one of these two scenarios. If not, an error message appears. Also, you cannot log the output of this port in a referenced model that executes in Accelerator mode. If logging is enabled for the port, Simulink software generates a "signal not found" warning during execution of the referenced model. |
The Integrator block's state port helps you avoid an algebraic loop when creating an integrator that resets itself based on the value of its output. Consider, for example, the following model.
This model tries to create a self-resetting integrator by feeding the integrator's output, subtracted from 1, back into the integrator's reset port. However, the model creates an algebraic loop. To compute the integrator block's output, Simulink software needs to know the value of the block's reset signal, and vice versa. Because the two values are mutually dependent, Simulink software cannot determine either. Therefore, an error message appears if you try to simulate or update this model.
The following model uses the integrator's state port to avoid the 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 integrator block's output port. Thus, Simulink software can determine whether the block needs to be reset before computing the block's output, thereby avoiding the algebraic loop.
The state port helps you avoid an algebraic loop when passing a state between two enabled subsystems. Consider, for example, the following model.
In this model, a constant input signal drives two enabled subsystems that integrate the signal. A pulse generator generates an enabling signal that causes execution to alternate between the two subsystems. The enable 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 condition port. The initial condition port of the integrator in each subsystem is connected to the output port of the integrator in the other subsystem.
This connection is intended to enable continuous integration of the input signal as execution alternates between two subsystems. However, the connection creates an algebraic loop. To compute the output of A, Simulink software needs to know the output of B, and vice versa. Because the outputs are mutually dependent, Simulink software cannot compute them. Therefore, an error message appears if you try to simulate or update this model.
The following version of the same model uses the integrator state port to avoid creating an algebraic loop when handing off the state.
In this model, the initial condition 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 simulation time step than the values of the integrator output ports. Thus, Simulink software can compute the initial condition of either integrator without knowing the final output value of the other integrator. For another example of using the state port to hand off states between conditionally executed subsystems, see the sldemo_clutch model.
Note Simulink software does not permit three or more enabled subsystems to hand off a model state. If Simulink software detects that a model is handing off a state among more than two enabled subsystems, it generates an error. |
By default Simulink software uses the absolute tolerance value specified in the Configuration Parameters dialog box (see Specifying Variable-Step Solver Error Tolerances) to compute the output of the Integrator block. If this value does not provide sufficient error control, specify a more appropriate value in the Absolute tolerance field of the Integrator block's dialog box. The value that you specify is used to compute all of the block's outputs.
When you select all options, the block icon looks like this.
The Integrator block accepts and outputs signals of type double on its data ports. The external reset port accepts signals of type double or Boolean.
Reset the states to their initial conditions when a trigger event occurs in the reset signal.
Default: none
Do not reset the state to initial conditions.
Reset the state when the reset signal rises from a zero to a positive value or from a negative to a positive value.
Reset the state when the reset signal falls from a positive value to zero or from a positive to a negative value.
Reset the state when the reset signal changes from a zero to a nonzero value or changes sign.
Reset the state when the reset signal is nonzero at the current time step or changes from nonzero at the previous time step to zero at the current time step.
Reset the state when the reset signal is nonzero at the current time step.
See Block-Specific Parameters for the command-line information.
Get the initial conditions of the states.
Default: internal
Get the initial conditions of the states from the Initial condition parameter.
Get the initial conditions of the states from an external block.
Simulink software does not allow the initial condition of this block to be inf or NaN.
Selecting internal enables the Initial condition parameter.
Selecting external disables the Initial condition parameter.
See Block-Specific Parameters for the command-line information.
Specify the states' initial conditions.
Default: 0
Simulink software does not allow the initial condition of this block to be inf or NaN.
Setting Initial condition source to internal enables this parameter.
Setting Initial condition source to external disables this parameter.
See Block-Specific Parameters for the command-line information.
Limit the block's output to a value between the Lower saturation limit and Upper saturation limit parameters.
Default: Off
On Limit the block's output to a value between the Lower saturation limit and Upper saturation limit parameters.
OffDo not limit the block's output to a value between the Lower saturation limit and Upper saturation limit parameters.
This parameter enables Upper saturation limit.
This parameter enables Lower saturation limit.
See Block-Specific Parameters for the command-line information.
Specify the upper limit for the integral.
Default: inf
Minimum: value of Output minimum parameter
Maximum: value of Output maximum parameter
Limit output enables this parameter.
See Block-Specific Parameters for the command-line information.
Specify the lower limit for the integral.
Default: -inf
Minimum: value of Output minimum parameter
Maximum: value of Output maximum parameter
Limit output enables this parameter.
See Block-Specific Parameters for the command-line information.
Add a saturation output port to the block.
Default: Off
See Block-Specific Parameters for the command-line information.
Add an output port to the block for the block's state.
Default: Off
On Add an output port to the block for the block's state.
OffDo not add an output port to the block for the block's state.
See Block-Specific Parameters for the command-line information.
Specify the absolute tolerance for computing the block output.
Default: auto
You can enter auto or a numeric value.
If you enter auto, Simulink uses the absolute tolerance value in the Configuration Parameters dialog box (see Solver Pane) to compute the block output.
If you enter a numeric value, that value overrides the absolute tolerance in the Configuration Parameters dialog box.
See Block-Specific Parameters for the command-line information.
Cause Simulink linearization commands to treat this block as unresettable and as having no limits on its output, regardless of the settings of the block's reset and output limitation options.
Default: Off
On Cause Simulink linearization commands to treat this block as unresettable and as having no limits on its output, regardless of the settings of the block's reset and output limitation options.
OffDo not cause Simulink linearization commands to treat this block as unresettable and as having no limits on its output, regardless of the settings of the block's reset and output limitation options.
Use this check box to linearize a model around an operating point that causes the integrator to reset or saturate.
See Block-Specific Parameters for the command-line information.
Select to enable zero-crossing detection. For more information, see Zero-Crossing Detection.
Default: On
On Use zero crossings to detect and take a time step at any of the following events: reset, entering or leaving an upper saturation state, entering or leaving a lower saturation state.
OffDo not use zero crossings to detect and take a time step at any of the following events: reset, entering or leaving an upper saturation state, entering or leaving a lower saturation state.
If you select this check box, Limit output, and zero-crossing detection for the model as a whole, the Integrator block uses zero crossings as described.
See Block-Specific Parameters for the command-line information.
Assign a unique name to each state.
Default: ' '
If this field is blank, no name assignment occurs.
To assign a name to a single state, enter the name between quotes, for example, 'velocity'.
To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.
The state names apply only to the selected block.
The number of states must divide evenly among the number of state names.
You can specify fewer names than states, but you cannot specify more names than states.
For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.
To assign state names with a variable in the MATLAB workspace, enter the variable without quotes. A variable can be a string, cell array, or structure.
See Block-Specific Parameters for the command-line information.
Direct Feedthrough | Yes, of the reset and external initial condition source ports |
Sample Time | Continuous |
Scalar Expansion | Yes, of parameters |
States | Inherited from driving block or parameter |
Dimensionalized | Yes |
Zero-Crossing Detection | Yes, if enabled and you select the Limit output option, one for detecting reset, one each to detect upper and lower saturation limits, and one when leaving saturation |
 | Integer Delay | Interpolation Using Prelookup |  |
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