PS Integrator

Integrate physical signal

• 

Libraries:
Simscape / Foundation Library / Physical Signals / Linear Operators

Description

The PS Integrator block outputs the integral of its input at the current time step. The following equation represents the output of the block:

$$y(t)={\displaystyle \underset{t_0}{\overset{t}{\int }}u(t)dt}+y_0$$

where:

• u is the physical signal at input port I.

• y₀ is the initial condition.

• y is the physical signal at output port O.

• t is time.

The PS Integrator block is a dynamic system with one state, its output. The input of the PS Integrator block is the time derivative of the state:

$$x=y(t)$$

$$x_0=y_0$$

$$\dot{x}=u(t)$$

The solver computes the output of the PS Integrator block at the current time step by using the current input value and the value of the state at the previous time step. The PS Integrator block saves its output at the current time step for the solver to use to compute the output at the next time step. The block also provides the solver with an initial condition to use to compute the initial state of the block at the beginning of a simulation run. The default value of the initial condition is 0 s. You can specify another value for the initial condition as either a block parameter or an input signal:

• To define the initial condition as a block parameter, specify the Initial condition source parameter as Internal and enter the value and unit for the Initial condition parameter.

• To provide the initial condition from an external source, specify the Initial condition source parameter as External. Selecting this option exposes port X0. Connect the external initial condition signal to this port.

Because the block performs integration of the input signal over time, the unit of the output signal equals the unit of the input signal multiplied by the unit of time, s. For example, if the input signal is in m/s, then the output signal is in m. The unit specified for the Initial condition parameter or the unit of the external initial condition signal at port X0 must be commensurate with the unit of the output signal.

Resetting the State

The block can reset its state to the specified initial condition based on an external signal. By default, the External reset parameter is set to None. To cause the block to reset its state, select one of the other External reset choices:

• Select Rising to reset the state when the reset signal rises from a negative or zero value to a positive value.

• Select Falling to reset the state when the reset signal falls from a positive value to a zero or negative value.

• Select Either to reset the state when the reset signal changes from zero to a nonzero value, from a nonzero value to zero, or changes sign.

Selecting any of these options exposes a trigger port, R. Connect the reset physical signal to this port.

Limiting the Output

The block can function as a limited integrator, holding its output within the specified saturation bounds:

• When the integral is less than or equal to the lower saturation limit, the block holds the output 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 block holds the output at the upper saturation limit.

Use the Limit output parameter to specify whether to limit the output at the lower bound, upper bound, or both. The Limit output source parameter provides two ways of specifying the upper and lower bounds:

• Internal — Define the saturation bounds using the Upper limit and Lower limit parameters.

• External — Define the saturation bounds using the external physical signals at ports U and L.

Examples

Nonlinear Inductor

An implementation of a nonlinear inductor where the inductance depends on the current. For best numerical efficiency, the underlying behavior is defined in terms of a current-dependent flux. In order to differentiate the flux to get voltage, a magnetizing lag is included. Simulation results are relatively insensitive to this lag provided that it is at least an order of magnitude faster than the fastest frequency of interest. Parameters for the source and lag are defined in the MATLAB® workspace so that the expected voltage can be calculated analytically.

• Open Model

Solenoid

A solenoid with a spring return. The solenoid is modeled as an inductance whose value L depends on the plunger position x. The back emf for a time-varying inductance is given by:

• Open Model

Ports

Input

I — Input physical signal, u, untyped

physical signal

Input physical signal.

The port name is not visible in the block icon, but you can see this name in the underlying source file by clicking the Source code link in the Description tab of the block dialog box.

R — Reset physical signal, R, untyped

physical signal

Reset physical signal. Depending on the External reset parameter value, the block resets the output to the initial condition on the rising edge, falling edge, or both the rising and the falling edge of the reset signal.

Dependencies

To enable this port, set the External reset parameter to Rising, Falling, or Either.

X0 — Initial condition physical signal, XO, untyped

physical signal

Physical signal input port that specifies the initial condition of the block. The unit of this signal must be commensurate with the unit of the output signal, y.

Dependencies

To enable this port, set the Initial condition source parameter to External.

U — Upper saturation bound physical signal, U, untyped

physical signal

Physical signal input port that specifies the upper saturation bound for the block output. The unit of this signal must be commensurate with the unit of the output signal, y.

Dependencies

To enable this port, set the Limit output parameter to Upper or Both and the Limit output source parameter to External.

L — Lower saturation bound physical signal, L, untyped

physical signal

Physical signal input port that specifies the lower saturation bound for the block output. The unit of this signal must be commensurate with the unit of the output signal, y.

Dependencies

To enable this port, set the Limit output parameter to Lower or Both and the Limit output source parameter to External.

Output

O — Output physical signal, y, untyped

physical signal

Output physical signal.

The port name is not visible in the block icon, but you can see this name in the underlying source file by clicking the Source code link in the Description tab of the block dialog box.

Parameters

External reset — Whether block resets to initial condition based on external reset signal

None (default) | Rising | Falling | Either

You can specify that the block resets its state to the specified initial condition based on an external signal. By default, the block does not reset its state. Setting this parameter to an option other than None exposes the input port R. Depending on the parameter value, the block resets its state on the rising edge, falling edge, or both the rising and the falling edge of the reset signal.

Initial condition source — Whether to specify initial condition as block parameter or additional input signal

Internal (default) | External

You can specify the initial condition of the block as either a block parameter or an input signal:

• Internal — Define the initial condition for integration using the Initial condition parameter.

• External — Define the initial condition for integration using the external physical signal at port X0.

Limit output — Whether to limit integrator output

None (default) | Upper | Lower | Both

You can specify upper and lower bounds for the output signal and cause the block to function as a limited integrator:

• None — Do not limit the output.

• Upper — Limit the output at the upper bound.

• Lower — Limit the output at the lower bound.

• Upper — Limit the output both at the upper and the lower bound.

For more information, see Limiting the Output.

Limit output source — Whether to specify saturation bounds as block parameters or input signals

Internal (default) | External

Select the way to specify the upper and lower bounds when limiting output:

• Internal — Define the saturation bounds using the Upper limit and Lower limit parameters.

• External — Define the saturation bounds using the external physical signals at ports U and L.

Dependencies

To enable this parameter, set the Limit output parameter to a value other than None.

Initial condition — Initial state for the integration

0 s (default) | scalar

Initial condition to use in computing the initial state of the block at the beginning of a simulation run.

The unit specified for the Initial condition parameter must match the unit of the output signal. By default, the input signal is unitless. Then the output signal is in s, and the Initial condition parameter unit is also s. If your input signal has a physical unit, multiply this unit by a unit of time to set the correct unit for the Initial condition parameter. For example, if the input signal is in m/s, then specify the Initial condition parameter unit as m.

Dependencies

To enable this parameter, set Initial condition source to Internal.

Upper limit — Upper saturation limit for block output

inf s (default) | scalar

Upper saturation limit for the block output. The unit specified for the Upper limit parameter must match the unit of the output signal.

Dependencies

To enable this parameter, set the Limit output parameter to Upper or Both and the Limit output source parameter to Internal.

Lower limit — Lower saturation limit for block output

-inf s (default) | scalar

Lower saturation limit for the block output. The unit specified for the Lower limit parameter must match the unit of the output signal.

Dependencies

To enable this parameter, set the Limit output parameter to Lower or Both and the Limit output source parameter to Internal.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2007a

R2022b: Use saturation bounds to limit block output

The block includes the Limit output, Limit output source, Upper limit and Lower limit parameters. Use these parameters to limit the output signal. For more information, see Limiting the Output.

R2021a: Reset block state at events

The block includes an additional parameter, External reset, which lets can specify that the block output resets to the initial condition when the physical signal at port R triggers a reset. The initial condition source can now be either a physical signal or a block parameter. If you set the Initial condition source parameter to External, the physical signal at port X0 supplies the initial condition value for integration and reset.

R2019a: Unit propagation

Prior to R2019a, this block did not propagate physical units.

If your model contains legacy blocks without unit propagation, use the Upgrade Advisor to upgrade your blocks to the latest version. For more information, see Upgrading Models with Legacy Physical Signal Blocks.