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Integrator with Wrapped State (Discrete or Continuous)

Discrete-time or continuous-time integrator with wrapped state

  • Library:
  • Simscape / Power Systems / Simscape Components / Control / General Control

Description

The Integrator with Wrapped State (Discrete or Continuous) block implements a wrapped state integrator in conformance with IEEE 421.5-2016[1].

Use this block to generate periodic signals such as angles or to represent a voltage-controlled oscillator. You can switch between continuous and discrete implementations of the integrator using the Sample time parameter.

Equations

Continuous

To configure the integrator for continuous time, set the Sample time property to 0. This representation is equivalent to the continuous transfer function:

G(s)=1s.

From the preceeding transfer function, the integrator defining equations are:

{x˙(t)=u(t)y(t)=x(t)x(0)=x0,

where:

  • u is the integrator input.

  • x is the integrator state.

  • y is the integrator output.

  • t is the simulation time.

  • x0 is the initial state of the integrator.

Discrete

To configure the integrator for discrete time, set the Sample time property to a positive, nonzero value, or to -1 to inherit the sample time from an upstream block. The discrete representation is equivalent to the transfer function:

G(z)=Tsz1,

where Ts is the sample time. From the discrete transfer function, the integrator equations are defined using the forward Euler method:

{x(n+1)=x(n)+Tsu(n)y(n)=x(n)x(0)=x0,

where:

  • u is the integrator input.

  • x is the integrator state.

  • y is the integrator output.

  • n is the simulation time step.

  • x0 is the initial state of the integrator.

Defining Initial Conditions

You can define the state initial conditions using Initial condition parameter.

Wrapping Cyclic States

The integrator wraps its state between the specified lower and upper values. This diagram shows the outputs of a wrapped and nonwrapped state integrator for a constant input.

In the diagram, the lower and upper limits are 0 and , respectively.

Ports

Input

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Integrator input.

Data Types: single | double

Output

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Integrator output.

Data Types: single | double

Parameters

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Integrator upper limit.

Integrator lower limit.

Integrator initial state.

Integrator sample time. Set this to 0 to implement a continuous integrator. To implement a discrete integrator, set this to -1 or a positive number.

References

[1] IEEE Recommended Practice for Excitation System Models for Power System Stability Studies. IEEE Std 421.5-2016. Piscataway, NJ: IEEE-SA, 2016.

Introduced in R2017b

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