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# Discrete PI Controller with Integral Anti-Windup

Discrete-time PI control with integral anti-windup

• Library:
• Simscape / Electrical / Control / General Control

## Description

The Discrete PI Controller with Integral Anti-Windup block implements discrete PI control with internal anti-windup. The figure shows the equivalent circuit for the controller with internal anti-windup.

### Equations

The block calculates the control signal using the backward Euler discretization method:

`$u\left(k\right)=\text{sat}\left({K}_{p}\text{e}\left(\text{k}\right)+\text{sat}\left({K}_{i}\frac{{T}_{s}z}{z-1}\text{e}\left(\text{k}\right),\text{A},\text{B}\right),A,B\right),$`

where:

• u is the control signal.

• Kp is the proportional gain coefficient.

• e is the error signal.

• Ki is the integral gain coefficient.

• Ts is the sampling period.

• A is the lower limit for saturation.

• B is the upper limit for saturation.

## Ports

### Input

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Error signal, e(k), obtained as the difference between the reference, r(k), and measurement y(k) signals.

Data Types: `single` | `double`

External reset (rising edge) signal for the integrator.

Data Types: `single` | `double`

### Output

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Control signal, u(k).

Data Types: `single` | `double`

## Parameters

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Proportional gain, Kp, of the PI controller.

Integral gain, Ki, of the PI controller.

Upper limit, B, of the output for the PI controller.

Upper limit, A, of the output for the PI controller.

Value of the integrator at simulation start time.

Time between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? (Simulink) and Specify Sample Time (Simulink).

For inherited discrete-time operation, specify `-1`. For discrete-time operation, specify a positive integer. For continuous-time operation, specify `0`.

If this block is in a masked subsystem, or other variant subsystem that allows you to switch between continuous operation and discrete operation, promote the sample time parameter. Promoting the sample time parameter ensures correct switching between the continuous and discrete implementations of the block. For more information, see Promote Parameter to Mask (Simulink).

## References

[1] IEEE Recommended Practice for Excitation System Models for Power System Stability Studies. IEEE Std 421.5/D39. Piscataway, NJ: IEEE-SA, 2015.