# Discrete PI Controller with Integral Anti-Windup

Discrete-time PI control with integral anti-windup

• Library:
• Simscape / Power Systems / Simscape Components / 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 interval between samples. If the block is inside a triggered subsystem, inherit the sample time by setting this parameter to `-1`. If this block is in a continuous variable-step model, specify the sample time explicitly. For more information, see What Is Sample Time? (Simulink) and Specify Sample Time (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.