PI Controller with Integral Anti-Windup (Discrete or Continuous)

Discrete-time or continuous-time PI control with integral anti-windup

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Libraries:
Simscape / Electrical / Control / General Control

Description

The PI Controller with Integral Anti-Windup (Discrete or Continuous) block implements discrete-time or continuous-tiime PI control with internal anti-windup. This 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:

$u(k)=\text{sat}\left(K_p\text{e}\left(\text{k}\right)+\text{sat}\left(K_i\frac{T_{s}z}{z-1}\text{e}\left(\text{k}\right),\text{A},\text{B}\right),A,B\right),$

$sat(x,A,B)=\min \left(\max \left(x,\text{A}\right),B\right),$

where:

• u is the control signal.

• K_p is the proportional gain coefficient.

• e is the error signal.

• K_i is the integral gain coefficient.

• T_s is the sampling period.

• A is the lower limit for saturation.

• B is the upper limit for saturation.

Examples

Energy Balance in a 48V Starter Generator

An interior permanent magnet synchronous machine (IPMSM) used as a starter/generator in a simplified 48V automotive system. The system contains a 48V electric network and a 12V electric network. The internal combustion engine (ICE) is represented by basic mechanical blocks. The IPMSM operates as a motor until the ICE reaches the idle speed and then it operates as a generator. The IPMSM supplies power to the 48V network, which contains the R3 power consumer. The 48V network supplies power to the 12V network which has two consumers: R1 and R2. The total simulation time (t) is 0.5 seconds. At t = 0.05 seconds, the ICE turns on. At t = 0.1 seconds, R3 switches on. At t = 0.3 seconds, R2 switches on and increases the load on the 12V electric network. The EM Controller subsystem includes a multi-rate PI-based cascade control structure which has an outer voltage-control loop and two inner current-control loops. The task scheduling in the Control subsystem is implemented as a Stateflow® state machine. The DCDC Controller subsystem implements a simple PI controller for the DC-DC Buck converter, which feeds the 12V network. The Scopes subsystem contains scopes that allow you to see the simulation results.

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IPMSM Torque Control in a Parallel HEV

A simplified parallel hybrid electric vehicle (HEV). An interior permanent magnet synchronous machine (IPMSM) and an internal combustion engine (ICE) provide the vehicle propulsion. The IPMSM operates in both motoring and generating modes. The vehicle transmission and differential are implemented using a fixed-ratio gear-reduction model. The Vehicle Controller subsystem converts the driver inputs into torque commands. The vehicle control strategy is implemented as a Stateflow® state machine. The ICE Controller subsystem controls the torque of the combustion engine. The Drive Controller subsystem controls the torque of the IPMSM. The Scopes subsystem contains scopes that allow you to see the simulation results.

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IPMSM Torque Control in a Series-Parallel HEV

A simplified series-parallel hybrid electric vehicle (HEV). An interior permanent magnet synchronous machine (IPMSM) and an internal combustion engine (ICE) provide the vehicle propulsion. The ICE also uses electric generator to recharge the high-voltage battery during driving. The vehicle transmission and differential are implemented using a fixed-ratio gear-reduction model. The Vehicle Controller subsystem converts the driver inputs into torque commands. The vehicle control strategy is implemented as a Stateflow® state machine. The ICE Controller subsystem controls the torque of the combustion engine. The Generator Controller subsystem controls the torque of the electric generator. The Drive Controller subsystem controls the torque of the IPMSM. The Scopes subsystem contains scopes that allow you to see the simulation results.

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Switched Reluctance Machine Speed Control

Control the rotor speed in a switched reluctance machine (SRM) based electrical drive. A DC voltage source feeds the SRM through a controlled three-arm bridge. To achieve both forward and backward rotation, this example adjusts the converter turn-on and turn-off angles using the speed error.

• Open Model

Ports

Input

e — Error signal

scalar

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

Data Types: single | double

Reset — Integrator gain reset

scalar

External reset (rising edge) signal for the integrator.

Data Types: single | double

Output

u — Control signal

scalar

Control signal, u(k).

Data Types: single | double

Parameters

Proportional gain — K_p

1 (default) | positive scalar

Proportional gain, K_p, of the PI controller.

Integral gain — K_i

1 (default) | positive scalar

Integral gain, K_i, of the PI controller.

Upper saturation limit — B

5 (default) | scalar greater than the value of the Lower saturation limit parameter

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

Lower saturation limit — A

-5 (default) | scalar

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

Integrator initial condition — Initial integrator value

0 (default) | scalar

Value of the integrator at simulation start time.

Sample time (-1 for inherited) — Block sample time

-1 (default) | 0 | positive scalar

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? and Specify Sample Time.

For inherited discrete-time operation, set this parameter to -1. For discrete-time operation, set this parameter to a positive integer. For continuous-time operation, set this parameter to 0.

If this block is in a masked subsystem or a variant subsystem that supports switching between continuous operation and discrete operation, promote this parameter to ensure correct switching between the continuous and discrete implementations of the block. For more information, see Promote Block Parameters on a Mask.

References

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

Extended Capabilities

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

Version History

Introduced in R2017b

R2025a: Support continuous-time simulation

The PI Controller with Integral Anti-Windup (Discrete or Continuous) block now supports continuous-time simulation. For continuous-time operation, set the Sample time (-1 for inherited) parameter to 0.