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Discrete PI Controller

Discrete-time PI controller with external anti-windup input

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  • Discrete PI Controller block

Libraries:
Simscape / Electrical / Control / General Control

Description

The Discrete PI Controller block implements discrete PI control with external anti-windup input.

This diagram is the equivalent circuit for the controller with external anti-windup input.

Equations

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

u(k)=[Kp+(Ki+du(k)Kaw)Tszz−1]e(k),

where

  • u is the control signal.

  • Kp is the proportional gain coefficient.

  • Ki is the integral gain coefficient.

  • Kaw is the anti-windup gain coefficient.

  • Ts is the sampling period.

  • e is the error signal.

To prevent excessive overshoot, the block can use back calculation to implement an external anti-windup mechanism. It inputs du(k), the difference between the saturated control signal, usat(k), and the calculated unsaturated control signal, u(k). It then multiplies the difference by the anti-windup coefficient and adds the amplified signal from the integral gain.

Examples

DC Motor Control

DC Motor Control

A cascade speed-control structure for a DC motor. A PWM controlled four-quadrant Chopper is used to feed the DC motor. The Control subsystem includes the outer speed-control loop, the inner current-control loop, and the PWM generation. The total simulation time (t) is 4 seconds. At t = 1.5 seconds, the load torque increases. At t = 2.5 seconds, the reference speed is changed from 1000 rpm to 2000 rpm.

Energy Balance in a 48V Starter Generator

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.

IPMSG Voltage Stabilization

IPMSG Voltage Stabilization

Control an Interior Permanent Magnet Synchronous Generator (IPMSG) based low voltage generator system for a hybrid electric vehicle (HEV). The Control 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 Scopes subsystem contains scopes that allow you to see the simulation results. An ideal angular velocity source, which represents a combustion engine, drives the IPMSG. The IPMSG supplies low-voltage power to loads R1 and R2. At t = 0.4 seconds, the switch closes, increasing the load.

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

Difference, du(k), between the saturated u^sat(k) and the unsaturated control signals, u(k). If du(k) is zero, the anti-windup is disabled.

Description

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.

Anti-windup gain, Kaw, of 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? and Specify Sample Time.

References

[1] Åström, K. and T. Hägglund. Advanced PID Control. Research Triangle Park, NC: ISA, 2005.

Extended Capabilities

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

Version History

Introduced in R2017b

See Also

Blocks