Gain Scheduling

Tuning of gain-scheduled controllers for nonlinear plants

A gain-scheduled controller is a controller whose gains are automatically adjusted as a function of time, operating condition, or plant parameters. Gain scheduling is a common strategy for controlling systems whose dynamics change with time or operating condition. Such systems include linear parameter-varying (LPV) systems and large classes of nonlinear systems. To tune gain-scheduled controllers in MATLAB^® or Simulink^®, you represent the variable gain as a function of the scheduling variables using the tunableSurface command. For an overview of the workflow for tuning gain-scheduled controllers, see Gain Scheduling Basics.

Functions

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Parameterize Scheduled Gain

`tunableSurface`	Create tunable gain surface for gain scheduling
`polyBasis`	Polynomial basis functions for tunable gain surface
`fourierBasis`	Fourier basis functions for tunable gain surface
`ndBasis`	Basis functions for tunable gain surface
`viewSurf`	Visualize gain surface as a function of scheduling variables
`evalSurf`	Evaluate gain surfaces at specific design points
`getData`	Get current values of tunable-surface coefficients
`setData`	Set values of tunable-surface coefficients
`codegen`	Generate MATLAB code for tunable gain surfaces

Control System Tuning

`systune`	Tune fixed-structure control systems modeled in MATLAB
`slTuner`	Interface for control system tuning of Simulink models
`systune (slTuner)`	Tune control system parameters in Simulink using `slTuner` interface
`voidModel`	Mark missing or irrelevant models in model array

Variable Tuning Goals

`varyingGoal`	Variable tuning goal for gain-scheduled controllers
`getGoal`	Evaluate variable tuning goal at specified design point

Blocks

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Continuous Time

Varying Lowpass Filter	Butterworth filter with varying coefficients
Varying Notch Filter	Notch filter with varying coefficients
PID Controller	Continuous-time or discrete-time PID controller
PID Controller (2DOF)	Continuous-time or discrete-time two-degree-of-freedom PID controller
Varying Transfer Function	Transfer function with varying coefficients
Varying State Space	State-space model with varying matrix values
Varying Observer Form	Observer-form state-space model with varying matrix values

Discrete Time

Discrete Varying Lowpass	Discrete Butterworth filter with varying coefficients
Discrete Varying Notch	Discrete-time notch filter with varying coefficients
Discrete PID Controller	Discrete-time or continuous-time PID controller
Discrete PID Controller (2DOF)	Discrete-time or continuous-time two-degree-of-freedom PID controller
Discrete Varying Transfer Function	Discrete-time transfer function with varying coefficients
Discrete Varying State Space	Discrete-time state-space model with varying matrix values
Discrete Varying Observer Form	Discrete-time observer-form state-space model with varying matrix values

Topics

Gain-Scheduled Control Systems

Gain Scheduling Basics
Gain scheduling is an approach to control of non-linear systems using a family of linear controllers, each providing satisfactory control for a different operating point of the system.
Model Gain-Scheduled Control Systems in Simulink
In Simulink, model gain schedules using lookup tables, interpolation blocks, or MATLAB Function blocks.

Tune Gain Schedules

Tune Gain Schedules in Simulink
Understand the general tuning workflow for using systune to tune gain-scheduled controllers.
Plant Models for Gain-Scheduled Controller Tuning
To tune a gain-scheduled control system, you need a collection of linear models describing the plant dynamics at the selected design points.
Multiple Design Points in slTuner Interface
For tuning a gain-scheduled control system, associate a family of linear plant models with the slTuner interface to your Simulink model.
Parameterize Gain Schedules
A gain surface parameterizes a variable gain in terms of the scheduling variables. Use gain surfaces to model variable gains in a gain-scheduled control system.
Change Requirements with Operating Condition
When tuning gain-scheduled controllers, you can specify tuning objectives that depend on the scheduling variables.
Validate Gain-Scheduled Control Systems
Tuning gain-scheduled controllers guarantees suitable performance only near each design point. It is important to validate the tuning results over the full range of operating conditions.

HL-20 Autopilot Case Study

Trimming and Linearization of the HL-20 Airframe
Linearize an airframe model at an array of design points to use for gain-scheduled control design.
Angular Rate Control in the HL-20 Autopilot
Tune gain-scheduled PI controllers for the inner loop of the HL-20 airframe model.
Attitude Control in the HL-20 Autopilot - SISO Design
Tune a gain-scheduled SISO architecture for controlling roll, pitch, and yaw of the airframe.
Attitude Control in the HL-20 Autopilot - MIMO Design
Tune a gain-scheduled MIMO architecture for controlling roll, pitch, and yaw of the airframe.
MATLAB Workflow for Tuning the HL-20 Autopilot
Design a gain-scheduled control system for the HL-20 airframe in MATLAB.

Featured Examples

Design Family of PID Controllers for Multiple Operating Points

If your nonlinear Simulink model operates over a wide range of operating conditions, you can design an array of PID controllers for multiple model operating points.

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Gain-Scheduled Control of a Chemical Reactor

Tune a gain-scheduled controller for a chemical reactor transitioning from low to high conversion rate.

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Tuning of Gain-Scheduled Three-Loop Autopilot

Uses systune to generate smooth gain-schedules for a two-dimensional grid of operating conditions for a control system modeled in Simulink.

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