# Gain Scheduling

Tune 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 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

## Blocks

## 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.

### Gain-Scheduled Autotuning

**Gain-Scheduled PID Autotuning a VTOL UAV During Forward and Backward Transition**

Tune gain-scheduled PID controller for VTOL UAV transitioning between operating modes.*(Since R2024a)***Gain-Scheduled PID Autotuning Torque Control for a Nonlinear PMSM**

Tune gain-scheduled PID controllers for d-axis and q-axis current loops of a nonlinear PMSM model.*(Since R2024a)*

### 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^{®}.