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
tunableSurface command. For an overview
of the workflow for tuning gain-scheduled controllers, see Gain Scheduling Basics.
Parametrize Scheduled Gain
|Create tunable gain surface for gain scheduling|
|Polynomial basis functions for tunable gain surface|
|Fourier basis functions for tunable gain surface|
|Basis functions for tunable gain surface|
|Visualize gain surface as a function of scheduling variables|
|Evaluate gain surfaces at specific design points|
|Get current values of tunable-surface coefficients|
|Set values of tunable-surface coefficients|
Control System Tuning
|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 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|
Gain-Scheduled PID Autotuning
|Closed-Loop PID Autotuner||Automatically tune PID gains based on plant frequency responses estimated from closed-loop experiment in real time|
|Change Operating Points||Switch between operating points during simulation (Since R2023b)|
|PID Gain Scheduler||Lookup table based gain scheduling with PID array (Since R2023b)|
|PID Gains Store and Update||Store and update tuned PID gains tuned using Closed-Loop PID Autotuner (Since R2023b)|
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
systuneto 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
slTunerinterface 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®.