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
tunableSurface command. For an overview
of the workflow for tuning gain-scheduled controllers, see Gain Scheduling Basics.
Parameterize 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|
|Generate MATLAB code for tunable gain surfaces|
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 Control Systems
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.
In Simulink, model gain schedules using lookup tables, interpolation blocks, or MATLAB Function blocks.
Tune Gain Schedules
Understand the general tuning workflow for using
systune to tune
To tune a gain-scheduled control system, you need a collection of linear models describing the plant dynamics at the selected design points.
For tuning a gain-scheduled control system, associate a family of linear plant models
slTuner interface to your Simulink model.
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.
When tuning gain-scheduled controllers, you can specify tuning objectives that depend on the scheduling variables.
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
Linearize an airframe model at an array of design points to use for gain-scheduled control design.
Tune gain-scheduled PI controllers for the inner loop of the HL-20 airframe model.
Tune a gain-scheduled SISO architecture for controlling roll, pitch, and yaw of the airframe.
Tune a gain-scheduled MIMO architecture for controlling roll, pitch, and yaw of the airframe.
Design a gain-scheduled control system for the HL-20 airframe in MATLAB.