Simulink Control Design™ - MathWorks

Model Gain-Scheduled Control Systems in Simulink

In Simulink, you can model gain-scheduled control systems in which controller gains or

coefficients depend on scheduling variables such as time, operating conditions, or model

parameters. The library of linear parameter-varying blocks in Control System Toolbox lets

you implement common control-system elements with variable gains. Use blocks such as

lookup tables or MATLAB Function blocks to implement the gain schedule, which gives

the dependence of these gains on the scheduling variables.

To model a gain-scheduled control system in Simulink:

(^1) Identify the scheduling variables and the signals that represent them in your model.
For instance, if your system is a cruising aircraft, then the scheduling variables might
be the incidence angle and the airspeed of the aircraft.
(^2) Use a lookup table block or a MATLAB Function block to implement a gain or
coefficient that depends on the scheduling variables. If you do not have lookup table
values or MATLAB expressions for gain schedules that meet your performance
requirements, you can use systune to tune them. See “Tune Gain Schedules in
Simulink” on page 11-15.
(^3) Replace ordinary control elements with gain-scheduled elements. For instance,
instead of a fixed-coefficient PID controller, use a Varying PID Controller block, in
which the gain schedules determine the PID gains.
4 Add scheduling logic and safeguards to your model as needed.
Model Scheduled Gains
A gain schedule converts the current values of the scheduling variables into controller
gains. There are several ways to implement a gain schedule in Simulink.
Available blocks for implementing lookup tables include:

• Lookup tables — A lookup table is a list of breakpoints and corresponding gain values.
  When the scheduling variables fall between breakpoints, the lookup table interpolates
  between the corresponding gains. Use the following blocks to implement gain
  schedules as lookup tables.
  
  
  • 1-D Lookup Table, 2-D Lookup Table, n-D Lookup Table — For a scalar gain that
    depends on one, two, or more scheduling variables.
  
  
  • Matrix Interpolation — For a matrix-valued gain that depends on one, two, or three
    scheduling variables. (This block is in the Simulink Extras library.)
  
  
  
  

11 Gain-Scheduled Controllers