Simulink Control Design™ - MathWorks

Gain-Scheduled Controllers

11

Gain Scheduling Basics............................... 11-2

Gain Scheduling in Simulink......................... 11-2

Tune Gain Schedules.............................. 11-3

Model Gain-Scheduled Control Systems in Simulink....... 11-4

Model Scheduled Gains............................ 11-4

Gain-Scheduled Equivalents for Commonly Used Control

Elements..................................... 11-7

Custom Gain-Scheduled Control Structures ............ 11-12

Tunability of Gain Schedules ....................... 11-13

Tune Gain Schedules in Simulink ..................... 11-15

Workflow for Tuning Gain Schedules ................. 11-15

Plant Models for Gain-Scheduled Controller Tuning ...... 11-18

Obtaining the Family of Linear Models................ 11-19

Set Up for Gain Scheduling by Linearizing at Design Points

........................................... 11-20

Sample System at Simulation Snapshots ............... 11-23

Sample System at Varying Parameter Values............ 11-23

Eliminate Samples at Unneeded Design Points.......... 11-24

LPV Plants in MATLAB ............................ 11-25

Multiple Design Points in slTuner Interface............. 11-26

Block Substitution for Plant........................ 11-26

Multiple Block Substitutions........................ 11-26

Substituting Blocks that Depend on the Scheduling Variables

........................................... 11-28

Resolving Mismatches Between a Block and its Substitution

........................................... 11-29

Block Substitution for LPV Blocks .................... 11-30

Parameterize Gain Schedules......................... 11-32

Basis Function Parameterization..................... 11-32

Tunable Gain Surfaces............................ 11-35

Tunable Gain With Two Independent Scheduling Variables

........................................... 11-36

Tunable Surfaces in Simulink ....................... 11-38

Tunable Surfaces in MATLAB ....................... 11-40

xxx Contents