gainscheduling

Gain scheduling is a control design methodology for nonlinear systems that uses a family of linear models parameterized by scheduling variables. The controller gains are allowed to vary as a function of these variables, enabling a single controller to operate effectively across a wide range of operating conditions.

The design process typically identifies one or more scheduling variables (such as speed, altitude, throttle, or other measurable quantities), constructs linear models around several operating points, and designs local linear controllers for each model (for example with LQR, H-infinity, or pole placement). Gains for the different models are then blended in real time by interpolating gains or using convex combinations as the scheduling variables change. Explicit gain scheduling uses a grid of operating points with precomputed gains, while dynamic gain scheduling updates the gains continuously as measurements evolve.

Viewed in a broader framework, gain scheduling can be formulated as a linear parameter-varying (LPV) system, where the plant matrices depend affinely on the scheduling variables. Stability and performance are sought through conditions such as quadratic stability or LPV theory, but guarantees often depend on remaining within the design region and on the quality of the plant models. In practice, unmodeled dynamics or rapid scheduling changes can challenge robustness, so designers may constrain the rate of change or incorporate robust or adaptive elements.

Applications are common in aerospace flight control (autopilots, flight controllers), automotive powertrains and chassis control, and robotics and process control, where operating conditions vary widely and linear controllers alone are insufficient.