gainscheduled

Gain scheduling, also known as gainscheduled control, is a control design technique used to handle nonlinear dynamics by adjusting a controller's gains as a function of an operating condition. The basic idea is to design a family of linear controllers for different operating points and then interpolate between them as the system operates across those points. The result is a controller that behaves like a nonlinear controller while remaining implementable with linear control theory.

A scheduling variable, or vector of variables, is measured in real time. Common choices include speed and altitude in aircraft, load factor, throttle setting, or temperature and flow in process systems. The gains are typically obtained by linearizing a detailed nonlinear model around selected points and designing a stabilizing controller for each linear model. During operation, the current value of the scheduling variable selects a suitable set of gains by interpolation, switching, or a convex combination across the neighboring designs.

Gain scheduling can be implemented in several ways. Direct interpolation of gain matrices, piecewise-linear control laws, or more systematic approaches based on linear parameter-varying (LPV) theory and robust control provide stability guarantees within a predefined scheduling domain. LPV methods place the varying parameters into a structured model that can be analyzed with convex techniques.

Advantages include simplicity, leverage of well-developed linear control, and good performance over moderate nonlinear ranges. Limitations include potential loss of robustness outside the scheduled domain, sensitivity to scheduling measurement noise, and the lack of a general global stability proof for all trajectories. Gain scheduling is widely used in aerospace, automotive, and process industries to manage nonlinear behavior across operating conditions.