For tuning gain schedules with systune, you use a parametric gain surface that is a
particular expansion of the gain in basis functions of σ:Kσ =K 0 +K 1 F 1 nσ +...+KMFMnσ.The basis functions F 1 ,...,FM are user-selected and fixed. These functions operate on n(σ),
where n is a function that scales and normalizes the scheduling variables to the interval [–
1,1] (or an interval you specify). The coefficients of the expansion, K 0 ,...,KM, are the
tunable parameters of the gain surface. K 0 ,...,KM can be scalar or matrix-valued,
depending on the I/O size of the gain K(σ). The choice of basis function is problem-
dependent, but in general, try low-order polynomial expansions first.11 Gain-Scheduled Controllers