B-splines and pseudo-inversion as tools for handling saturation constraints in the optimal set-point regulation

This paper deals with the optimal output transition problem under saturation constraints on the control effort. The recently proposed pseudo inversion approach is here adopted to define a feedforward action optimizing the set-point following response of a given stable closed-loop system Σ_f,c. To take into account saturating actuators, the optimal external input reference r(t) forcing Σ_f,c is assumed to be given by a B-spline function. The actual control input u(t) yielded by r(t) and forcing the plant is optimally approximated by a B-spline û(t), whose control points û(t) are chosen in such a way to satisfy the saturation constraints on u(t). If û(t) is a sufficiently accurate approximation of u(t), the exact fulfillment of saturation constraints by û(t) are transferred to u(t). The simulations on a practical case show excellent results.