Set point tracking optimisation by causal nonparametric modelling

This manuscript presents a causal method to design the feedforward part of two-degree-of-freedom (2-d.o.f.), linear time-invariant (LTI), industrial controllers for optimal tracking, independent of the structure of the feedback controller, of the way it is designed, and of the characteristics of the set point signal. The method relies on a nonparametric model of the control loop, expressed in terms of a finite set of ‘control’ and ‘output base functions’, and allows to cast various tracking problems into a unified optimisation framework. The manuscript shows and discusses both how to determine the base functions and how to state and solve the tracking optimisation problems. Simulation examples demonstrate the method’s effectiveness, simplicity, and practical usefulness.