Optimal reference processing in two-degrees-of-freedom control

This paper deals with the realisation of two degrees of freedom (2-DOF) compensators. The advantages of using a 2-DOF compensator are well known: the closed-loop properties can be shaped independently of the reference tracking transfer function. This allows us to consider the separation and independence of properties which will depend on the kind of processing we apply to the reference signal. Depending on the design approach to be applied, separation could be preferred even when independence may seem to be desirable. What we analyse is the kind of reference processing that results from an optimisation problem. It will be seen that the optimal solution involves complete separation and independence. It turns out that the optimal 2-DOF controller that results is seen to have a concise structure that accounts for a complete separation of the reference properties and a complete independence with respect to the feedback controller.