Fictitious Reference Tuning of the Feed-Forward Controller in a Two-Degree-of-Freedom Control System

In this paper, we provide a new effective tuning method to obtain the optimal parameter of the feed-forward controller in a two-degree-of-freedom (2DOF) control system for the purpose of achieving the desired response without using a mathematical model of a plant. The first author proposed “fictitious reference iterative tuning” (which is abbreviated to FRIT) as an effective method for the tuning of parameters of a controller by using only one-shot experimental data instead of using mathematical models of a plant. Here, we extend FRIT to the tuning of the feed-forward controller in a 2DOF control system and develop the off-line computation so as to be done by the least squares method. For these purposes, we introduce a new cost function consisting of the fictitious reference and the actual data (since we do not have to do iterative computation in the least squares method, we call the proposed method here as “fictitious reference tuning”). Since the new cost function is quadratically-parameterized, it is possible to analyze how far the obtained parameter is apart from the desired one. Thus, we then derive a pre-filter which is applied to the actual data so as to guarantee that the obtained parameter is close to the desired one. We also show that the proposed method is applicable to the case in which the initial experiment is performed in the conventional 1DOF control system. Finally, we illustrate experimental results in order to show the utility and the validity of the proposed method.