Fictitious reference tuning for the optimal parameter of a feedforward controller in the two-degree-of-freedom control system

In this paper, we propose an effective tuning method to obtain the optimal parameter of a feedforward controller in the two-degree-of-freedom (2DOF) control system for the sake of achieving the desired output without mathematical model of a plant. The first author proposed the 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, which is called “fictitious reference iterative tuning” (which is also abbreviated to FRIT). Here, we develop FRIT for the tuning of the feedforward controller in 2DOF control system. We introduce a new cost function consisting of the fictitious reference and the actual data for the purpose of that the required computation can be done by the least squares method (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 cost function is quadratically-parameterized, it is possible to analyze how far the obtained parameter is apart from the desired one. For this purpose, we derive the pre-filter to be applied to the actual data. In addition, we also show that our proposed method is applicable for the case in which the initial experiment is performed in the one-degree-of-freedom control system. Finally, we illustrate an example in order to show the utility and the validity of our proposed method.