Comparison of VRFT, NCbT and VRFT with spline fitting

In order to design an optimal controller for a feedback system with an unknown plant, it is a common way to identify the plant by performing plural experiments. On the contrary, certain methods used to design a controller using the data from one-time experiments have been proposed. Such methods include Virtual Reference Feedback Tuning (VRFT) and Noniterative Correlation-based Tuning (NCbT). These methods are expected to reduce the design cost. However, VRFT cannot be used to design an optimal controller from a data with noise and NCbT is limited in that there is no correlation of a reference signal with noise. An actual plant often has higher harmonics of an input signal as noise. Such noises are correlated with a reference signal. Therefore, a controller design must be able to deal with various kinds of noises. This paper proposes a method of applying spline fitting to VRFT. To verify the effectiveness of this technique, we compared the response of the proposed method with that of VRFT and NCbT on a simulator. Then, we designed each controller using VRFT, NCbT, and VRFT+SF, respectively, by providing white Gaussian noise and periodic noise. As a result, this paper shows that the proposed method surpasses the original VRFT and NCbT based on overall experimental results.