FRIT (Fictitious Reference Iterative Tuning) directly tunes control parameters from closed-loop input and output measurements without using mathematical models of the controlled plant. The pre-filter is used for initial input and output measurements for controller parameter tuning, and makes the data-driven cost function approximate to the original cost function as close as possible. This paper gives a design method for an optimal pre-filter in FRIT using closed-loop step response data by

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... ing the method for VRFT. The paper shows that both the data-driven cost function and the original one have the same second order Taylor expansion with extended parameter descriptions. Finally, a numerical example shows the effectiveness of the proposed method.