## 1 Introduction
It is based on the idea of constructing a virtual reference signal and on model reference control. The performance index is minimized using input data, and pre-filtering in VRFT requires the desired closed loop response and its sensitivity function. Both FRIT and VRFT have similar ideas and reference signals, where the fictitious reference signal is for FRIT and the virtual reference signal is for VRFT. Both FRIT and VRFT have similar performance index formulas and purposes to obtain the optimal controller parameter by minimizing the performance index using input and output data taken from a one-shot experiment. The performance index of VRFT focuses on the input, while the performance index of FRIT focuses on the output, so that FRIT is more understandable than VRFT [13]. The FRIT method is easier to use in this research than the VRFT method because the performance index used focuses on the output, and researchers give more attention to the FRIT method than the VRFT method to design the controller parameters. VRFT and FRIT only need one-shot experimental data to obtain the optimal controller parameters, so VRFT and FRIT are more effective or efficient than IFT. The FRIT method is easier to implement than the VRFT method to obtain the controller parameter of PMSM speed control. The step reference model and disturbance reference model can be formed following the output data in the FRIT method, but these reference model cannot be formed following the input data in the VRFT method like the input data of the PMSM speed control. The FRIT method is very useful to implement to obtain the optimal controller parameter of PMSM speed control. [PERSON] et al. [8; 9] proposed FRIT; [PERSON] et al. [10] proposed an online-type controller parameter tuning method based on modification of the standard FRIT; and [PERSON] et al. [11] proposed the FRIT-particle swarm optimization (FRIT-PSO) method to design proportional-integral-derivative (PID) controllers for control systems. These researchers studied tuning methods using FRIT in a one-degree-of-freedom control system. [PERSON] et al. [12; 13; 14; 15] proposed the use of the FRIT method for tuning of the feedforward controller in a 2 DOF control system. The FRIT method is now the focus of research for many control systems researchers. However, these researchers studied tuning methods using FRIT that were without a disturbance response. Tuned PID controllers are not optimal when a disturbance is applied to the control system. The advantages of a 2 DOF method cannot be found in papers where the set-point and the disturbance rejection are practically optimal. The present study proposes the use of a disturbance reference model for the ideal response in addition to the step reference model in the FRIT method. [PERSON] et al. [16] proposed the use of the FRIT method for tuning of a proportional-integral (PI) controller in a speed control system for a PMSM using an FPGA for a high-frequency SiC MOSFET inverter. [PERSON] [17] proposed a direct PID gains method for speed control of a DC motor using the input-output data generated by the disturbance response. This paper focused on step-type disturbances to generate the initial one-shot input and output data for PID gain tuning. [PERSON] [23] proposed a 2 DOF design for motor drives. This paper used the mathematical model of the plant and introduced some definitions and lemmas to design the controller parameters. However, it is not effective and efficient to tune controller parameters, because it takes several times, and it needs some procedures to tune the controller parameters. [PERSON] et al. [24] proposed the use of FPGA-based digital hardware control for PMSM speed control. However, the speed response presented in this paper is without disturbance response. This paper proposes the use of the FRIT method to obtain optimal PI-P controller parameters in a 2 DOF control system for speed control of a PMSM using a SiC MOSFET inverter. The step reference and disturbance reference models are used to produce the ideal response in the FRIT method.