## 1 Introduction  
This paper presents the use of the fictitious reference iterative tuning (FRIT) method for tuning of a two-degree-of-freedom (2 DOF) proportional-integral/proportional (PI-P) controller in a new speed control system for a permanent magnet synchronous motor (PMSM) using a field-programmable gate array (FPGA) for a high-frequency SiC MOSFET (metal oxide semiconductor field-effect transistor) inverter. High-switching frequency operation can be achieved using the SiC MOSFET because of its superior material characteristics [1; 2; 3; 4]. Variable-frequency drives (VFDs) can be operated efficiently at carrier frequencies in the 50 to 200 kHz range when using this device [5]. PI-P controller is feedback-type (FB-type) 2 DOF control system. The 2 DOF PI-P controller offers a powerful way to make both the set-point response and the disturbance response practically optimal [6]. FPGA-based digital hardware control is used to ensure fast processing operation for the high-frequency switching of the SiC MOSFET inverter. FPGA has advantages, such as high-speed processing and rewritablility. High-speed calculation is obtained using the ability of hardware processing. The synthesis process, the generate programming file process and the configure target device process must be performed before downloading the programming file to an FPGA, so that it is not effective nor efficient to tune PI-P controller parameters only to determine the value of controller parameters by trial and error. It takes several times of tuning the PI-P controller parameters. To overcome this problem, the FRIT method is used to tune PI-P controller parameters, which require one-shot experimental data, so tuning PI-P controller parameters is effective and efficient. A high-performance motor control system requires a high-responsivity system and immediate recovery to the steady-state condition when a motor under load is affected by any disturbance [7]. To achieve this aim, a high-frequency pulse-width modulation (PWM) method is needed when using the SiC MOSFET inverter. High-responsivity and optimal disturbance rejection can be achieved using the 2 DOF control system with high-frequency PWM. There are many advantages to using high- frequency PWM (in the 50 to 100 kHz range) in motor drive applications, including high motor efficiency, fast control response, reduced motor torque ripple, near-ideal sinusoidal motor current waveforms, reduced filter sizes and lower filter costs [5]. Recently, FRIT, which can be used to obtain optimal controller parameters using the input and output data from one-shot experimental data, has been studied by several researchers [8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. The data are used to determine the plant dynamics without knowing the mathematical model of the plant [13]. FRIT is used to obtain optimal controller parameters by optimizing a performance index that consists of the squared error between reference and experimental outputs. Many published studies that have considered direct control parameter tuning methods, such as iterative feedback tuning (IFT), virtual reference iterative tuning (VRFT) and fictitious reference iterative tuning (FRIT). [PERSON] [18] developed iterative feedback tuning. This requires signal and gradient quantities to achieve optimal performance. It also performs many experiments to update the controller parameters to minimize the performance index, so that it is not effective nor efficient to tune controller parameters, because it takes several times and costs. [PERSON] et al. [19] proposed virtual reference feedback tuning (VRFT); [PERSON] et al. [20] proposed 2 DOF VRFT; [PERSON] et al. [21] proposed a feedforward formulation of the VRFT method based on a 2 DOF control configuration; and [PERSON] et al. [22] proposed a VRFT method for iterative controller design and fine tuning. VRFT uses a set of measured input/output data for the design of a controller with the desired structure, but without restrictions on data generation.