FPGA-Based High-Frequency Voltage Injection Sensorless Control with Novel Rotor Position Estimation Extraction for Permanent Magnet Synchronous Motor

Abstract

This study developed a realization of sensorless control for a permanent magnet synchronous motor (PMSM) using a field-programmable gate array (FPGA). Both position and speed were estimated using a high-frequency (HF) injection scheme. Accurate estimation is essential to ensure the proper functioning of sensorless motor control. To improve the estimation accuracy of the rotor position and reduce the motor speed ripple found in conventional methods, a new extraction strategy for estimating the rotor position and motor speed is proposed. First, signal modulation compensation was applied to expand the information of the error function in order to provide more accurate data to the tracking loop system for rotor position extraction. Second, to minimize the motor speed ripple caused by the HF injection, motor speed estimation was performed after obtaining the rotor position information using a differential equation with a low-pass filter (LPF) to avoid the direct effect of the injected signal. Verified experimentally, the results showed that the rotor position error did not exceed 10 el.deg, so these methods effectively reduce the rotor position estimation error by about 30%, along with the motor speed ripple. Therefore, better performance in sensorless PMSM control can be achieved in motor control applications.

1. Introduction

Permanent magnet synchronous motors (PMSMs) have been increasingly used in many industrial applications in recent years due advantages such as high efficiency, high power density and high reliability. One of them is in the field of electric vehicles, with all the advantages that make for a promising and reliable motor drive system [1]. However, the reliability of the PMSM also depends significantly on accurate rotor position information to achieve an optimal motor drive system [2]. In high performance PMSM drive systems, position sensors are required to obtain rotor position information. Typically, a mechanical position sensor is installed on the rotor shaft of the motor to detect the rotor position. However, these position sensors are often undesirable in industrial applications due to several disadvantages they impose on drive systems [2,3]. In addition to increasing cost, the mechanical sensor is difficult to mount on the shaft of the PMSM, requires additional wiring, and increases volume and weight. Therefore, it is desirable to eliminate these position sensors, and methods designed for this purpose are commonly referred to as sensorless motor control. Hence, sensorless motor control for PMSM drives has attracted attention in recent decades and has been extensively developed and achieved good performance [4].

Sensorless techniques in general can be categorized based on whether the motor is operating at medium to high speeds or at low speeds. The medium to high-speed sensorless technique, which relies on the electromotive force (EMF) model to estimate rotor position, can be successfully achieved [5]. In [6], an improvement in rotor position estimation using back-EMF information is presented. In this study, a fuzzy rule-based computational system is applied to the rotor position extraction process using an observer model. The rotor position estimation results show smoother performance, thereby reducing system chatter and observation errors. On the other hand, the use of a traditional phase lock loop (PLL) in back-EMF observer systems generally cannot be used when the motor rotation direction is switched from forward to reverse. Consequently, the tangent function was implemented to replace the PLL concept. In addition, compensation systems represent an attractive approach to improve the extraction of rotor position information. The predictive control model system is designed as a computational method that provides compensation to achieve robust performance and fast response times in rotor position estimation [7]. Therefore, the performance of back-EMF observer models, which are commonly used to detect rotor position information, can be improved. Furthermore, improvements in observer models have also continuously focused on reducing errors during observation, overcoming the limitations of trigonometric functions in determining rotor position, and increasing the efficiency of filter usage in the observation process to achieve superior sensorless PMSM control systems [8,9,10]. Unfortunately, at low speed, the back-EMF is too small to be observed. It is not enough to estimate the rotor position. Various techniques for observing the rotor position based on the salient pole effect or salient pole saturation effect in motors have been proposed [11,12] to address the challenges associated with the indistinct back-EMF in the low-speed region, typically below 10% of the nominal speed [12]. Among these techniques, the HF injection signal is the most widely used. The HF injection-based salient pole tracking method is independent of back-EMF and motor parameter information, enabling more accurate estimation in the low-speed region, even down to zero speed [13]. In [14], a saliency-based method for rotor position detection in PMSM is presented. This method utilizes inductance changes caused by HF injection as a parameter to obtain rotor position information. In general, the HF injection method can be categorized based on the types of injected signals into three main groups: square wave voltage injection [15,16], rotating sinusoidal voltage injection [17,18], and pulsating sinusoidal voltage injection [19,20]. Furthermore, considering the used extraction of rotor position information, these methods can be further classified into HF voltage injection in the stationary α–β reference frame [21] and HF voltage injection in the rotating d–q reference frame [22]. The improvement in rotor position estimation in the HF injection method was discussed in [23], where the use of oversampling in the motor current vector to obtain current signal information for rotor position observation through a PLL concept was explained. The estimation error of the rotor position was reported to be decreased in sensorless motor control implementation, providing the established correct control process is followed [13,23]. However, the scheme strongly depends on the digital-to-analog conversion of the current measurement, which has some noise in the low-speed operation of the motor. Moreover, the effect of high frequency on the motor current during the oversampling process needs to be considered in the application of sensorless motor control to maintain good control performance. In addition, to achieve higher precision control of sensorless PMSMs using HF injection, parallel processing with FPGA has been adopted to replace digital signal processing systems [24,25], thereby improving the real-time performance of sensorless motor control implementation. However, this study does not discuss the ripple that can occur in the extraction system, which can affect the acquisition of rotor position and motor speed estimation results in the HF injection method. Nevertheless, it has been reported that this approach improves control accuracy and addresses the challenges of low-speed operation in tracking the magnetic saliency by signals modulated to extract the rotor position information.

The aforementioned studies demonstrate that the accuracy of rotor position estimation plays a crucial role in the successful implementation of sensorless PMSM control. Therefore, an effective strategy for rotor position estimation methods is essential to enhance the overall performance of the control process, particularly in actual motor control applications. In this study, the estimation of rotor position and motor speed are extracted using a new strategy in the HF injection sensorless scheme. Compensation coefficients are applied to expand the error information used by the tracking loop control system, where the modulation function is designed to obtain accurate error information during observation, thereby achieving a more accurate estimation of rotor position compared to conventional methods. In addition, it is also necessary to consider the ripple that occurs in the motor speed estimation results when implementing PMSM sensorless control. The reduction of the motor speed ripple in sensorless motor control could be achieved by applying an LPF to the differential equation in order to obtain the motor speed, resulting in a smoother estimated motor speed. Thus, the reduction of the speed estimation ripple will provide more accurate speed information for processing in the control system to achieve better realization of sensorless control performance. Therefore, the main contributions of this study are as follows:

• Implementation of a new strategy for extracting rotor position information using compensated signal modulation in sensorless PMSM by an HF injection scheme.
• Implementation of a differential equation with a digital filter to obtain smooth motor speed estimation in sensorless control systems.
• Enhancement of rotor position accuracy and reduced motor speed ripple in sensorless PMSM control applications, facilitating the development of correct motor control designs.
• Realization of hardware implementation for sensorless PMSM control using a fast-processing system by FPGA.

The rest of this paper is organized as follows. In Section 2, the mathematical model and analysis of the new strategy for extracting the rotor position information in the HF injection method for the sensorless PMSM are explained. The architecture of FPGA as the hardware implementation for the enhancement in rotor position and speed estimation is presented in Section 3. Section 4 presents the experimental results of the HF injection method, which demonstrate the effectiveness of the proposed sensorless control strategy. Finally, conclusions are presented in Section 5.

2. Analysis of Proposed Sensorless PMSM Control in HF Injection Scheme

2.1. Mathematical Model for HF Injection Sensorless PMSM

The voltage equations for a PMSM can be expressed in d–q reference frames, which are essential for analysis and control of the motor dynamics. The transformation of the three-phase voltages into the d–q reference frames simplifies the mathematical modeling and facilitates the implementation of vector control. These equations are as follows [12]:

$$\left[\begin{array}{c}{v}_d\\ v_q\end{array}\right]=\left[\begin{array}{cc}R& -{\omega }_r{L}_q\\ {\omega }_r{L}_d& R\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\left[\begin{array}{cc}{L}_d& 0\\ 0& L_q\end{array}\right] p\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\left[\begin{array}{c}0\\ {\omega }_r{\phi }_f\end{array}\right]$$

(1)

where $v_d, v_q, i_d, i_q, R, L_d, L_q$ are the stator voltage in the d–q axis, the current voltage in the d–q axis, and the resistance of the motor and the inductances in d–q axis, respectively; meanwhile p,${ \omega }_r, {\phi }_f$ are the differential operator, rotational speed of the motor and the permanent linkage of the motor, respectively.

At low speeds, the back EMF and cross-coupling effects as correlated in (1) can be neglected. Consequently, the equation for the PMSM can be simplified as follows:

$$\left[\begin{array}{c}{v}_d\\ v_q\end{array}\right]=\left[\begin{array}{cc}R& 0\\ 0& R\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\left[\begin{array}{cc}{L}_d& 0\\ 0& L_q\end{array}\right] p\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]$$

(2)

In this study, the rotational frequency of the motor itself is smaller than the frequency of the injected signal. Therefore, the PMSM equation is equivalent to the pure inductance model and can be expressed as follows:

$$\left[\begin{array}{c}{v}_{dh}\\ v_{qh}\end{array}\right]=\left[\begin{array}{cc}{L}_d& 0\\ 0& L_q\end{array}\right] p\left[\begin{array}{c}{i}_{dh}\\ i_{qh}\end{array}\right]$$

(3)

where $v_{dh}, v_{qh}, i_{dh}, i_{qh}$ are the stator voltage in the d–q axis of high frequency and the current voltage in the d–q axis of high frequency, respectively.

When an HF signal is injected into the real d–q axis of the stator, the resulting current response can be analyzed to estimate the position of the rotor. The process involves comparing the response in the real d–q reference frame with the estimated $\widehat{d}–\widehat{q}$ reference frame. The difference between these frames indicates the rotor position error, which is to converge to zero in order to acquire the accurate rotor position of the motor. Figure 1 illustrates the relationship between the estimated $\widehat{d}–\widehat{q}$ rotating reference frame and the actual d–q two-phase rotating reference frame. Here, $\theta , \widehat{\theta }$, and $\Delta \theta$ represent the actual rotor position, the estimated rotor position, and the difference between the actual rotor position and the estimated rotor position, respectively. According to Figure 1, the differential equation for the current response under the estimated d–q two-phase rotating reference frame in HF injection can be calculated by utilizing rotational matrix, referred to as T^R in the following:

$$T^R=\left[\begin{array}{cc}\mathit{cos}(\Delta \theta )& sin(\Delta \theta )\\ -sin(\Delta \theta )& cos(\Delta \theta )\end{array}\right]$$

(4)

$$p\left[\begin{array}{c}{\widehat{i}}_{dh}\\ {\widehat{i}}_{qh} \end{array}\right]=T^{R^{-1}}p\left[\begin{array}{c}{i}_{dh}\\ i_{qh}\end{array}\right]$$

(5)

where $T^R, {\widehat{i}}_{dh}, {\widehat{i}}_{qh}$ are the rotation transformation matrix and the current voltage in the estimated d–q axis of high frequency, respectively. Furthermore, when an HF sinusoidal pulsating voltage is injected into the estimated $\widehat{d}$-axis, the voltage equation in the $\widehat{d}–\widehat{q}$ rotating reference frame can be expressed as follows:

$$F^i=\left[\begin{array}{c}{\widehat{v}}_{dh}\\ {\widehat{v}}_{qh}\end{array}\right]=u_{inj} \left[\begin{array}{c}cos\left({\omega }_{inj}t\right)\\ 0\end{array}\right]$$

(6)

where $u_{inj}$ and ${\omega }_{inj}$ are the amplitude and frequency of the injected voltage, respectively. According to (6) and the difference between actual rotor position and estimated rotor position, the voltage in the d–q axis rotating frame after injection of HF can be rewritten as the following equation:

$$\left[\begin{array}{c}{v}_{dh}\\ v_{qh}\end{array}\right]= \left(F^i\right) T^R=u_{inj} \left[\begin{array}{c}\mathit{cos}\left(\Delta \theta \right)cos\left({\omega }_{inj}t\right)\\ -\mathit{sin}\left(\Delta \theta \right)cos\left({\omega }_{inj}t\right)\end{array}\right]$$

(7)

By combining (3) and (7), the d–q axis current response in HF can be seen (8). The current response in the d–q axis after injection of HF, related to the current components in the estimated $\widehat{d}–\widehat{q}$ axis in (9), can be obtained by substituting (3) into (5).

$$\left\{\begin{array}{c}{i}_{dh}=\int {\displaystyle \frac{F^i cos\Delta \theta }{L_d}} dt={\displaystyle \frac{u_{inj}sin\left({\omega }_{inj}t\right)cos\Delta \theta }{L_d{\omega }_{inj}}} \\ i_{qh}=\int -{\displaystyle \frac{F^i sin\Delta \theta }{L_q}} dt=-{\displaystyle \frac{u_{inj}sin\left({\omega }_{inj}t\right)sin\Delta \theta }{L_q{\omega }_{inj}}}\end{array}\right.$$

(8)

$$p\left[\begin{array}{c}{\widehat{i}}_{dh}\\ {\widehat{i}}_{qh}\end{array}\right]= T^{R^{-1}}\left[\begin{array}{cc}{\displaystyle \frac{1}{L_d}}& 0\\ 0& {\displaystyle \frac{1}{L_q}}\end{array}\right]\left[\begin{array}{c}{v}_{dh}\\ v_{qh}\end{array}\right]$$

(9)

According to the coordinate axis of the injected HF signal, the relationship between current and voltage in the estimated $\widehat{d}–\widehat{q}$ axis rotating reference frame can be obtained. By substituting (7) into (9), when the HF is injected in the $\widehat{d}$-axis, the position information can be extracted from the induced current signal in the estimated rotating reference frame, as shown in the following equation:

$$\left\{\begin{array}{c}\left[\begin{array}{c}{\widehat{i}}_{dh}\\ {\widehat{i}}_{qh}\end{array}\right]={\displaystyle \frac{u_{inj}\mathit{sin}{(\omega }_{inj}t)}{{\omega }_{inj}{L}_d{L}_q}} \left[\begin{array}{c}{L}_q {cos}^2\Delta \theta +L_d {sin}^2\Delta \theta \\ {\displaystyle \frac{\mathit{sin}\left(2\Delta \theta \right)}{2}} \left(L_q-L_d \right)\end{array}\right]\\ {\widehat{i}}_{dh}={(k}_1+k_2 cos(2\Delta \theta ))sin({\omega }_{inj}t) \\ {\widehat{i}}_{qh}=k_2\mathit{sin}\left(2\Delta \theta \right)\mathit{sin}\left({\omega }_{inj}t\right) \end{array}\right.$$

(10)

where $k_1$ and $k_2$ are expressed in the equation below:

$$\left\{\begin{array}{c}{k}_1={\displaystyle \frac{u_{inj}\left(L_q+L_d \right)}{2{\omega }_{inj}{L}_d{L}_q}}\\ k_2={\displaystyle \frac{u_{inj}\left(L_q-L_d \right)}{2{\omega }_{inj}{L}_d{L}_q}}\end{array}\right.$$

(11)

The rotor position estimation error $\Delta \theta$ is included in the estimated HF components’ $\widehat{d}–\widehat{q}$ axis, as shown in (10). Specific modulation techniques can be used to extract the information for $\Delta \theta$. It can be seen that the estimated rotor position can be equal to the actual rotor position when $\Delta \theta$ is adjusted to zero by an appropriate closed-loop control system. A digital filter, including a band pass filter (BPF) and a low pass filter (LPF), is used in the extraction system. First, the BPF is used to maintain the signal amplitude containing the rotor position information during high frequency signal injection. Secondly, the LPF is applied to the modulated signal to obtain the $\Delta \theta$ function for the tracking loop for the estimation system. Finally, the HF injection sensorless method can be effectively achieved to detect the rotor position.

2.2. Proposed Extraction of Rotor Position Estimation in HF Injection Scheme

Based on the HF pulsating sinusoidal voltage injection principle, the $\Delta \theta$ can be extracted to obtain rotor position information by detecting the $\widehat{q}$-axis current and performing appropriate processing on the current signal with modulating signal $\sin \left({\omega }_{\mathit{inj}}t\right)$. Hence, the rotor position information contained in the amplitude of the motor current signal can be obtained as long as the error in $\Delta \theta$ converges to zero. However, the amplitude of signal error in the $\widehat{q}$-axis current is reduced by half due to the multiplication by the modulated signal, so the compensation signal is applied to expand the information for the error signal. Conventionally, as shown in Figure 2a, after the multiplier, and through a low pass filter, the function of $\Delta \theta$ can be expressed as follows,

$$f\Delta \theta =LPF \left({\widehat{i}}_{qh} \mathit{sin}\left({\omega }_{inj}t\right)\right)={\displaystyle \frac{1}{2}}{k}_2 \mathit{sin}\left(2\Delta \theta \right)$$

(12)

In (12), it is important to note that the amplitude of the error in the modulated signal is only half, and the linearization of the sinusoidal term in ∆θ is required. Therefore, signal compensation is proposed in the implementation of the rotor position information extraction system to expand the ∆θ information, so that it can be used to obtain a more accurate rotor position estimation. An outline of the proposed rotor position extraction scheme is shown in Figure 2b. An additional signal is applied to generate a compensation term, and the linearization of the sinusoidal injection is considered by the coefficient $\left(l\right)$ for the scaling ratio of the ∆θ function. It is important to set the optimum value of $\left(l\right)$, based on the experiment, as a higher value makes the sensorless control response unstable, because the error value is high and because of the ripple contained in the information for ∆θ. Therefore, it is necessary to adjust this value to achieve good system performance. Thus, the expansion of ∆θ with signal compensation can be obtained, so that the error information is more clearly utilized in the tracking loop control systems to estimate the rotor position of the motor. In detail, the function of ∆θ with compensation term ${(e}^c)$ can be determined by the following equation:

$$\left\{\begin{array}{c}f\Delta \theta =LPF\left[{\widehat{i}}_{qh}\left(\mathit{sin}\left({\omega }_{inj}t\right)\left(e^c\right)\right)\right]\\ e^c=l {\displaystyle \frac{1}{k_2}}=l {\displaystyle \frac{2{\omega }_{inj}{L}_d{L}_q}{u_{inj}\left(L_q-L_d \right)}} \end{array}\right.$$

(13)

After obtaining $\Delta \theta$, it can be used in the tracking loop control system to acquire the rotor position information. The PLL system is adopted for rotor position estimation in the tracking loop control, utilizing proportional and integral coefficients. The $\Delta \theta$ is used as input to extract the rotor position and speed of the motor. Typically, the estimation of rotor position is obtained by directly integrating the estimation of rotor omega, which is the output of the system tracking loop, as shown in Figure 3a. However, the ripple in the estimation of angular motor speed still remains, which is caused by the noise from the high-frequency signal injection in the sensorless HF injection system [16]. In contrast to conventional methods, to minimize the ripple, in (14) the proportional and integral coefficients of the PLL for the rotor position estimation tracking loop are designed to obtain the rotor position information earlier, as shown in Figure 3b. Then, a differential equation is applied to obtain the rotor omega information. Thus, the equations for estimating both the rotor position and the rotor omega can be expressed as follows:

$$\widehat{\theta }=\int \left(K_P\Delta \theta \left(t\right)+\int K_I\Delta \theta \left(t\right) dt \right)dt$$

(14)

$$\left\{\begin{array}{c}{K}_P={\displaystyle \frac{f_C}{2}} \sqrt{{cos}^2\left({\varnothing }_m\right)} \\ K_I={\displaystyle \frac{{f_C}^2}{2}} {\displaystyle \frac{\mathit{sin}\left({\varnothing }_m\right)\sqrt{{cos}^2\left({\varnothing }_m\right)}}{\mathit{cos}\left({\varnothing }_m\right)}}\end{array}\right.$$

(15)

$$\widehat{\omega }=LPF \left({\displaystyle \frac{\widehat{\theta }\left(k\right)-\widehat{\theta }\left(k-1\right) }{dt}}\right)$$

(16)

where ${\widehat{\theta }, \widehat{\omega } , K}_P, K_I, f_c$, and ${\varnothing }_{\mathrm{m}}$ are the estimation of rotor position, estimation of rotor omega, proportional coefficient, integral coefficient, cut off frequency of extraction filter, and angular margin, respectively.

Motor speed information is essential in motor control systems. In particular, in sensorless motor control schemes, establishing accurate motor speed information as feedback in the control process is critical to achieving high performance sensorless motor control. This study demonstrates a reduction in motor speed ripple, which provides more accurate speed information compared to conventional methods. In general, motor speed estimation is obtained directly in the tracking loop control system using PLL, where high-frequency injection effects are still present. Unlike conventional methods, the proposed tracking loop control system includes an LPF, and the motor speed estimation is derived by the differential equation of the rotor position estimation, which reduces the motor speed ripple, as shown in Figure 4. The results show that ripple reduction is achievable with the proposed method, making it effective in minimizing the ripple in the motor speed estimation compared to conventional methods.

3. FPGA-Based System Implementation

In this section, the implementation of FPGA for proposed sensorless control for the PMSM is discussed. FPGA is chosen because of its ability to provide fast executing systems suitable for promotion of the rotor position estimation, which requires fast processing and high accuracy in real-time motor control.

In this study, the development of PMSM sensorless control systems consists of two parts: vector control and extraction of rotor position estimation. The implementation of rotor position estimation consists of two steps, the modulated signal containing the compensation signal. and the tracking loop to acquire the rotor position information. The phase currents are converted to d–q axis currents to implement PMSM vector control. In addition to the current signal, rotor position information is also required in the d–q transform system. In this system, the rotor position information is obtained from the estimation result by extracting the current signal in the d–q transform component which contains the rotor position information due to the HF signal injection. Therefore, fast processing is essential to obtain accurate rotor position information in real-time. Figure 5 presents the hardware architecture developed for vector control used for sensorless motor control with the HF injection signal.

Figure 6 shows the hardware architecture developed for rotor position and motor speed estimation. Speed and position information is typically derived from an incremental encoder in industrial drive systems. Here, these measured data are only used to validate the proposed estimation method. In this study, this information is estimated using the high-frequency effect through a modulated signal and applied tracking loop control systems, used to obtain the rotor position and speed information of the motor. In detail, the specification of the FPGA used for the implementation of the entirety of the proposed systems is presented in

Table 1. The specification of FPGA.

Feature	Specification
Product Variant	Arty Z7-20 Zynq-7000 SoC Development Board
Zynq Processor	650 MHz dual-core Cortex-A9 Processor
Memory	DDR3 memory controller with 8 DMA channels
Zynq Part	XC7Z020-1CLG-400
Look-up Tables (LUTs)	53.200
Flip-Flops	106.400
Block RAM	630 KB
Digital Signal Processing (DSP) Slices	220
Clock Management Tiles	4

.

4. Experimental Results

To evaluate and verify the proposed sensorless control scheme on a prototype motor control with a 400 W IPMSM, the experimental setup is shown in Figure 7. The system mainly consists of an inverter module, a SoC-FPGA for the embedded sensorless control system, a PC used only for sending speed commands and controller gain to the FPGA, and a Hi-CORDER for displaying the system results. The electrical parameters of the PMSM are shown in

Table 2. Motor parameters.

Parameter	Value
Rated Power (W)	400
Rated Voltage (V)	163
Rated Current (A)	1.7
Frequency (Hz)	87.5
Rated Speed (min−1)	1750
Poles	6
Motor Resistance (Ω)	2.247
d-Axis Inductance (mH)	22.32
q-Axis Inductance (mH)	32.50

.

In the experimental setup, the frequency of the motor control system is set to 50 kHz. For rotor position estimation, the magnitude of the injected sinusoidal signal voltage is 5 V with a frequency of 1 kHz. The motor speed is set to 100 min⁻¹. Figure 8a shows the experimental waveform for rotor position estimation based on the conventional HF pulsating sinusoidal voltage injection method, while Figure 8b shows the experimental waveform of rotor position estimation using the proposed HF pulsating sinusoidal voltage injection method.

The experimental waveforms show that both HF injection methods can effectively estimate the rotor position. The steady-state error between the measured rotor position and the estimated rotor position of the conventional HF pulsating sinusoidal voltage injection method is about 0.22 rad, while the steady-state error of the proposed method is about 0.15 rad. Based on these results, the proposed system improves the estimation accuracy and demonstrates better performance in reducing the estimation error.

Further experiments were conducted to verify that the system could function properly regardless of the direction of the motor. Figure 9 and Figure 10 show the experimental waveforms of the rotor position when the motor direction suddenly changes from 100 min⁻¹ to −100 min⁻¹ and vice versa, by the conventional HF pulsating sinusoidal voltage injection method and the proposed method, respectively. The experimental waveforms show that both HF injection methods are effective in observing rotor position information during sudden forward to reverse direction changes. Ignoring the transient control response, in the steady state, the conventional HF pulsating sinusoidal voltage injection method shows an estimated rotor position error of 0.29 rad. In contrast, the proposed method has an estimated rotor position error of 0.19 rad, indicating a smaller angular observation error compared to the conventional method. In addition, both methods also effectively track the rotor position during sudden changes in reverse to forward direction from −100 min⁻¹ to 100 min⁻¹. The proposed method exhibits an estimated rotor position error of 0.15 rad, which is significantly reduced from the 0.27 rad error observed in the conventional method.

The performance of the proposed sensorless motor control system is also tested under loaded conditions in the following experiments. As shown in Figure 11a, the system effectively estimates the rotor position when a load is added. Based on the results, the rotor position estimation error does not exceed 0.19 rad under a load of 0.3 Nm. Furthermore, the response of the system to a sudden increase in load was observed, and the results are shown in Figure 11b, which illustrates the relationship between the rotor position estimation error and the addition of the sudden load. This is expected to provide an overview of the optimal load application in sensorless motor control design.

In addition, the elimination of the use of a speed sensor to overcome drawbacks such as difficulty in mounting, complex wiring and increasing volume in the implementation of the PMSM motor drive system, has been addressed by the proposed sensorless motor control scheme. In this study, a new concept is explained for the extraction of the information for rotor position and motor speed by compensating through the applied coefficient value to expand the error information in the tracking loop control system, in order to obtain a more accurate estimated rotor position than in the conventional method. Furthermore, the reduction in estimated motor speed ripple is also achieved in the realization of sensorless motor control by applying LPF in the differential equation to obtain the estimated motor speed. To verify the realization of the proposed sensorless motor control design, a comparison between the sensored system and the sensorless systems was performed to demonstrate the performance of the systems. Based on the results in Figure 12, the proposed system successfully achieved sensorless motor control by accurately estimating the rotor position and motor speed, which were identical to the rotor position and speed information by measurement. In addition, to evaluate the transient response of the system, a step response test was performed by increasing the motor speed from 120 min⁻¹ to 150 min⁻¹. The test results show that the proposed sensorless system can reach the setpoint with a rise time of 0.07s and a settling time of 0.15s under step response, which were identical to the results in sensored systems, indicating that the system demonstrates small error and good control response in both transient and steady state. Thus, the proposed system promises high performance with fast time computation for the system using FPGA in the realization of sensorless motor control. A detailed comparison of the step response between the sensored and sensorless systems is shown in

Table 3. Comparison control response of sensored and sensorless motor control.

Parameter	Sensored	Proposed Sensorless
Rise Time (s)	0.08	0.07
Settling Time (s)	0.13	0.15
Overshoot (%)	<3	<5
Undershoot (%)	none	none

. Finally, the proposed system demonstrates its viability for real implementation in motor control applications, particularly in sensorless PMSM motor drive systems. To further extend its applicability, exploring the feasibility of implementing the control scheme on a low-cost, compact hardware platform could also make this system more suitable for a wider range of practical industrial applications.

5. Conclusions

Position and speed sensorless control technique for a PMSM using an HF pulsating sinusoidal voltage injection scheme was developed and implemented in FPGA systems. In this study, a new strategy for extracting the rotor position and speed estimation was applied to improve the accuracy of the rotor position estimation and to reduce the ripple of the motor speed estimation.

The proposed system provides an extended error function in the modulated current signal containing rotor position information by applied coefficient value in the compensation signal modulation, in order to make the error function information more accurate in the tracking loop system for estimating rotor position. The proposed extraction systems for the HF injection scheme are effective and can improve the accuracy of the estimation result. It is verified by experiment that there is a reduction in estimation error in the rotor position. The results show that the rotor position estimation error does not exceed 0.19 rad in several variations of tests conducted with loaded 0.3 Nm.

In addition, the proposed system obtains the estimated motor speed using a differential equation with an LPF to reduce the motor speed ripple. This ripple reduction method improves the estimation of motor speed in sensorless motor control, providing more stability and avoiding fluctuations in motor speed information in a feedback system for the control process, making it more suitable for applications requiring precise sensorless motor control.

According to the results, the proposed system demonstrates smaller error and ripple than conventional systems, both verified by experiment, making the sensorless PMSM control performance of this method better than that of the previous method. In future work, sensorless control at a wide speed range should be considered, to realize industrial motor control for EV application with a reliable compact hardware platform.