Field-oriented control (FOC) is a well-known method for three-phase motor control. In the three-phase PMSM control with a position sensor, as shown in Figure 1, the position signal of the rotor is used to calculate the speed of the motor and then provide feedback for comparison with the reference speed.

Figure 1: 
Field-oriented control block diagram with a sensor PMSM

Normally, the SVPWM block in the FOC operates with continuous space-vector pulse-width modulation (CSVPWM). CSVPWM is shown in Figure 2. CSVPWM has a power loss problem owing to its high switching loss. Hence, discontinuous pulse-width modulation (DPWM) was used instead of CSVPWM. Although DPWM produces more harmonics in the output current than CSVPWM, DPWM can significantly reduce the switching loss of a three-phase inverter. Switching loss is the amount of power loss in semiconductor switches when the inverter operates at a high frequency. This phenomenon cannot be avoided by reducing the size of the device or by reducing harmonics. Therefore, the device must operate under high-frequency conditions.

Figure 2: 
Continuous SVPWM

Fundamentally, the DPWM operation for the three-phase inverter control of PMSMs is the creation of either one of two ineffective voltage vectors, namely, the zero vector or the seventh ineffective voltage vector within a single switching cycle. This is in contrast to CSVPWM, which generates both ineffective voltage vectors during each switching cycle. With this strategy, the control system can reduce the ineffective voltage vectors and the number of switchings. The two typical variants of DPWM in the PMSM-controlled three-phase inverter introduced in this study are DPWMMIN and DPWMMAX. Graphical representations of the DPWMMIN and DPWMMAX waveforms are shown in Figure 3.

Figure 3: 
DPWM: (a) DPWMMAX and (b) DPWMMIN

In 60-degree discontinuous modulation, if the zero-ineffective voltage vector is generated across all six sectors and the reference voltage is clamped at the lower part of the DC bus, this type is called DPWMMIN. Conversely, when only the seventh ineffective voltage vector is created and the reference voltage is clamped on the upper DC bus, it is called DPWMMAX. Because of the clamping to the lower or upper DC bus, the output voltage of each phase is clamped at zero of the DC bus sequentially for DPWMMIN and clamped at the maximum of the DC bus for DPWMMAX. During the clamped output voltage period, the switches at each phase remain in turn-on or turn-off status. As a result, the switching loss is reduced by the DPWM [16][17].

A conventional sliding mode observer (SMO) was established using the αβ stationary reference frame voltage equation to observe rotor position and estimate the speed of sensorless PMSM based on back electromotive force (back emf). Figure 4 shows a conventional sliding mode observer diagram with the rotor position and speed in the output.

Figure 4: 
Conventional sliding mode observer diagram

In the sliding mode observer, back emf was obtained from the difference between the estimated αβ currents and real measured currents of the motor with signum function and low pass filter. The real measured currents are i_α and i_β and the real measured voltages are v_α and v_β. The estimated αβ currents were calculated using Equation (5).

where K is the gain of the observer and is multiplied by the sign function. K gain must be sufficiently large and satisfy the condition of K > max(|e_α||e_β|). And back emf is as Equation (6).

Because z_α and z_β include a large number of interferences to achieve accurate back emf (e_α and e_β), using low pass filter (LPF) for the value of z_α and z_β is necessary.

where w_c is the cut-off frequency and τ is the time constant of LPF. Thus, based on Equation (4), the position and speed of the rotor can be estimated using Equations (8) and (9).

Using a conventional sliding-mode observer, an experiment was conducted to evaluate the observer’s ability, and the results are presented in the experimental section.

Conventional sliding-mode observers have some weaknesses in that they cannot completely attenuate the interference and chatter in the estimated position signal. Because of the disturbance that appears in the estimated position signal, the output current can also be affected and distorted. Therefore, this study proposed an improved sliding-mode observer with a Park-phase-locked loop. In the proposed method, the estimated αβ frame back emf is exchanged to the dq frame. By exchanging the dq frame, the dq frame back EMF signal had two direct lines; therefore, it was more effective when implementing two filters in the output. Hence, the output signal was attenuated by interference and chattering. A block diagram of the sliding-mode observer with a Park phase-locked loop is shown in Figure 5.

Figure 5: 
Improved sliding mode observer with a Park phase-locked loop block diagram

As illustrated in the block diagram, the Park block converted the αβ frame back emf to dq frame back emf. The conversion was implemented using Equation (10).

After the conversion process, the values of the returned emf and dq components were filtered through a first-order filter. Here, the first-order filter was a low-pass filter.

where w_c2 is cut-off frequency and different from the cutoff frequency in Equation (7). The rotor position was obtained using Equation (12).

In the above equation, K_g is the voltage gain, and the sign is the signum function. The speed was obtained easily by deriving the estimated rotor position.

With an additional Park PLL at the output of the SMO, the interference and chattering of the estimated rotor-position signal were significantly reduced. Hence, the output current in the inverter phases were more stable and the harmonics were reduced. The results of this method are compared with those of the conventional SMO in the experimental results section.

Figure 6 shows a block diagram of the Sensorless PMSM control method. The control method was field-oriented with a modified sliding-mode observer to respond to speed and position feedback. The DPWMMAX strategy was utilized in the SVPWM block, and the parameters of the PMSM used to compute the SMO are listed in Table 1.

Figure 6: 
Control strategy block diagram

The experimental setup for the sensorless PMSM is shown in Figure 7. The system used a three-phase variable DC power supply to provide a 24 V DC input to the inverter. The 24 V DC input was converted to a three-phase AC voltage for application to the PMSM. In the DC-to-AC converter board, six IGBTs were controlled in the gate terminal by a switching pulse. Switching pulses were generated using a DSP TMS320F28335D on the control board. The DSP TMS320F28335D also implemented the proposed algorithm and received an analog feedback signal from the sensors on the control board. The experimental data were saved and plotted in MATLAB using a JTAG emulator (XDS 300S) of Syncworks, and the current waveform and switching pulse were measured using a digital oscilloscope.

Figure 7: 
Experimental setup

A. Conventional Sliding Mode Observer

Figure 8 shows the rotor position estimated using a conventional sliding-mode observer and the actual rotor position measured using a mechanical encoder integrated with the PMSM. Using Figure 8 as a reference, it can be observed that the estimated rotor position closely approximated the rotor-position determined by the encoder. However, the estimated signal exhibited discernible chatter and lacked clarity. Owing to the presence of noise in the estimated rotor position, the operational performance of the IGBT gate drivers, specifically the speed and reference switching times, was adversely affected. As shown in Figure 9, the motor speed was unstable between 600 and 700 rpm, and the reference phase-voltage waveform became distorted compared with the ideal phase-voltage waveform shown in Figure 3(a). In addition, the inverter operated with the gate-drive switching pulses of the DPWMMAX, and the output phase current is shown in Figure 10.

Figure 8: 
Estimated and actual rotor posistions

Figure 9: 
Reference phase voltage of DPWM and motor speed

Figure 10: 
IGBT gate drive pulse and output phase current

Under the feedback signals of the conventional SMO, the total harmonic distortion of the output phase current was 40.92% at a fundamental frequency of 60 Hz, as shown in Figure 11.

Figure 11: 
Output phase current total harmonic distortion

B. Improved Sliding Mode Observer with Park PLL

Similar to the conventional sliding-mode observer, Figure 12 shows the estimated rotor position obtained using the sliding-mode observer in conjunction with a Park PLL. This estimated position was closer to the actual rotor position, and the chatter was significantly reduced. Therefore, the speed of the motor was more stable at 700 rpm. The reference phase voltage waveform is as ideal phase voltage waveform in Figure 3(a) as shown in Figure 13, and the phase current waveform was almost sinusoidal, as shown in Figure 14.

Figure 12: 
Estimated and actual rotor positions.

Figure 13: 
Reference phase voltage of DPWM and motor’s speed

Figure 14: 
IGBT gate drive pulse and output phase current

Additionally, the harmonics existing in the current phase were significantly reduced, as indicated by the THD coefficient shown in Figure 15.

Figure 15: 
Output phase current total harmonic distortion

In the case of a PMSM operating with an improved sliding-mode observer with a Park PLL, the total harmonic distortion of the output phase current was 25.40% at a fundamental frequency of 60 Hz, as shown in Figure 15.