**6. Implementation**

A digital signal processor (DSP), type SH 7237 (manufactured by Renesas Electronics Corporation, Tokyo, Japan), and an FPGA, type 10M16SAU16917G (manufactured by Intel Corporation, Santa Clara, CA, USA), were used to execute the control algorithms. The sampling interval of the speed-loop was 1 ms, and the sampling interval of the current-loop was 100 μs. The switching frequency of the matrix converter was 10 kHz. The PMSM was an 8-pole motor, which had a 2000 r/min rated speed, 9.55 N·<sup>m</sup> of rated torque, 9 A of rated current, 0.58 Ω of stator resistance, 1.3 mH of *d*-axis inductance, 1.7 mH of *q*-axis inductance, 0.003 N·m·s/rad of inertia, and a 1.14 N·m/A torque constant. The three-phase input filter of method 1 had the following parameters: *Rd* = 15 Ω, *Lf* = 1.5 mH, and *Cf* = 6.8 μF. In addition, the three-phase input filter of method 2 had the following parameters: *Rd* = 22 Ω, *Lf* = 1.5 mH, and *Cf* = 4.7 μF. Figure 9a shows the software and hardware block diagrams of the control system. Figure 9b shows the circuits for a matrix converter, including a clamped circuit, some drivers, a matrix converter, an AC/DC power supply, and a control circuit.

**Figure 9.** *Cont*.

**Figure 9.** The implemented matrix-converter PMSM drive system. (**a**) Block diagram, (**b**) photo of matrix-converter.

### **7. Experimental Results**

Several experimental results are shown here. Figure 10a demonstrates the measured input A-phase current of the matrix converter without using an input filter. The input Aphase current is close to a square-wave high-frequency PWM current, which has a 132.14% THD. Two simplified three-phase input AC filter design methods were proposed without using computer simulations. Figure 10c demonstrates the measured A-phase current using the proposed method 1 of the three-phase input AC filter, in which the parameters include *λ*1 = 0.11, *λ*2 = 0.019, and *λ*3 = 0.0006. The measured A-phase current is nearly a sinusoidal waveform with a 9.55% THD. Figure 10e demonstrates the measured A-phase current using the proposed method 2 input three-phase AC filter, in which the parameters include *ωres* = 12,570 rad/s, *Qres* = 1.23, and *ξ* = 0.4. The *A*-phase current using method 2 includes a 12.08% THD. As we can observe, the current without using an input filter has the highest THD. The major reason is that the high-frequency PWM current creates a lot of harmonic currents. The proposed method 1 of the three-phase input AC filter design provides lower THD than the proposed method 2. The major reason is that method 1 focuses on harmonic currents and voltages; method 2, however, focuses on frequency responses.

Figure 11a demonstrates the measured output currents of the a-phase matrix converter using a PI current controller, which produces an 11.91% THD. Figure 11c demonstrates the measured output currents of the a-phase matrix converter using a predictive current controller, which has a 9.25% THD, which is lower than the THD of the PI current controller.

Figure 12a illustrates the measured 300 r/min step-input speed responses by using a PI controller, a one-step predictive speed controller, and a two-step predictive speed controller. The PI controller is designed by pole assignment with two major poles *P*1 = −10.6 + j7.5 and *P*2 = −10.6 − j7.5. As we can observe, the PI controller provides the highest overshoot among the three different speed controllers. The one-step predictive speed controller, which chooses a weighting factor *q* = 0.25, has the quickest transient response when compared to the two-step predictive speed controller and the PI controller. The two-step predictive speed controller, which chooses a weighting factor *η* = 0.25 0 0 0.25 and *ρ* = 0.5, has the lowest overshoot but the slowest transient response when compared to the PI controller and the one-step predictive speed controller. Figure 12b illustrates the load disturbance responses at 300 r/min with a 2 N·<sup>m</sup> external load. The one-step predictive controller provides the smallest speed drop and the fastest recovery time relative to the PI controller and the two-step predictive controller. However, the two-step predictive controller provides fewer steady-state errors than the PI controller and the one-step predictive speed controller.

Figure 13a demonstrates the measured *q*-axis current response by using the PI controller, which has a higher overshoot and slower response than the one-step predictive

current controller. Figure 13b demonstrates the measured *q*-axis current response by using the one-step predictive controller. As can be observed, the one-step predictive current controller performs better than the PI controller again, including faster transient responses and lower overshoot.

Table 2 shows the comparison of the input harmonic currents. Method 1 has fewer input harmonic currents than method 2. Table 3 shows the comparison of the speed responses. The one-step predictive speed controller provides quicker transient responses and quicker recovery time. However, the two-step predictive speed controller provides fewer speed drops and smaller overshoots than any other controller.

**Figure 10.** *Cont*.

**Figure 10.** *Cont*.

**Figure 10.** Measured input waveforms (**a**) *iAN* without filter, (**b**) THD without filter, (**c**) *iAN* with method 1. (**d**) THD method 1, (**e**) *iAN* with method 2, (**f**) THD with method 2.

**Figure 11.** *Cont*.

**Figure 11.** Measured a-phase output currents of matrix-converter using different current controllers. (**a**) PI, (**b**) THD, (**c**) predictive, (**d**) THD.

**Figure 12.** Measured speed responses. (**a**) Step-input responses, (**b**) load-disturbance responses.

**Figure 13.** Measured current responses. (**a**) PI current controller, (**b**) predictive current controller. **Table 2.** Comparison of input harmonic currents.



**Table 3.** Comparison of speed responses.

### **8. Conclusions**

In this paper, two different design methods, which are simpler than the traditional numeric methods, using a computer for a three-phase input AC filter for matrix-converter PMSM-drive systems, are investigated and compared. The first method requires only analytic processes, which is simpler than the traditional numeric method using a computer. The second method uses frequency responses to determine the R-L-C parameters of the AC filter. In addition, a two-step predictive speed controller and a one-step predictive speed controller are investigated to improve the dynamic responses of speed-loop control systems. Moreover, a predictive current controller is designed to provide smaller harmonic currents than a PI current controller. Experimental results show that the proposed methods can effectively improve the performance of matrix converter-based PMSM drive systems, including obvious improvements in the input AC harmonic currents, output AC harmonic currents, and dynamic responses.

**Author Contributions:** Conceptualization, T.-H.L.; methodology, J.-H.L.; software, J.-H.L.; validation, T.-H.L.; formal analysis, T.-H.L. and J.-H.L.; investigation, T.-H.L. and J.-H.L.; resources, T.-H.L.; data curation, J.-H.L.; writing—original draft preparation, T.-H.L. and J.-H.L.; writing—review and editing, T.-H.L.; visualization, J.-H.L.; supervision, T.-H.L.; project administration, T.-H.L.; funding acquisition, T.-H.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Ministry of Science and Technology, under Grant MOST-110-2221-E-011-086.

**Conflicts of Interest:** The authors declare no conflict of interest.
