## 5 Experimental Results
### Experimental Verification of Luenberger-Type Back-EMF Observer in Sensorless FOC  
In this section, similar experimental results are presented in order to compare the control performance of both sensorless techniques. The input parameters for the sensorless FOC are available in Table 11 of Appendix A. As stated in the Introduction, the model-based methods are not applicable at low speeds due to the unfavorable signal-to-noise ratio of the voltage measurements. Due to this disadvantage, stable \(V/f\) with CPF loop was used as a start-up control strategy for sensorless FOC. It uses a required \(d\)-axis voltage \(v_{d}^{*}\) to start-up the machine, while the required q-axis voltage \(v_{q}^{*}\) is maintained at zero. As evident in Figure 27, the motor start-up is smooth, without huge oscillations. Figure 27: The motor start-up in stable \(V/f\) control with CPF and transition to the sensorless FOC with Luenberger-type back-EMF observer: speed, \(dq\) voltages, \(dq\) currents. Figure 26: Speed profile up to nominal reference speed with no-load and required power factor of 0.95: speed, \(dq\) voltages, \(dq\) currents. Transition to the sensorless FOC is applied at the rotational speed \(n_{r}\) of 500 rpm. Evaluation of low speed limit was discussed and verified in [25]. At the threshold speed, the estimated rotational speed \(\hat{n}_{r}\) is set as a feedback value for the speed controller, as well as the estimated electrical position \(\hat{\theta}_{e}\) to the Park transformations. During the transition between \(V/f\) and sensorless FOC, a small decrease in rotational speed \(n_{r}\) can be observed. The whole transition is considered to be a small disadvantage of such an approach. However, the decrease in the rotational speed \(n_{r}\) has not had a huge impact on the system stability and control performance of the sensorless method. After the transition, the \(d\)-axis current \(i_{d}\) is controlled to zero, while the \(q\)-axis current \(i_{q}\) provides the necessary torque to the machine. In Figure 28, the ramp-up to the nominal reference speed of 3000 rpm, 50% load applied at steady-state, and change in speed direction is illustrated. The figure shows the robustness of the observer to the applied load disturbance and also a sufficient change in speed direction from the nominal speed of the machine 3000 rpm to \(-\)3000 rpm. At the lower speeds, sensorless FOC with Luenberger-type back-EMF observer was switched to the stable \(V/f\) control with CPF loop to provide adequate operation. Figure 29 shows a similar experimental verification. However, 75% load is applied to the machine. The experimental results show similar behavior and also robustness against such load disturbance. Finally, in Figure 30, the applied load is increased to 100%, which corresponds to the nominal torque of the experimental PMSM machine. It is obvious that the sensorless FOC with Luenberger-type back-EMF observer is also operating properly under full-load machine conditions. Compared to the same experimental procedure with stable \(V/f\) control in Figure 24, it is evident that stable \(V/f\) control with CPF has a better response to the load disturbance. In the sensorless FOC, the decrease in speed after the applied load is more significant. Figure 31 shows the speed profile up to the nominal reference speed of 3000 rpm with no-load conditions. Figure 28: Ramp-up and ramp-down with the nominal reference speed and 50% load applied at steady-state: speed, \(dq\) voltages, \(dq\) currents. Figure 30: Ramp-up and ramp-down with the nominal reference speed and 100% load applied at steady-state: speed, _dq_ voltages, _dq_ currents. Figure 29: Ramp-up and ramp-down with the nominal reference speed and 75% load applied at steady-state: speed, _dq_ voltages, _dq_ currents. This figure can be used to determine the accuracy of the sensorless FOC with Luenberger-type back-EMF observer in a wide speed range.