**7. Discussion**

The optimization procedures conducted in the study show improvements in the speed tracking response of the induction machine drive. Figure 9 shows the improvement when using multi-objective optimization over single-objective optimization, whose results are represented by Figure 7. The reason for the improvement is that torque overshoot penalization is added via a second objective function, and the result is a Pareto front that offers a range of solutions to chose from, based on the application. Figure 10 shows further improvements: single-objective optimization is used and torque overshoot can be arbitrarily penalized using a weighing factor, which results in the smallest amount of overshoot and good speed tracking behavior. A comparison between the proposed method and PCC method that utilizes a classic PI speed controller is shown in Figure 13. In Figure 13a, it can be seen that the speed response is greatly improved, with a much smaller value of maximum speed tracking error but similar settling time. Torque responses are filtered to better represent overshoots, and as can be seen from the same figure, the optimized fuzzy speed controller produces less torque overshoot than the classic PI controller. The reason for the better response is the fact that the fuzzy speed controller acts on the speed tracking error derivative along with the speed tracking error. The speed tracking error derivative can be understood as a form of torque estimation which increases control action in the instances when the torque is changing. The classic PI controller does not have this advantage, since it only acts on the speed tracking error. Figure 13b shows the unfiltered torque response for both methods. It can be seen that the chattering produced by both

methods is in the same range. To further confirm the effectiveness of the method, two more comparisons with different predictive control methods are conducted. Figure 14 shows a comparison of the proposed method with Finite Control Set-Predictive Current Control (FCS-PCC), while Figure 15 represents a comparison of the proposed method with Finite Control Set-Predictive Torque Control (FCS-PTC). To gain an understanding of both methods, the reader is referred to [48,49]. It can be seen from Figures 14a and 15a that the speed tracking error and filtered torque responses are similar to the original comparison: the proposed method has less torque overshoot and superior speed tracking. Table 5 represents relevant numerical values for each method. Figures 14b and 15b show unfiltered torque responses. It can be concluded that finite control set methods produce a larger amount of chattering compared to the proposed method, which means that the proposed method produces less stress on the rotor shaft during operation.


**Table 5.** Comparison of proposed method with other model predictive control methods.

In future research, alternative inputs to the FLC will be investigated, since the speed derivative has several drawbacks: it can be computationally unstable and it can be a cause of high control action. Estimated load torque can be explored as an alternative input to the FLC. This could provide more stable input to the controller, which would produce a more stable output with less control action and potentially less torque overshoot.

**Figure 13.** System response comparison between proposed method and classic PCC method. (**a**) Speed tracking error and filtered torque response. (**b**) Unfiltered torque response.

**Figure 14.** System response comparison between proposed method and FCS-PCC method. (**a**) Speed tracking error and filtered torque response. (**b**) Unfiltered torque response.

**Figure 15.** System response comparison between proposed method and FCS-PTC method. (**a**) Speed tracking error and filtered torque response. (**b**) Unfiltered torque response.
