## 4 Test Results and Discussion  
To verify the efficiency of the proposed data-driven weighting factor tuning approach, numerical simulations of varied motor operating conditions were run. The main objective of this work is to achieve high-performance control of PMSMs used in spindles or servo drive applications that are commonly used in industry. A comprehensive comparative study between a baseline MOGA-based neural network and a TD3-based DRL agent, detailed in Section 3, was performed using a laptop running Windows 11 with an Intel i7, 32 GB RAM, and an NVIDIA RTX 3000 GPU. The parameters used for the MOGA and training of the RL agent are presented in Table 6.  
Using the learning strategy described in Section 3.2, the evolution of the cumulative reward obtained per episode and the average reward are presented in Figure 7. Although the reward is initially high, it shows notable fluctuations as a result of the agent's exploratory \begin{table}
\begin{tabular}{c l l} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(\lambda_{i}\), \(\overline{\lambda}_{i}\) & Lower and upper bound for the weighting factor \(\lambda_{i}\) & 0.01 and 20 \\ \(\underline{\lambda}_{f}\), \(\overline{\lambda}_{f}\) & Lower and upper bound for the weighting factor \(\lambda_{f}\) & 0.01 and 2.5 \\ \(N_{\text{MOGA}}\) & MOGA population size & 120 \\ \(N_{\text{gen}}\) & Number of MOGA generations & 50 \\ \(N_{\text{episode}}\) & Number of RL training episodes & 800 \\ \(N_{\text{steps}}\) & Episode steps & \(4\times 10^{6}\) \\ \(i_{\text{tol}}\) & Tolerance margin for the current error & 0.3 A \\ \(\text{card}(\mathcal{B})\) & Size of the mini-batch in Algorithm 1 & 256 \\ \(\text{card}(\mathcal{D})\) & Size of the replay buffer & \(1\times 10^{4}\) \\ \(\alpha_{\text{lr}}\) & Learning rate & \(1\times 10^{-4}\) \\ \(\zeta\) & Weight for average update of the target critics & 0.005 \\ \(\gamma\) & Agent discount factor & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MOGA and TD3 learning parameters. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Aspect** & **DRL** & **MOGA-Based ANN** \\ \hline
**Learning approach** & Trial-and-error interaction & Offline optimization followed by supervised learning \\
**Adaptability** & Dynamically adjusting to changing conditions & Pre-trained for specific scenarios \\
**Computational load** & High during training and deployment & High for training but low for online use \\
**Multi-objective handling** & Implicit in reward design & Explicit via Pareto-optimal solutions \\
**Implementation complexity** & High (requires advanced DRL setup) & Moderate (MOGA and ANN integration) \\
**Robustness to variations** & Strong but need proper selection & Dependent on training dataset \\  & of state and reward & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Qualitative comparison of DRL and MOGA-based ANN for weighting factor optimization in MPCC. behavior and early policy selection. These variations show the agent's effort to learn from the dynamic system environment while balancing between switching transition reduction and current convergence. After episode 300, the agent has converged on an ideal tuning strategy, as the reward stabilizes with fewer oscillations. Both the per-episode cumulative reward and average reward become consistent, reflecting the successful learning of weighting factor adjustments for robust MPCC performance. We start by evaluating rotor speed, phase current, and torque responses of the drive motor during acceleration and deceleration at a constant load torque of 2 Nm, as presented in Figure 8. The results obtained with the DRL-based strategy show a significant improvement on the current response with respect to the MOGA-NN-based approach, with reduced harmonic content. Indeed, it can be seen on the phase current response using DRL of Figure 8b that the total harmonic distortion (THD) is of 6.95 % while it is of 9.25 % for the MOGA-NN in Figure 8a.