## 4 Optimization of Adaptive Control Parameters for Permanent Magnet Synchronous Motors
### Partial Sample Shannon Entropy Evaluation  
In assessing the performance of a permanent magnet synchronous motor, a pivotal metric is the motor output torque. However, as research in this field progresses, it becomes apparent that effectively evaluating motor output torque is very intricate. To address this challenge, we introduce the concept of the Shannon quotient in this section, proposing a novel evaluation approach termed Partial Sample Shannon Entropy Evaluation (PSSEE). This method enables a more intuitive and effective assessment of motor torque, both pre- and post-optimization. Through PSSEE, we can discern the strengths and limitations of torque performance, facilitating a comparative analysis between the optimization effects of Undominated Genetic Algorithm II and the Multi-objective Particle Swarm Optimization algorithm. Such comparisons aid in the development of an enhanced optimization algorithm for control strategy and a more rational control parameter. This section will delve into the Shannon quotient and the PSSEE evaluation method. The concept of entropy was initially introduced and elucidated by the German physicist [PERSON] within the framework of the second law of thermodynamics. Initially, its application primarily pertained to the thermodynamic domain, where it served to characterize irreversibility in energy transformations and thermal processes. However, as the understanding of entropy deepened, its scope began to broaden. In the mid-20 th century, American mathematician [PERSON] extended the concept of entropy into information theory, paving the way for its utilization in cryptography, data compression, and various other domains. With the maturation of [PERSON]'s theory, entropy found applications in diverse fields such as ecology, environmental science, and machine learning. Classical Shannon entropy is mathematically expressed as follows:  
\[H(X)=-\sum_{i=1}^{n}p(x_{i})\cdot\log p(x_{i}) \tag{43}\]  
where \(H(X)\) denotes the Shannon entropy value, \(p(xi)\) represents the probability of occurrence of data aggregation \(x_{i}\), and \(n\) signifies the number of segmented regions. Figure 6: The convergence curve of the parameter. Shannon entropy has been subject to varied definitions across multiple disciplines, evolving to meet the specific demands of different studies. In the context of this paper, which focuses on minimizing the speed and torque overshoot of a permanent magnet synchronous motor, traditional methods of torque evaluation prove insufficient, particularly when observing torque dynamics solely through output curves. Thus, this paper proposes the Partial Sample Shannon Entropy Evaluation method, rooted in classical Shannon entropy principles, to assess motor output torque. This novel evaluation approach facilitates an intuitive assessment of control parameters derived from the two optimization algorithms discussed in Section 4.2 of the motor system. By considering the local torque aggregation degree and the cumulative torque value, the advantages and limitations of these optimization algorithms can be comprehensively evaluated. The procedural framework of the PSSEE assessment methodology is delineated below. Initially, the torque output results from the PMSM are input into the PSSEE control algorithm, thus generating a dataset as illustrated in Equation (44). In this dataset, \(x_{1}\), \(x_{2}\), \(x_{3}\), \(\ldots\), \(x_{\text{n}}\) denote the instantaneous torque of the motor at various time instances throughout the simulation. To ensure the validity of the results, this study extracts 50,000 time points from the entire simulation duration at uniform intervals for analysis. Let \(M\) represent the comprehensive dataset. The acquired torque data from the motor will subsequently undergo additional analysis within \(M\).