# Optimization of Ship Permanent Magnet Synchronous Motor ADRC Based on Improved QPSO
## 1 Introduction
Their study confirmed that optimal parameter configurations are crucial for maximizing ADRC's control performance. To address the issue of optimal parameter configuration, [PERSON], [PERSON] et al. [14] proposed a parameter tuning method based on the improved Vulture Search Algorithm, analyzing the limitations of traditional tuning methods on UAV control system performance. This method enhances algorithm efficiency by combining global exploration with local exploitation strategies. [PERSON], [PERSON] et al. [15] proposed an ADRC parameter optimization method based on the Dynamic Bionic Optimization (DBO) algorithm, which simulates adaptive biological behaviors in dynamic environments to effectively search for the optimal solution in high-dimensional parameter spaces. [PERSON], [PERSON] et al. [16] introduced an improved ADRC method based on optimized repetitive control, which strengthens the system's ability to reject periodic disturbances by incorporating a repetitive control module and optimizes the ESO's performance. [PERSON], [PERSON] et al. [17] proposed a parameter optimization approach for ADRC based on an adaptive multi-population genetic algorithm. This method introduces a collaborative mechanism among multiple populations, enabling faster identification of the global optimum in high-dimensional parameter spaces and avoiding local optima. Despite these advancements in ADRC parameter optimization, challenges such as high computational complexity, slow convergence, and sensitivity to parameter tuning persist. To address the issues in the PMSM control system with the ADRC controller, this paper aims to make the following contributions: First, as the error increases, the nonlinear function may lead to excessively aggressive control signals. In this paper, the nonlinear fal function is optimized to develop a new smooth nonlinear function. This new function processes the error in different ranges through piecewise handling, effectively balancing the intensity of the response. This improvement mitigates the impact of large tracking errors, which previously caused significant deviations between the observer state and the actual system state, thereby enhancing control performance. Second, to optimize the ADRC parameters, this paper employs the Quantum-behaved Particle Swarm Optimization (QPSO) algorithm [18]. In contrast to traditional optimization algorithms, QPSO integrates quantum mechanics concepts into the conventional Particle Swarm Optimization (PSO) framework. By improving particle search diversity through a quantum-behavior model, QPSO prevents particles from being confined to deterministic paths, enhancing global exploration. Moreover, it addresses the common oscillation issue in the later stages of convergence, effectively avoiding premature convergence to local optima [19]. To address issues such as the insufficient randomness in the traditional QPSO position update formula, this paper replaces the randomness term with a dual-wave function that combines Gaussian and Cauchy distributions. The use of the dual-wave function enables the algorithm to explore a wide range during the search process, preventing premature convergence to a local optimum and ensuring the global optimum can be found. For nonlinear, multi-modal optimization problems (such as the Rastrigin and Ackley functions), local optima often obstruct the search for the global optimum. Additionally, the weight of each term in the bi-wave function can be adaptively adjusted at different stages of the search, allowing the optimization algorithm to flexibly balance global exploration and local exploitation as needed. The structure of the paper is organized as follows:  
Section 2 provides a detailed description of the mathematical model of the Permanent Magnet Synchronous Motor (PMSM). Section 3 presents the design of the ADRC controller, which incorporates a newly designed smooth nonlinear function.