PID controller is used in most of the current-speed closed-loop control of permanent magnet synchronous motors (PMSM) servo system. However, , , and of PID are difficult to tune due to the multiple objectives. In order to obtain the optimal PID parameters, we adopt a NSGA-II to optimize the PID parameters in this paper. According to the practical requirement, several objective functions are defined. NSGA-II can search the optimal parameters according to the objective functions with better robustness. This approach provides a more theoretical basis for the optimization of PID parameters than the aggregation function method. The simulation results indicate that the system is valid, and the NSGA-II can obtain the Pareto front of PID parameters. 1. Introduction The high-field-strength neodymium-iron-boron (NdFeB) magnets have become commercially available with affordable prices, so the permanent magnet synchronous motors (PMSM) servo system is receiving increasing attention due to its high speed, power density, and efficiency. It is suitable for some applications of high-performance requirement, for example, robotics, aerospace, electric ship propulsion systems, and wind power generation systems [1–3]. PMSM can provide significant performance improvement in many variable speed applications [4]. PMSM is a multivariable, nonlinear, time-varying, and strongly coupled system. With the development of control theory, various alternative control methods, including feedback linearization, feedback-feedforward, sliding mode variable structure, neural network control, adaptive control, fuzzy control, H∞, and antistep control, have been proposed [5–12]. However, some advanced control techniques are too complex to implement in practical control due to the problem of instantaneity or memory size. Therefore, PID is the most popular controller in the motor control. It provides proportional, integral, and derivative actions for the feedback control system. PID controller has the advantage of simple structure, good stability, and high reliability [13, 14]. In the process industry, more than 90% of the controllers are PID controllers [15]. Although the number of parameters to adjust in a PID is very small, there are many tuning rules [1]. It has been experimentally checked that more than 30% of controllers are operating in manual mode and 65% of the loops operating in automatic mode are poorly tuned because of the inappropriate parameters [16]. Currently, most of the current-speed closed-loop control in the PMSM servo system adopts PID controller [17]. Nevertheless, the PID
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