Fourth-order active disturbance rejection control with proximal policy optimization for parameter tuning

To suppress speed fluctuations in Permanent Magnet Synchronous Motors (PMSMs) under periodic load disturbances, this study proposes a fourth-order nonlinear active disturbance rejection control (4th-NLADRC) system. The system parameters are optimized using proximal policy optimization (PPO) reinforcement learning (RL). The method first constructs a Fourth-order Extended State Observer Proximal Policy Optimization (4th-ESO-PPO) tuning framework, which reduces a single parameter-tuning cycle to 24 min and yields two observer-parameter structures: Fourth-order Linear Extended State Observer (4th-LESO) and Fourth-order Nonlinear Extended State Observer (4th-NLESO). By analyzing the pole-zero characteristics of the control system in the z-domain, the influence of key parameters is clarified, thereby guiding the tuning sequence. Simulation results show that, compared with a conventional third-order system, the proposed 4th-NLADRC reduces the total harmonic content by 95%–98% under periodic load disturbances, and reduces the peak speed fluctuation by 24% under step load changes. Both the 4th-NLADRC and the fourth-order linear active disturbance rejection control (4th-LADRC) demonstrate excellent performance in suppressing periodic load disturbances.