Design of PID Compensation Controller in High-Noise Environments

Abstract To address PID performance degradation under coupled measurement noise, random delay, actuator nonlinearities, and external disturbances, this paper studies a composite discrete-time control framework comprising a band-limited disturbance observer (DOB), a physics-informed GRU observer, adaptive state fusion, residual compensation, and Peak-Event gated feedforward. The contribution is the causal integration and conditional coordination of these elements rather than a new PID law or a new generic recurrent-network training algorithm. Evaluation uses disjoint training, validation, and test seeds, 20 paired closed-loop trials per principal setting, a 16-condition robustness matrix, and targeted 10-seed boundary tests. Relative to the same sign-consistent, re-tuned PID-DOB backbone, the complete framework reduces mean tracking RMSE by 10.78% in feasible tracking but increases it by 0.024% in hard stress. Across the 16-condition matrix, the gain ranges from -7.97% to +10.92%. Under a predeclared operational criterion, the proposed loop passes through a gyro-noise standard deviation of 0.15 rad/s and a fixed measurement delay of 80 ms, then first fails at 0.20 rad/s and 100 ms, respectively; all simulations remain numerically bounded through the highest tested values of 3 rad/s and 320 ms. Across five withheld disturbance families, it lowers RMSE by 2.46%--3.00% relative to PID-DOB, with all five paired comparisons significant after Holm correction. In a paired 60-configuration joint-uncertainty audit, both controllers meet the declared criterion in every run, while the proposed controller lowers mean RMSE by 1.49% (Pt=1.21*10^{-4}). A CPU timing study gives a mean complete-loop throughput of 0.284 ms per cycle, but individual deadline misses preclude a hard real-time claim. The results therefore support a condition-dependent tracking trade-off and a finite-grid robustness envelope. All results are obtained from controlled, seed-paired simulations of a single-axis velocity servo system, providing a fully reproducible basis for subsequent hardware deployment.