Constraint-Aware Discrete-Time PID Gain Optimization for Robotic Joint Control Under Actuator Saturation

2026-01-26

AI Summary

This study addresses performance degradation in discrete-time PID control of robotic joints, commonly caused by actuator saturation, sampling delays, and measurement noise. To tackle these practical constraints, the authors propose a tuning method that integrates the Jury stability criterion, an anti-windup mechanism, and a safety-constrained Bayesian optimization framework within a zero-order hold discretization model. The approach optimizes controller gains with respect to the Integral Absolute Error (IAE) while incorporating behavioral safety certification to pre-eliminate infeasible parameter candidates, thereby significantly improving sample efficiency. Simulation results under uncertain conditions demonstrate that the median IAE is reduced from 0.843 to 0.430, overshoot remains below 2%, and 11.6% of unsafe gain configurations are effectively excluded during the optimization process.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The precise regulation of rotary actuation is fundamental in autonomous robotics, yet practical PID loops deviate from continuous-time theory due to discrete-time execution, actuator saturation, and small delays and measurement imperfections. We present an implementation-aware analysis and tuning workflow for saturated discrete-time joint control. We (i) derive PI stability regions under Euler and exact zero-order-hold (ZOH) discretizations using the Jury criterion, (ii) evaluate a discrete back-calculation anti-windup realization under saturation-dominant regimes, and (iii) propose a hybrid-certified Bayesian optimization workflow that screens analytically unstable candidates and behaviorally unsafe transients while optimizing a robust IAE objective with soft penalties on overshoot and saturation duty. Baseline sweeps ($\tau=1.0$~s, $\Delta t=0.01$~s, $u\in[-10,10]$) quantify rise/settle trends for P/PI/PID. Under a randomized model family emulating uncertainty, delay, noise, quantization, and tighter saturation, robustness-oriented tuning improves median IAE from $0.843$ to $0.430$ while keeping median overshoot below $2\%$. In simulation-only tuning, the certification screen rejects $11.6\%$ of randomly sampled gains within bounds before full robust evaluation, improving sample efficiency.

Problem

• actuator saturation
• discrete-time PID
• robotic joint control
• stability
• constraint-aware optimization

Innovation

• discrete-time PID
• actuator saturation
• anti-windup
• Bayesian optimization
• stability certification