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

TL;DR

This paper develops a comprehensive, implementation-aware workflow for tuning saturated discrete-time PID controllers in robotic joints, improving robustness and efficiency through analytical stability analysis and Bayesian optimization.

Contribution

It introduces a hybrid Bayesian optimization method that screens unstable candidates and unsafe transients, enhancing robust PID tuning under actuator saturation and discrete-time effects.

Findings

Robust tuning reduces median IAE from 0.843 to 0.430.

Median overshoot remains below 2% after tuning.

Certification screening improves sample efficiency by rejecting unsafe gains.

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.