Immune-PID Control for Underactuated Systems with Safe Experimentation Dynamics Tuning

Abstract

This paper develops a novel data-driven immune-PID control scheme for underactuated systems. The Safe Experimentation Dynamics (SED) method is adopted to optimize the parameters of the proposed immune-PID structure for minimizing both tracking error and control effort. The key advantage of this approach is that it enables fast, data-driven tuning using only the system’s input and output data, with no need for an explicit mathematical model of the plant. Integrating the immune mechanism into PID control offers clear performance benefits over standard PID, which we validate on an underactuated container crane model by evaluating trolley position tracking, hoist rope length regulation, and payload sway angle suppression. Numerical simulation results indicate that the cumulative tracking error index drops from 1.1462 to 0.8890, the cumulative control energy index falls from 50.6462 to 12.6255, and the total objective function value decreases from 180.2534 to 122.5754. The data-driven immune-PID method delivers superior control performance relative to the standard PID controller.