Zeroing neurodynamics proportional-integral-derivative controller for order-2 system: design, analysis, and verification

Abstract

This paper presents a zeroing neurodynamics proportional-integral-derivative (PID) controller for an order-2 single-input single-output (SISO) affine-in-control nonlinear system. The controller is derived from zeroing neurodynamics (ZN) and reformulates PID gains through ZN parameters, establishing an explicit correspondence to the closed-loop poles of the error dynamics. This enables systematic pole placement for stability and performance tuning, eliminating empirical trial-and-error. Theoretical analysis proves exponential convergence of the tracking error. The inverted pendulum, a benchmark system with strong geometric nonlinearity, is used to verify the controller. Simulations with large initial offsets and constant references show that the proposed controller maintains stable tracking in operating conditions where the conventional PID controller exhibits substantial performance degradation. The resulting framework provides a model-based and theoretically grounded alternative for nonlinear control.