Nonlinear Tracking Differentiator-Based Prescribed Performance Zeta-Backstepping Control With Its Application to a Quad-Rotor Hover

This paper proposes a nonlinear tracking differentiator-based prescribed performance zeta-backstepping control method for uncertain nonlinear systems with unmodeled dynamics and external disturbances. Unlike traditional prescribed performance control methods, the proposed approach allows direct adjustment of the system damping ratio through parameter regulation while ensuring that the tracking error remains within prescribed performance boundaries. To address unmodeled dynamics and external disturbances, the developed feedforward-compensated nonlinear tracking differentiator provides uncertainty estimation. The analysis of a second-order linear differential equation inequality rigorously proves that the closed-loop system achieves adjustable damping characteristics and guaranteed error performance. Finally, this control method is applied to a quad-rotor hover system, and experimental results confirm its effectiveness and advantages.