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. Note to Practitioners—The damping ratio of a system is critically important in engineering applications, as it serves as a key parameter for balancing the convergence rate and overshoot. On the other hand, the prescribed performance control (PPC) allows for setting the tracking error boundary and ensures that the tracking error remains within the prescribed range. Inspired by engineering applications, the proposed control method combines an adjustable damping ratio with the prescribed performance control, enabling the damping ratio to be systematically designed via specific parameter selection rules while maintaining the tracking error within the prescribed performance boundary. As a result, both the transient and steady-state responses of the system can be precisely regulated under the proposed controller, which is highly beneficial for practical engineering applications. Specific applications include: automotive suspension control systems (optimizing driving stability and comfort), aircraft attitude control systems (enhancing dynamic stability and flight safety), and robotic control systems (improving motion accuracy and ensuring successful task completion).