Hybrid funnel control with derivative feedback and intelligent proportional-integral for higher-order systems

This paper introduces a new control strategy, referred to as hybrid funnel control with derivative feedback and intelligent proportional-integral for higher-order systems, which combines funnel control with derivative feedback and an intelligent proportional–integral controller. The proposed approach leverages funnel control with derivative feedback to regulate transient errors, while intelligent proportional-integral ensures steady-state tracking, resulting in bounded tracking errors and zero steady-state error. In contrast with classical funnel control approaches, the hybrid funnel control with derivative feedback and intelligent proportional-integral naturally extends to higher-order systems without relying on an explicit model. A rigorous Lyapunov-based analysis is developed to guarantee the closed-loop stability and to characterize the influence of funnel boundary adaptation. The effectiveness and robustness of the proposed controller are demonstrated through simulation studies on a mass-spring system mounted on a car, highlighting accurate tracking, robustness to uncertainties, and resilience to measurement noise. The results confirm that the proposed controller provides a simple yet powerful solution for practical model-free control of complex dynamical systems.