Prescribed performance control with adaptive erupting funnel function for a class of unknown discrete-time systems and undefined disturbances

Abstract

This paper presents a prescribed performance controller tailored for practical systems with unknown discrete-time dynamics, effectively addressing uncertainties and disturbances to maintain tracking errors within predefined bounds. The control law is derived using an analytical equivalent model and an adaptive funnel function, specifically designed to ensure robust tracking performance even under real-world conditions. By employing a sliding function through filtered error transformation, the approach directly analyzes the convergence region without complex nonlinear functions like exponentials or logarithms. The adaptable funnel function further enhances the controller’s ability to handle sudden disturbances, keeping the tracking error constrained within desired limits. Experimental validation on a DC motor torque control system highlights the controller’s practical effectiveness, showing its superiority in managing high-frequency control efforts compared to traditional methods.