Conditional funnel control: A simple approach to prescribed performance asymptotic tracking and its industrial applications

Funnel control is remarkably a low-complexity control technique which ensures a model-free tracking of reference signal for nonlinear systems. It also ensures a prescribed transient behaviour of error signal; however, it only guarantees the error signal to remain within or close to the funnel boundary rather than to converge to zero. Therefore, for ensuring the asymptotic convergence of the error to zero, in this paper, we introduce the concept of conditional error in funnel control without any complex condition or requirement(s). Thus, we first introduce the idea of conditional funnel control for relative degree one systems and then, we extend this idea for arbitrary relative degree nonlinear systems. Mathematical analyses are provided to ensure the boundedness of the tracking error within the funnel boundary as well as the occurrence of asymptotic convergence. For validating the efficacy of the proposed scheme, we provide numerical examples to compare the numerical results with the recently proposed schemes. Finally, we demonstrate the industrial applications (through simulation case-studies) of the proposed method for a Continuous Stirred Tank Reactor (CSTR), Bioreactor and Flexible Joint Manipulator.