Family of controllers based on sector non‐linear functions: an application for first‐order dynamical systems

This study proposes the design of a family of controllers based on sector non‐linear functions for first‐order dynamical systems. Three new controllers that incorporate these types of functions are presented and analysed to validate the authors' premise. The proposed nominal controllers and an augmented version with integral action are presented. Asymptotic stability is proven under the Lyapunov theory and the controllers' performance is compared against a traditional proportional controller. An empirically tuned relation depending on a constant bound value and an operation range is proposed; this is used to compute the gains of each controller. Simulation results with all of the controllers under saturation bounds are presented to illustrate the effectiveness of the method at solving the output regulation and the tracking control problems, under practical physical assumptions. The numerical comparison utilises theL 2 andL ∞ norms over the output error, and over the control variable, applying the same saturation bounds for each controller.