Frequency-Domain Properties of the Hybrid Integrator-Gain System and Its Application as a Nonlinear Lag Filter

Abstract

This brief investigates frequency-domain properties of the hybrid integrator-gain system (HIGS) by analytically deriving its higher-order sinusoidal input describing functions (HOSIDFs). Furthermore, a novel application of this nonlinear control element is proposed, where it is utilized as a nonlinear lag filter. Hereby, the closed-loop stability can be guaranteed based on a non-parametric plant model—while ensuring robustness against plant uncertainties—by utilizing a circle criterion-like argument. Control design is initially based on a describing function (DF) analysis of the HIGS. This yields magnitude characteristics similar to those of a linear lag filter, while having the freedom to tune the induced phase lag. However, the excitation of higher-order harmonics by the HIGS is, in that case, neglected. Based on the derived HOSIDFs, it is shown that the validity of this assumption depends on the properties of the plant and the controller, as well as the spectral properties of the external inputs. Finally, the potential of the nonlinear lag filter is investigated by means of simulations and experiments on a high-precision industrial motion stage, showing performance improvements compared with a linear lag filter.