A negative imaginary approach to hybrid integrator-gain system control

TL;DR

This paper establishes a theoretical link between hybrid integrator-gain systems and negative imaginary systems, demonstrating stability and control applications, including a MEMS nanopositioner example.

Contribution

It introduces the concept that HIGS are nonlinear negative imaginary systems and proves stability when interconnected with linear NI systems.

Findings

HIGS are shown to be NNI systems.

Stable positive feedback interconnection with linear NI systems.

Successful application to MEMS nanopositioner control.

Abstract

In this paper, we show that a hybrid integrator-gain system (HIGS) is a nonlinear negative imaginary (NNI) system. We prove that the positive feedback interconnection of a linear negative imaginary (NI) system and a HIGS is asymptotically stable. We apply the HIGS to a MEMS nanopositioner, as an example of a linear NI system, in a single-input single-output framework. We analyze the stability and the performance of the closed-loop interconnection in both time and frequency domains through simulations and demonstrate the applicability of HIGS as an NNI controller to a linear NI system.