Digital Control of Negative Imaginary Systems Using Discrete-Time Multi-HIGS: Application to a Dual-Stage MEMS Force Sensor

TL;DR

This paper introduces a digital control method using discrete-time multi-HIGS controllers for negative imaginary systems, demonstrating effective resonance suppression and stability in a dual-stage MEMS force sensor.

Contribution

It develops a novel digital control approach with multi-HIGS controllers for NI systems, including stability analysis and practical application to a MEMS sensor.

Findings

Multi-HIGS controllers preserve NI properties in discrete-time.

Closed-loop system effectively suppresses resonances.

Experimental results confirm robustness and stability.

Abstract

In this paper, we propose a digital control approach for multi-input multi-output negative imaginary (NI) systems using discrete-time hybrid integrator-gain systems (HIGS) controllers. We show the NI property of the bimodal and trimodal discrete-time HIGS, as well as the parallel combinations of them, which are referred to as the multi-HIGS. Also, we demonstrate that linear NI systems can be asymptotically stabilized using discrete-time HIGS in digital control. We apply discrete-time bimodal and trimodal multi-HIGS controllers to a two-input two-output dual-stage force sensor with lightly damped resonant modes. To validate the theoretical findings, the closed-loop performance is evaluated in both time and frequency domains. Experimental results show that the discrete-time multi-HIGS effectively suppresses resonances while preserving favorable phase characteristics, which highlights its potential as a robust nonlinear NI controller for the digital control of NI systems.