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

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.