Negative Imaginary Control Using Hybrid Integrator-Gain Systems: Application to MEMS Nanopositioner

In this article, we propose a new approach to address the control problem for negative imaginary (NI) systems by using hybrid integrator-gain systems (HIGSs). We investigate the single HIGS of its original form and its two variations, including a multi-HIGS and the serial cascade of two HIGSs. A single HIGS is shown to be a nonlinear NI system and so is the multi-HIGS and the cascade of two HIGSs. We show that these three types of HIGSs can be used as controllers to asymptotically stabilize linear NI systems. The results of this article are then illustrated in a real-world experiment where a 2-DOF microelectromechanical system (MEMS) nanopositioner is stabilized by a multi-HIGS.