Nonlinear parameter-varying state-feedback design for a gyroscope using virtual control contraction metrics

TL;DR

This paper introduces a novel nonlinear control design method using virtual control contraction metrics for gyroscopes, providing exact stability and performance guarantees superior to traditional LPV methods.

Contribution

It develops a VCCM-based nonlinear parameter-varying control approach that ensures exponential stability and $ ext{L}_2$-gain performance for gyroscope control, outperforming standard LPV techniques.

Findings

Simulation results demonstrate improved stability and performance.

Experimental validation confirms effectiveness in real gyroscope systems.

Method achieves exact guarantees unlike conventional LPV control.

Abstract

In this paper, we present a virtual control contraction metric (VCCM) based nonlinear parameter-varying (NPV) approach to design a state-feedback controller for a control moment gyroscope (CMG) to track a user-defined trajectory set. This VCCM based nonlinear stabilization and performance synthesis approach, which is similar to linear parameter-varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and $\mathcal{L}_2$-gain performance on nonlinear systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully- and under-actuated operating modes of the CMG show effectiveness of this approach compared to standard LPV control methods.