Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures with Free Body Motion

TL;DR

This paper extends negative imaginary systems theory to include free body dynamics, enabling robust control of highly resonant structures with free motion, demonstrated through a robotic arm case study.

Contribution

It introduces a generalized NI system definition accommodating free body motion and provides order-independent stability conditions for positive feedback control.

Findings

New NI system definition for free body dynamics

Order-independent stability conditions

Successful control of a flexible robotic arm

Abstract

Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. The stability conditions in this paper are given purely in terms of properties of the plant and controller transfer function matrices, although the proofs rely on state space techniques. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented.