Robust feedback control of negative imaginary systems: From foundations to benchmark applications

The emerging theory of negative imaginary systems is attracting increasing interest amongst control systems researchers because it captures a wide range of practical problems. Negative imaginary dynamics often arise as a simple fundamental consequence of Newton's second law of motion. Often control systems performance can be significantly improved, despite demanding robustness requirements and difficult dynamics, by directly exploiting system properties. The study of negative imaginary systems can lead to potential improvements in several engineering fields including areas of advanced technology such as nano-positioning systems, control of multi-agent dynamical systems, distributed network control, mechatronics and robotics among others.

This work will develop new results in the theory of negative imaginary systems. These results will underpin controller design methods and controller tuning guidelines for this class of systems. The developed methodologies will be applied to several specific benchmark applications and case studies. Wide dissemination of the advantages of the negative imaginary concepts will be a key aspect of this work.

The proposed research will be most beneficial to industries that rely on precision mechatronic motion control systems, active vibration suppression systems and multi-agent distributed motion control systems. The unifying thread across these seemingly disparate engineering fields is the underlying negative imaginary dynamics that arises in each of these fields from fundamental Newtonian laws of motion. The proposed research fills important gaps that have been identified in negative imaginary systems theory to develop control systems design methodologies that will be demonstrated on five distinct benchmark case studies from the aforementioned engineering fields. High value industries in the UK that rely on the above technologies include the semiconductor industry which relies on precision mechatronic control of wafer stages in Integrated Circuit manufacture, the nano-technology industry which relies on nano-resolution positional control to achieve fine precise movements in physical processes such as nano-litography, nano-patterning or nano-manipulation through advanced instruments such as atomic force microscopes, the aerial drones industry that relies on vibration suppression to provide useful sensor feeds for surveillance, and the robotics and autonomous systems industry that exploits swarm behaviours to form sensor networks or vehicle platoons in multi-agent dynamical interconnected systems technologies.