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

Lead Research Organisation: University of Manchester
Department Name: Electrical and Electronic Engineering


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.

Planned Impact

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.


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Description This project makes substantial inroads in developing a comprehensive theory for negative imaginary systems. Theoretical results in three distinct directions are developed: (a) analysis results that are the least conservative possible for this class of dynamical systems; (b) synthesis methods that allow negative imaginary systems properties to be generated; and (c) controller design paradigms and tuning guidelines that are intuitive and easy to use in application. Several laboratory-based benchtop instrumented test rigs are also constructed to test the developed methodologies and to show the significance of the newly developed theory. Negative imaginary dynamics often arise as a simple fundamental consequence of Newton's second law of motion and hence negative imaginary systems theory is ideal for precision position control of inertial systems when actuated through co-located force/torque actuators. Negative Imaginary systems theory is an important counterpart to passivity theory when position regulation (as opposed to velocity regulation) is the key requirement.
Exploitation Route This work brings several opportunities for theoretical academic researchers to build upon because the ability to understand at a fundamental level the technical challenges associated with analysis, synthesis and control design for a new class of systems is of intrinsic scientific value to the control engineering academic community as such new knowledge often sheds new light onto our grasp of existing methodologies. The theoretical implications of the results derived during this research are being studied and used by other academic groups.

The design methods and tuning guidelines will be relevant for applied researchers in industry seeking to exploit these new control methodologies. The study of negative imaginary systems can lead to potential benefits in several applied engineering fields including areas of advanced technology such as nano-positioning systems, active vibration suppression and isolation, highly resonant mechatronic systems, flexible robotics and co-ordinated distributed control of multi-agent dynamical systems among others.
Sectors Aerospace, Defence and Marine,Education,Manufacturing, including Industrial Biotechology,Transport

Description This research has led to academic collaborations with Australia, the Netherlands, Italy, France, Cyprus, Ecuador and China and industrial collaborations within the UK. This work has also led to the award of an Australia-USA-UK collaborative grant on the robust control of highly resonant, flexible and nanoscale systems where negative imaginary systems techniques are to be applied to control highly flexible and nanoscale systems. This project has also led to the award of an EPSRC Impact Acceleration Account Relationship Incubator grant with a UK SME on applying modelling and robust feedback control concepts to battery management systems. Furthermore, negative imaginary systems theory is being used with colleagues in China to design control algorithms for platooning of train carriages.
First Year Of Impact 2021
Sector Aerospace, Defence and Marine,Education,Manufacturing, including Industrial Biotechology,Transport
Impact Types Economic

Description Exploring modelling and robust feedback control collaboration opportunities in Battery Management Systems
Amount £10,000 (GBP)
Funding ID IAA 254 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 03/2019 
End 07/2019
Description Robust control of highly resonant flexible and nanoscale systems
Amount $430,000 (AUD)
Funding ID DP190102158 
Organisation Australian Research Council 
Sector Public
Country Australia
Start 06/2019 
End 07/2022