Output Feedback Control for Uncertain Variable Structure Systems with Resets

Lead Research Organisation: University of Kent
Department Name: Sch of Engineering & Digital Arts

Abstract

Discontinuous systems are studied in very different research fields such as economics, electrical circuit theory, mechanical engineering (impact theory, plasticity theory), biosciences, systems and control theory. Such systems are typically viewed as a simple model of hybrid systems, consisting of a finite family of subsystems, equipped with rules determining how to switch between them. The literature on robust control of complex nonlinear systems with set-valued equilibrium such as discontinuous systems using output information is very sparse. This project seeks to extend a framework that has been developed for output feedback control of continuous systems to robust control of complex discontinuous systems using only measured output information. The practical need for such a framework has been demonstrated by recent applications to biped robots, for example, from Chevallereau et al. (2003) and Westervelt et al. (2007) and is also supported by the needs of industry where tighter controls on efficiency are producing increasing levels of monitoring. Incorporating this information in the control loop is a natural next step and discontinuous systems often result. Theoretical developments will be facilitated by interaction between the proposed Visiting Researcher, Professor Orlov, who is a recognised expert on stability analysis and robust control synthesis of uncertain discontinuous systems within the framework of methods of nonsmooth Lyapunov functions and the PI, who is recognised for her work on robust sliding mode control and observation. The applied research will focus on the production of significant implementation studies relating to control of impact mechanical systems and the control of industrial production processes to demonstrate the efficacy of the underlying philosophy and the new design algorithms. These are pertinent design studies to inform the development of the theoretical research programme as well as being used to illustrate the research outcomes.

Publications

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Description Discontinuous (or switched) systems are present in many significant application areas such as economics, electrical circuit theory, mechanical engineering (impact theory, plasticity theory), biosciences, systems and control theory. Such systems are typically viewed as a finite family of subsystems, equipped with rules determining how to switch between them. The analysis and control of such complex systems is challenging and the desire to achieve results which will establish finite time behaviours adds to the complexity of the problem. Many important classes of dynamical system exhibit finite time behaviours e.g. cycle of a cell or the gait cycle of a biped robot. The contact of a foot with the ground creates impact, for example, and discontinuity is frequently found as a result of evolution in biology where cells or organisms exist at any particular time in one of several mutually exclusive states. The application of classical analysis tools that are based upon analysing differential equations where the solutions are defined over an infinite time span are limiting in such contexts. This project has involved a blend of theoretical development and practical implementation, where exploiting the synergy between the two areas has been an important focus. The project has developed frameworks for stability analysis that readily translate into constructive methods which can be applied to practical problems. The ability to deal with uncertainty has also been an important focus. The classes of dynamical systems under consideration are highly complex and there will be a mismatch between the system itself and the model used for design and analysis. The analysis tools resulting from this project have been able to prescribe finite time stability in the presence of such bounded uncertainty. Further, the control paradigm developed enables a designer to specify a desired finite settling time. A controller parameterisation is returned which will ensure the desired settling time is achieved. The methodology has been demonstrated with application to a fully actuated biped robot where a robust controller with a priori determined controller gains achieves a given finite settling time for reference trajectory tracking. Each joint converges to the desired trajectory in the prescribed finite time period before the next impact occurs with the ground. The control signal is smooth thus ensuring abrupt changes in the applied torque do not cause the robot to trip and fall. An electronic circuit implementation has been developed to move the results of the theoretical elements of the project into an environment that can be readily demonstrated to industry and business hence facilitating technology transfer.
Exploitation Route JLR are fully funding a PhD studentship which is seeking to develop regenerative ABS systems for next generation electric vehicles. The fundamental work accomplished within this EPSRC grant on controller and observer developments will be used in the current project.
The results are underpinning and thus have the potential to contribute in any sector where efficiency is key to improving productivity.
Sectors Aerospace, Defence and Marine,Agriculture, Food and Drink,Electronics,Energy,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Transport

 
Description Public lectures have been presented in various locations within the UK relating to the application of control not just in classical engineering situations but also considering control systems appearing in biology.
First Year Of Impact 2015
Sector Education
Impact Types Societal

 
Description EPSRC
Amount £329,465 (GBP)
Funding ID EP/J018295/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 07/2012 
End 06/2015