Research objectives and content
The widespread existence of chaotic dynamical systems in physical systems has fostered great interest in the development of practical chaos control techniques. The extreme sensitivity and complex behaviour that characterize chaotic systems prohibit long-range prediction of their behaviour but paradoxically allow one to control them with tiny perturbations. Chaos control techniques exploit the sensitivity of chaos to initial conditions by applying feedback perturbations to an accessible system parameter such that the system's state point is attracted towards the stable direction of a targeted unstable periodic orbit (UPO). This is the base of the well-known Ott-Grebogi-Yorke (OGY) approach. However, the OGY technique is limited to the control of low-dimensional systems and, hence, it is not applicable to the majority of real-world (i.e. high-dimensional) systems. For this reason new algorithms and control techniques have to be developed. On the other hand, impact oscillators occur in many technical situations. Mechanical collisions are ubiquitous in manufacturing, engineering, sports and every day life. A classical example occurs in loose fitting joints which are designed in most mechanical devices to allow for thermal expansion. These systems, even the simplest ones, exhibit a rich bifurcation behaviour in going from periodic motion to chaos. Furthermore, it has been seen that they are high-dimensional, i.e. they have more than one positive Lyapunov exponent, and hence, the control of such devices poses a challenging problem with many practical applications. The main research objective of this proposal is to develop, implement and test experimentally control algorithms able to stabilize impact systems. Different chaos control algorithms and recently developed nonlinear control techniques will be modified to deal with impact systems.
Training content (objective, benefit and expected impact)
The work will produce a family of nonlinear controllers able to stabilize unstable periodic orbits on impact oscillators. This is expected to be applicable in many practical cases to improve the performance of a considerable number of industrial devices. The possibility of developing, implementing and testing a number of control techniques will increase considerably my actual competencies. The results of this research will be disseminated through scientific publications, patents as well as direct contacts with interested industry, i.e. car manufacturing, industrial machines, building firms, etc. I expect to gain further knowledge on control and improve my skills in practical development and experimental verification of control devices.
Links with industry / industrial relevance (22)
This research is related to the BRITE Project ACE (Active Control in Civil Engineering) (BRPR-CT97-0402) carried out in collaboration with construction and control industries, for example: Bouygues (France), DRA and CEG Marconi (UK), Mannesmann (Germany), etc. Therefore, collaboration and feedback from industry is expected during this work.