{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/279020"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/279020","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Disturbance Attenuation in Mass Chains with Passive Interconnection","abstract":"This thesis is concerned with disturbance amplification in interconnected systems which may consist of a large number of elements. The main focus is on passive control of a chain of interconnected masses where a single point is subject to an external disturbance. The problem arises in the design of multi-storey buildings subjected to earthquake disturbances, but applies in other situations such as bidirectional control of vehicle platoons. It is shown that the scalar transfer functions from the disturbance to a given intermass displacement can be represented as a complex iterative map. This description is used to establish uniform boundedness of the $\\mathcal{H}_\\infty$-norm of these transfer functions for certain choices of interconnection impedance. A graphical method for selecting an impedance such that the $\\mathcal{H}_\\infty$-norm is no greater than a prescribed value for an arbitrary length of the mass chain is given. A design methodology for a fixed length of the mass chain is also provided. A case study for a 10-storey building model demonstrates the validity of this method.","abstract_html":"This thesis is concerned with disturbance amplification in interconnected systems which may consist of a large number of elements. The main focus is on passive control of a chain of interconnected masses where a single point is subject to an external disturbance. The problem arises in the design of multi-storey buildings subjected to earthquake disturbances, but applies in other situations such as bidirectional control of vehicle platoons. It is shown that the scalar transfer functions from the disturbance to a given intermass displacement can be represented as a complex iterative map. This description is used to establish uniform boundedness of the <span class=\"etd-inline-math\">\\mathcal{H}<sub>\\</sub>infty</span>-norm of these transfer functions for certain choices of interconnection impedance. A graphical method for selecting an impedance such that the <span class=\"etd-inline-math\">\\mathcal{H}<sub>\\</sub>infty</span>-norm is no greater than a prescribed value for an arbitrary length of the mass chain is given. A design methodology for a fixed length of the mass chain is also provided. 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