Controller Design for Multistorey Buildings via Convex Optimisation
Abstract: Earthquakes, wind and traffic may cause unwanted vibrations in buildings. Vibration control devices are often installed between floors to suppress such disturbances. In the context of buildings, controllers are commonly designed using methods which are subject to a number of limitations: we cannot discuss optimal performance or conclude that no controller exists which satisfies a given set of design specifications. In this thesis, we address these shortcomings by considering convex optimisation for controller design in buildings. Given a restricted set of design specifications typical in vibration control, we show that the controller design problem may be formulated as a convex optimisation problem when the building is modelled as a chain of masses interconnected by linear springs and dampers. The design specifications for which this is shown are internal stability, achievability by some controller, and upper and lower bounds in the frequency and time domain. This method is then demonstrated for a chain of five masses subjected to an impulse. A set of controller design problems are formulated and solved using CVX in Matlab. A specific design problem is also solved for different finite-dimensional approximations, and the result suggests convergence to some minimum. Tradeoff curves comparing actuator effort to intermass displacement in both the frequency and time domain are successfully computed. These results are then compared with the performance of the corresponding passive system in which dampers have been added. It is found in particular that the greatest damper force can be over 200 times larger than that of an optimal controller achieving the same performance.
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