Regeneratively and Passively Constrained Control of Vibratory Networks

This dissertation is focused on the control of vibratory networks. Mechanical examples of vibratory systems include a civil structure, automobile, and a cantilever beam. These systems are excited by external disturbances such as earthquakes, wind, or uneven road elevations. Both passive and active control laws can be utilized to suppress vibrations in these networks. Each type of control law possesses inherent advantages and drawbacks. Active control provides the highest performance but is expensive, relies on an external power source, and is complicated to implement and maintain. Passive control devices (composed of springs, inertial elements, dashpots) represent the cheapest option and provide energy-autonomy, but have inferior performance when compared to an active control device. Due to their reliability and low cost, passive control technologies set the baseline for comparison for other, more sophisticated technologies. On the other hand, although it yields superior performance, active control presumes availability of unlimited energy, which may be an impractical or unreliable assumption. This dissertation examines a new class of control technologies, called regenerative control systems. A regenerative control system theoretically possesses energy-autonomy, but does so with better performance when compared to a passive control system. However, regenerative control devices are more expensive than passive and therefore the improved performance they attain must warrant utilization. A regenerative control device is assumed to be connected to a large energy storage device (battery, supercapacitor, etc). At times, the control device will draw energy from the energy storage device in order to actuate the network. At other times, the control device converts mechanical energy from the network into electrical energy and replenishes the energy in the storage device. The regenerative controller is constrained such that, on average, it generates more energy than it expends. This constraint, which is a relaxation of a passive control law constraint, ensures the local energy storage device never completely depletes. One of the main focuses of this research is to develop theory which can can solve for optimal regenerative and passive control laws. Optimizing control laws for both types of technology, in the context of the same problem, allows for a fair comparison.The regenerative control design problem can be formulated as a convex optimization and therefore can be solved easily with many commercial solvers. Passively constrained control design is a nonconvex problem and a new technique, Iterative Convex Over-Bounding (ICO) is proposed and developed to solve this nonconvex optimization. We show that optimal regenerative control outperforms optimal passive control if parasitic losses are sufficiently small. We also propose a technique to quantify how large the parasitics can be for a regenerative controller to still outperform a passive controller for a given problem.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138455/1/erwarner_1.pd

Entwurf robuster modellbasierter Fehlerisolationsfilter

Die vorliegende Arbeit behandelt den Entwurf robuster modellbasierter Fehlerisolationsfilter für lineare zeitinvariante Systeme. Die Verfahren erlauben eine zuverlässige Lokalisierung von Fehlern auf Basis eines quantitativen Systemmodells. Zunächst wird die Dualität des Fehlerisolationsproblems zu Methoden des Entkopplungsreglerentwurfes herausgearbeitet. Auf dieser Grundlage werden Methoden zum Entwurf von Fehlerisolationsbeobachtern präsentiert. Die Robustheit der Beobachter sowohl hinsichtlich exogener Störungen als auch bezüglich unsicherer Systemparameter wird dabei unter Rückgriff auf lineare Matrixungleichungen optimiert. Schließlich werden Fehlerisolationsfilter allgemeinerer Struktur betrachtet, die gegenüber den beobachterbasierten Methoden einen vereinheitlichenden Entwurf liefern. Dieser erfolgt optimierungsbasiert und erlaubt eine einfache Auslegung, bei der lediglich intuitive Parameter einzustellen sind