Energy-Optimal Control of Over-Actuated Systems - with Application to a Hybrid Feed Drive

Over-actuated (or input-redundant) systems are characterized by the use of more actuators than the degrees of freedom to be controlled. They are widely used in modern mechanical systems to satisfy various control requirements, such as precision, motion range, fault tolerance, and energy efficiency. This thesis is particularly motivated by an over-actuated hybrid feed drive (HFD) which combines two complementary actuators with the aim to reduce energy consumption without sacrificing positioning accuracy in precision manufacturing. This work addresses the control challenges in achieving energy optimality without sacrificing control performance in so-called weakly input-redundant systems, which characterize the HFD and most other over-actuated systems used in practice. Using calculus of variations, an optimal control ratio/subspace is derived to specify the optimal relationship among the redundant actuators irrespective of external disturbances, leading to a new technique termed optimal control subspace-based (OCS) control allocation. It is shown that the optimal control ratio/subspace is non-causal; accordingly, a causal approximation is proposed and employed in energy-efficient structured controller design for the HFD. Moreover, the concept of control proxy is proposed as an accurate causal measurement of the deviation from the optimal control ratio/subspace. The proxy enables control allocation for weakly redundant systems to be converted into regulation problems, which can be tackled using standard controller design methodologies. Compared to an existing allocation technique, proxy-based control allocation is shown to dynamically allocate control efforts optimally without sacrificing control performance. The relationship between the proposed OCS control allocation and the traditional linear quadratic control approach is discussed for weakly input redundant systems. The two approaches are shown to be equivalent given perfect knowledge of disturbances; however, the OCS control allocation approach is shown to be more desirable for practical applications like the HFD, where disturbances are typically unknown. The OCS control allocation approach is validated in simulations and machining experiments on the HFD; significant reductions in control energy without sacrificing positioning accuracy are achieved.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146104/1/molong_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