140 research outputs found
A new parametrization of observers
No full textThis paper extends and generalizes recent results on the characterization and parametrization of observers for linear systems in the behavioral framework. We formulate the results in the language of quotient signal modules that was developed by Oberst and first used in the context of observer theory by the first author. The resulting characterization of observers in terms of a generalized internal model principle is both elegant and concise. It includes all such results known to the authors as special cases, including the classical results for linear time-invariant state space systems. Moreover, this new characterization of observers leads to a clean and simple one-to-one parametrization result with only free parameters. This new parametrization allows to decide certain additional observer properties (such as input/output structure or nonintrusiveness) purely by inspection
Trumpf : the story of a family business
No full textIngenuity, entrepreneurial courage and a very special company culture - these are the hallmarks of TRUMPF, and these are the qualities that have turned the company based in Ditzingen, Germany, into the world's leading manufacturer of machine tools. This detailed history of TRUMPF written by Jochen Streb offers both fascinating and instructive insights into German economic history from the 1920s to today
Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs
No full textAbstract not availableAlireza Khosravian, Jochen Trumpf, Robert Mahony, Christian Lagema
Observers for linear time-varying systems
No full textWe give characterizations and necessary and sufficient existence conditions for track-ing and asymptotic observers for linear functions of the state of a linear finite-dimensional time-varying state space system. We specialize the results to affine parameter varying systems and bilinear control systems
Observers for linear time-varying systems
No full textAbstractWe give characterizations and necessary and sufficient existence conditions for tracking and asymptotic observers for linear functions of the state of a linear finite-dimensional time-varying state space system. We specialize the results to affine parameter varying systems and bilinear control systems
Dead-zone compensation via passivity-based control for a class of mechanical systems
No full textThis manuscript introduces a passivity-based control methodology for fully-actuated mechanical systems with symmetric or asymmetric dead-zones. To this end, we find a smooth approximation of the inverse of the function that describes such a nonlinearity. Then, we propose an energy and damping injection approach — based on the PI-PBC technique — that compensates for the dead-zone. Moreover, we provide an analysis of the performance of the proposed controller near the equilibrium. We conclude this paper by experimentally validating the results on a two degrees-of-freedom planar manipulator.</p
Nonlinear MPC for Tracking Piecewise-Constant Reference Signals: the Positive Semidefinite Stage Cost Case
No full textModel Predictive Control (MPC) is a successful control strategy, with solid theoretical and practical backgrounds. Currently, several stabilizing MPC formulations are available to deal with tracking of piecewise constant references. In particular, it is well understood that, in many cases, the use of artificial reference variables in the optimisation problem allows to sensibly extend the region of attraction of the controller. This work proposes a modified MPC for tracking formulation which is able to guarantee nominal stability also in presence of positive semidefinite stage cost. This can be particularly useful when dealing with high order and/or black-box models, as it allows penalizing the outputs or a subset of states of the system without compromising stability. The algorithm design is based on terminal ingredients and a cost detectability assumption which is explicitly accounted for in the algorithm formulation. Such assumption can be verified by means of input-output-to-state stability arguments, as well as dissipativity ones, thus exploiting techniques already available in the literature
System of Qualitative Auditing of Processes in a Selected Company
No full textDiplomová práce na téma Systém kvalitativního auditování procesů ve vybraném podniku se zabývá systémem managementu kvality a auditování ve skupině TRUMPF. Práce se zaměřuje především na zlepšení dálkového auditování dodavatelů ve společnosti TRUMPF Liberec, s r.o. Hlavním cílem diplomové práce je vytvoření konceptu dálkového auditování dodavatelů ve společností TRUMPF Liberec. První část diplomové práce pojednává o teoretických východiscích spojených se systémem managementu kvality a auditování. Následně je podrobně popsán systém managementu kvality a auditování ve skupině TRUMPF, a to včetně podpůrných informačních systémů, které jsou k tomu využity. Autor se úžeji zaměřil na proces dálkového auditování dodavatelů ve společnosti TRUMPF Liberec. Nejprve byl zmapován a analyzován předchozí stav a následně byl představen současný průběh procesu dálkového auditování dodavatelů, který zahrnuje změny navržené autorem práce. Závěr diplomové práce tvoří shrnutí všech poznatků autora a doporučení pro další rozvoj.The master thesis on the topic of System of quality auditing of processes in a selected company explores the system of quality management and auditing in the TRUMPF Group. Its main focus is the improvement of remote auditing of suppliers for the company TRUMPF Liberec, s r.o. The main objective of the thesis is to create a concept of remote auditing of suppliers in TRUMPF Liberec. The first part of the thesis is concerned with theoretical background related to the quality management system and auditing. Further, interpretations of the quality management and auditing system in the TRUMPF Group and the supporting information systems used for this purpose are presented. The author focuses more closely on the depiction of the process of remote auditing of suppliers in TRUMPF Liberec, a mapping of the previous state and a presentation of the current state, which includes changes proposed by the author of the thesis. The conclusion ends with a summary of all the author's findings and recommendations for further development.
Über die Geometrie und Parametrisierung von fast invarianten Unterräumen und Beobachtertheorie
No full textIn my Ph.D. thesis "On the geometry and parametrization of almost invariant subspaces and observer theory" I consider the set of almost conditioned invariant subspaces of fixed dimension for a given fixed linear finite-dimensional time-invariant observable control system in state space form. Almost conditioned invariant subspaces were introduced by Willems. They generalize the concept of a conditioned invariant subspace requiring the invariance condition to hold only up to an arbitrarily small deviation in the metric of the state space. One of the goals of the theory of almost conditioned invariant subspaces was to identify the subspaces appearing as limits of sequences of conditioned invariant subspaces. An example due to {\"O}zveren, Verghese and Willsky, however, shows that the set of almost conditioned invariant subspaces is not big enough. I address this question in a joint paper with Helmke and Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003). Antoulas derived a description of conditioned invariant subspaces as kernels of permuted and truncated reachability matrices of controllable pairs of the appropriate size. This description was used by Helmke and Fuhrmann to construct a diffeomorphism from the set of similarity classes of certain controllable pairs onto the set of tight conditioned invariant subspaces. In my thesis I generalize this result to almost conditioned invariant subspaces describing them in terms of restricted system equivalence classes of controllable triples. Furthermore, I identify the controllable pairs appearing in the kernel representations of conditioned invariant subspaces as being induced by corestrictions of the original system to the subspace. Conditioned invariant subspaces are known to be closely related to partial observers. In fact, a tracking observer for a linear function of the state of the observed system exists if and only if the kernel of that function is conditioned invariant. In my thesis I show that the system matrices of the observers are in fact the corestrictions of the observed system to the kernels of the observed functions. They in turn are closely related to partial realizations. Exploring this connection further, I prove that the set of tracking observer parameters of fixed size, i.e. tracking observers of fixed order together with the functions they are tracking, is a smooth manifold. Furthermore, I construct a vector bundle structure for the set of conditioned invariant subspaces of fixed dimension together with their friends, i.e. the output injections making the subspaces invariant, over that manifold. Willems and Trentelman generalized the concept of a tracking observer by including derivatives of the output of the observed system in the observer equations (PID-observers). They showed that a PID-observer for a linear function of the state of the observed system exists if and only if the kernel of that function is almost conditioned invariant. In my thesis I replace PID-observers by singular systems, which has the advantage that the system matrices of the observers coincide with the matrices appearing in the kernel representations of the subspaces. In a second approach to the parametrization of conditioned invariant subspaces Hinrichsen, M{\"u}nzner and Pr{\"a}tzel-Wolters, Fuhrmann and Helmke and Ferrer, F. Puerta, X. Puerta and Zaballa derived a description of conditioned invariant subspaces in terms of images of block Toeplitz type matrices. They used this description to construct a stratification of the set of conditioned invariant subspaces of fixed dimension into smooth manifolds. These so called Brunovsky strata consist of all the subspaces with fixed restriction indices. They constructed a cell decomposition of the Brunovsky strata into so called Kronecker cells. In my thesis I show that in the tight case this cell decomposition is induced by a Bruhat decomposition of a generalized flag manifold. I identify the adherence order of the cell decomposition as being induced by the reverse Bruhat order.In meiner Doktorarbeit "On the geometry and parametrization of almost invariant subspaces and observer theory" betrachte ich die Menge der fast (C,A)-invarianten Unterräume fester Dimension zu einem vorgegebenen linearen endlichdimensionalen zeitinvarianten beobachtbaren Kontrollsystem in Zustandsraumdarstellung. Der Begriff der fast (C,A)-invarianten Unterräume geht auf Willems zurück. Er verallgemeinert das Konzept eines (C,A)-invarianten Unterraums dahingehend, daß die Invarianzeigenschaft nur bis auf eine beliebig kleine Abweichung in der Metrik des Zustandsraumes erfüllt sein muß. Eines der Ziele der Theorie der fast (C,A)-invarianten Unterräume war es, diejenigen Unterräume zu charakterisieren, die als Grenzwerte von Folgen (C,A)-invarianter Unterräume auftreten. Özveren, Verghese und Willsky haben jedoch ein Beispiel angegeben, das zeigt, daß die Menge der fast (C,A)-invarianten Unterräume hierfür nicht groß genug ist. Auf diese Problematik gehe ich in einer gemeinsamen Arbeit mit U. Helmke und P.A. Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003) ein, die nicht Teil meiner Dissertation ist. Antoulas hat eine Beschreibung von (C,A)-invarianten Unterräumen als Kerne von permutierten und abgeschnittenen Erreichbarkeitsmatrizen geeigneter Größe angegeben. Diese Beschreibung benutzen Fuhrmann und Helmke um einen Diffeomorphismus von der Menge der Ähnlichkeitsklassen bestimmter kontrollierbarer Matrizenpaare auf die Menge der "tight" (C,A)-invarianten Unterräume zu konstruieren. In meiner Dissertation verallgemeinere ich dieses Resultat auf fast (C,A)-invariante Unterräume, indem ich sie mit Hilfe von "restricted system equivalence"-Klassen kontrollierbarer Matrizentripel darstelle. Darüberhinaus identifiziere ich die kontrollierbaren Matrizenpaare, die in der Kerndarstellung (C,A)-invarianter Unterräume auftreten, als Korestriktionen des ursprünglichen Systems auf den jeweiligen Unterraum. Es besteht eine enge Verbindung zwischen (C,A)-invarianten Unterräumen und partiellen Beobachtern. In der Tat existiert ein "tracking" Beobachter für eine lineare Funktion des Zustandes des beobachteten Systems genau dann, wenn der Kern dieser Funktion (C,A)-invariant ist. In meiner Dissertation zeige ich, daß die Systemmatrizen der Beobachter mit den Korestriktionen des beobachteten Systems auf die Kerne der beobachteten Funktionen übereinstimmen. Diese wiederum stehen in enger Beziehung zu partiellen Realisierungen. Weiter beweise ich, daß die Menge der "tracking" Beobachter-Parameter fester Größe, das heißt der "tracking" Beobachter fester Ordnung zusammen mit den beobachteten Funktionen, eine glatte Mannigfaltigkeitsstruktur trägt. Ich konstruiere eine Vektorbündelstruktur auf der Menge der (C,A)-invarianten Unterräume fester Dimension zusammen mit ihren "Freunden", das heißt den "output injections", welche den jeweiligen Unterraum invariant machen, wobei die Beobachtermannigfaltigkeit als Basisraum dient. Willems und Trentelman haben das Konzept eines "tracking" Beobachter verallgemeinert, indem sie auch Ableitungen des Ausgangs des beobachteten Systems in die Beobachtergleichungen aufnahmen (PID-Beobachter). Sie haben gezeigt, daß ein PID-Beobachter für eine lineare Funktion des Zustands des beobachteten Systems genau dann existiert, wenn der Kern dieser Funktion fast (C,A)-invariant ist. In meiner Dissertation ersetze ich die PID-Beobachter durch singuläre Systeme, was den Vorteil hat, daß die Systemmatrizen des Beobachters mit den Matrizen übereinstimmen, die in der Kerndarstellung des Unterraums auftauchen. (C,A)-invariante Unterräume lassen sich auch als Bildräume von Block-Toeplitz-Matrizen beschreiben. Hinrichsen, Münzner und Prätzel-Wolters, Fuhrmann und Helmke, und Ferrer, F. Puerta, X. Puerta und Zaballa benutzen diesen Zugang, um eine Stratifizierung der Menge der (C,A)-invarianten Unterräume fester Dimension in glatte Mannigfaltigkeiten zu konstruieren. Diese sogenannten Brunovsky-Strata bestehen aus all den Unterräumen, für die die Einschränkung des Systems auf den Unterraum jeweils vorgegebene Beobachtbarkeitsindizes hat. Obige Autoren konstruieren auch eine Zellzerlegung der Brunovsky-Strata in sogenannte Kronecker-Zellen. In meiner Dissertation zeige ich, daß im "tight" Fall diese Zellzerlegung von einer Bruhat-Zerlegung einer verallgemeinerten Fahnenmannigfaltigkeit induziert wird. Ich identifiziere die Adhärenzordnung der Zellzerlegung als inverse Bruhat-Ordnung
- …
