Frank Woittennek

• Doctor of Engineering
• Professor (Full) at UMIT - Private Universität für Gesundheitswissenschaften, Medizinische Informatik und Technik

Open-loop control design for a one-dimensional shallow water model with moving boundary and arbitrary cross section is considered. Despite the moving boundary, the transition to material-fixed coordinates allows to reformulate the model on a constant spatial domain. The focus is on achieving smooth transitions between steady states. Apart from the...

An efficient approach to compute near time-optimal trajectories for linear kinematic systems with oscillatory internal dynamics is presented. Thereby, kinematic constraints with respect to velocity, acceleration and jerk are taken into account. The trajectories are composed of several motion primitives, the most crucial of which is termed jerk segm...

A fast algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. In this algorithm, trajectories are assembled from special motion primitives called jerk segments, which are connected by segments of constant acceleration and velocity respectively. It was shown, that...

One‐dimensional distributed‐parameter systems consisting of several convection‐reaction equations, which are distributedly coupled with a reaction equation, are considered. To solve the open‐loop control problem for these kind of systems, an inversion‐based approach is proposed. Along the common characteristic projection, the system can be reduced...

In this study, we introduce higher‐order approximation schemes for a 1D shallow‐water model with a moving boundary and arbitrary cross‐section. The model equations are formulated using Lagrange coordinates to handle the time‐varying spatial domain. By discretizing the action functional on a material‐fixed grid and applying an appropriate quadrature...

This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based control...

This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based control...

This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based control...

Zusammenfassung Das VGF-Verfahren ist ein moderner Prozess zur Züchtung von Einkristallen, der Grundlage für nahezu alle elektronischen Anwendungen. Die sukzessive Erstarrung der Schmelze zum Einkristall wird dabei durch geeignete Ansteuerung der als Aktoren in der Anlage zur Verfügung stehenden Heizer realisiert. Dieses Regelungsproblem ist Gegens...

Infinite-dimensional linear systems with unbounded input and output operators are considered. For the purpose of finite-dimensional observer-based state feedback, an observer approximation scheme will be developed which can be directly combined with existing late-lumping controllers and observer output injection gains. It relies on a decomposition...

Distributed-parameter systems represented by linear one-dimensional 2 × 2 hyperbolic PDEs with nonlinear finite-dimensional differentially flat dynamics at one boundary and control acting linearly via the opposite boundary are considered. Flatness of the overall system, deduced from the flatness of the boundary system, allows for the parametrizatio...

Flatness-based control schemes for a heavy rope with freely movable suspension point are compared in simulation and experiment. These schemes are based on a nonlinear distributed parameter model (DPM) of the chain and two different approximations, firstly a rigid body approximation as a physical pendulum, secondly a tangent linearization of the ori...

Late-lumping feedback design for infinite-dimensional linear systems with unbounded input operators is considered. The proposed scheme is suitable for the approximation of backstepping and flatness-based designs and relies on a decomposition of the feedback into a bounded and an unbounded part. Approximation applies to the bounded part only, while...

Modeling and simulation of shallow water waves in a tube with moving boundary and arbitrary cross-section are considered. Based on the a variational formulation of the well known one dimensional Saint-Venant equations in material fixed coordinates, energy-conserving finite-dimensional approximations are directly derived by the principle of least ac...

Two nonlinear infinite dimensional models of a Lithium-ion battery are introduced. The proposed models interpolate linear fractional models which are obtained from a widely spread equivalent circuit model. The linear models are parameterized by means of so-called dynamic impedance measurements, i.e. impedance measurements in several operating point...

Zusammenfassung Der Beitrag behandelt die Folgeregelung von Flachwasserwellen in einer partiell gefüllten Röhre, in der der Flüssigkeitspegel durch einen beweglichen Kolben variiert werden kann. Zur Beschreibung der Flachwasserwellen werden die Saint-Venant-Gleichungen in Euler-Koordinaten verwendet, ein quasilineares hyperbolisches Differentialgle...

Zusammenfassung Es werden verteilt-parametrische Modelle hergeleitet, die das nichtlineare fraktionale Verhalten von Lithium-Ionen-Zellen beschreiben. Die vorgestellten Modelle interpolieren lineare verteilt-parametrische Kleinsignalmodelle, die sich als diffusive Realisierungen fraktionaler Übertragungsfunktionen in den Arbeitspunkten ergeben. Die...

Non-collocated feedback control of water waves in a tube with moving boundary described by the one-dimensional Saint-Venant equations is considered. Two control approaches are developed both relying on a measurement of the water level at the non-actuated boundary. Firstly, a flatness based approach for a partially linearized model of the system is...

Non-collocated feedback control of water waves in a tube with moving boundary described by the one-dimensional Saint-Venant equations is considered. Two control approaches are developed both relying on a measurement of the water level at the non-actuated boundary. Firstly, a flatness based approach for a partially linearized model of the system is...

The hyperbolic distributed-parameter system under consideration comprises a second-order partial differential equation that is bidirectionally coupled with a first-order ordinary differential equation. The system models the transmission at a pneumatic test bench with boundary control and collocated measurement, yet stands in place for several other...

In this contribution, tracking control designs using output feedback are presented for a two-phase Stefan problem (SP) arising in the modeling of the vertical gradient freeze process. The two-phase SP, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying spatial extent of t...

Dieser Beitrag befasst sich mit der zeitoptimalen Trajektorienplanung von Portalsystemen. Die betrachtete Konfiguration besteht aus zwei parallelen H-Portalen, welche sich durch eine elastische Kopplung im Grundgestell gegenseitig beeinflussen. Es wird ein Optimalsteuerungsproblem zur Planung einer Ruhelagenüberführung formuliert, welches die nicht...

Efficient late‐lumping strategies for transformation‐based observers for distributed parameter systems are discussed. This is achieved by extending previously introduced ideas for the approximation of state‐feedback designs to the observer gain approximation for Riesz spectral systems.

Open-loop control design for a fluid in a pipe is considered. The position (resp. the velocity) of a piston moving within the tube acts as control input. The system dynamics are described by the so-called Saint-Venant equations with a moving boundary condition. Rest-to-rest transitions are parameterized by means of the so called flatness-based appr...

Various models describing a plug flow through a pipe are used for model-based control design in industrial processes. This contribution presents a feed-forward controller based on a new modeling approach for plug flow through a pipe. The latter model combines the advantages of partial-differential and delay-differential equation approaches. This st...

Bei hochpräzisen Positionieraufgaben kommt es häufig zu elastischen Verformungen in der Größenordnung der gewünschten Positioniergenauigkeit im zu regelnden System. Werden diese Verformungen nicht durch Sensoren gemessen, kann mittels Anpassung der Referenztrajektorie die unerwünschte Schwingung unterdrückt werden. In diesem Beitrag werden drei ver...

This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varyi...

This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varyi...

Various models describing a plug flow through a pipe are used for model-based control design in industrial processes. This contribution presents a feedforward controller based on a new modeling approach for plug flow through a pipe. The latter model combines the advantages of partial differential and delay differential equation approaches. This str...

A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used one-dimensional distributed parameter model, which explicitly takes into account the heat capacity of the jacket of the pipe. The main result of the present contribution is the constitution of the equivalence...

Model based approaches are used for the control of exhaust emissions of gas engines to observe the national regulations. As a consequence sophisticated control oriented models are needed, capable to reproduce the essential behaviour of the SCR catalysts. Besides the physical modelling the experimental parameter-identification of the models is one o...

A novel continuously working force regulation algorithm aimed for the pick-and-place-units in a thermo-compression bonding application is proposed. The system setup considered consists of two co-linearly mounted axes. The larger of these axes is responsible for an accurate positioning. The controller of the smaller axis, which is mounted on the sli...

In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying extent of the...

Control design for a fluid in a pipe with arbitrary cross-sectional area is considered. The position (resp. the velocity) of a piston moving within the tube acts as control input. The system dynamics are described by the so-called Saint-Venant equations defined on a varying spatial domain. The flatness-based approach is utilized in order to paramet...

A novel continuously working force regulation algorithm aimed for the pick-and-place-units in a thermo-compression bonding application is proposed. The system setup considered consists of two co-linearly mounted axes. The larger of these axes is responsible for an accurate positioning. The controller of the smaller axis, which is mounted on the sli...

In many cases handling processes rely on precise and fast pick-and-place operations. This may be achieved by means of so-called H-gantry systems. In order to increase the throughput of such devices they are often extended by a second, asynchronously working gantry. Due to the finite stiffness of the mounting base of the linear motors and vibrations...

A novel approach to the efficient numerical approximation and implementation of transformation based state feedback originating from backstepping or flatness based approaches is applied to a flatness based feedback law for the so called heavy rope system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Force regulation is an important topic in pick-and-place applications. To this end, a novel control concept for a setup consisting of two serially and co-linearly mounted axes is proposed. The position trajectory of the larger axis is tracked by a standard PD-controller. The feedback-law for the second and smaller axis mounted on the slide of the l...

Zusammenfassung Im Beitrag wird das thermische Verhalten von durchströmten Rohren untersucht. Dazu werden detaillierte physikalische Modelle unterschiedlicher Komplexität hergeleitet, wobei die Wärmespeicherfähigkeit der Rohrwand jeweils explizit berücksichtigt wird. Für die vorgeschlagenen verteilt-parametrischen Modelle werden geschlossene Lösung...

This paper presents an approach for the efficient numerical implementation of transformation based state feedback laws for linear distributed parameter systems. The control laws considered may originate from backstepping or flatness-based design methods. They are, therefore, directly based on the underlying distributed parameter systems. In general...

Für die Bestückung von Mikrochips in der Halbleiterindustrie werden häufig Flächenportale herangezogen, da diese schnelle und sehr präzise Positionswechsel ermöglichen. Um den Durchsatz zu steigern, gibt es Anwendungsfälle, bei denen Antriebstechnologien mit zwei Portalschlitten zum Einsatz kommen. Bedingt durch diesen Aufbau können allerdings uner...

Zusammenfassung Der Entwurf invarianter Folgeregler für allgemeine nicht-holonome n -Anhänger-Systeme wird diskutiert. Zwei Fälle werden betrachtet: Für das allgemeine 1-Anhänger-System wird auf der Basis bekannter Ergebnisse zur Flachheit dieses Systems ein Regler vorgeschlagen. Für das allgemeine nicht-flache n -Anhänger-System ( n > 1) wird ein...

In this contribution we present a new variant for the well-known buck converter. We substitute the lumped parameter components of the circuit by the distributed parameter model of a transmission line. For discussion, methods for modeling and simulation will be explained followed by some simulation results.

Zusammenfassung In diesem Beitrag wird ein neues Sensorprinzip für einen Tastsensor vorgestellt, das auf der Verformung eines elastischen Kontinuums beruht. Mit Hilfe eines mathematischen Modells des Kontinuums sollen örtlich verteilte Kontaktkräfte aus der mit einer Kamera gemessenen Deformation berechnet werden. Die Lösbarkeit dieses Problems wir...

Zusammenfassung Für lineare parabolische Systeme mit punktförmigem inneren Eingriff werden Zustandsrückführungen entworfen. Dazu wird die Zustandsäquivalenz dieser Systeme zu randgesteuerten Systemen gezeigt, für die der Reglerentwurf mit Hilfe der bekannten Backstepping-Methode erfolgt. Für die Implementierung der untersuchten Methode wird ein lei...

This contribution deals with the feed-forward control design for distributed parameter systems governed by quasi-linear hyperbolic equations. This is achieved in two steps: Firstly, the basic ideas underlying existing flatness-based approaches to nonlinear distributed parameter systems are restated in a general form. As a result the control problem...

State feedback design for linear parabolic systems with in-domain actuation and general Robin boundary conditions is considered. To this end the system is shown to be state equivalent to a boundary controlled system. By means of the backstepping transformation the latter system is shown to be feedback equivalent to a stable parabolic equation. With...

Observer design for 1D linear distributed parameter systems of hyperbolic type with boundary measurement is discussed. The approach is based on the observer canonical form introduced on the basis of a functional-differential equation (f.d.e.) equivalent to the original posed boundary value problem. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim...

Considered is the feed-forward control design for an elastic heavy rope that is model by a quasilinear partial differential equation of hyperbolic type. The problem is solved by means of a flatness-based approach that involves the solution of a Cauchy problem associated with the model equation. Simulation results are given to illustrate the results...

The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oil well drilling system. The considered model consists of a system of wave equations with non-linear coupled boundary conditions. We propose a flatness-based control approach to tackle the trajectory tracking problem guaranteeing th...

The main purpose of this study is the control of both axial and torsional vibrations occurring along a rotary oil well drilling system. The considered model consists of a system of wave equations with non-linear coupled boundary conditions. We propose a flatness-based control approach for suppressing harmful dynamics. Moreover, numerical simulation...

ISBN: 978-9973-0-0852-7; 1er trimestre 2009 Il est bien admis et depuis longtemps que les mathématiques constituent un passage obligatoire pour tout développement en matière de recherche et développement. Plusieurs outils sont actuellement disponibles sous forme de programmes permettant à l’ingénieur et au chercheur de résoudre le problème qui se p...

An efficient and well-established technology for power transmission across long distances is high-voltage direct current transmission (HVDC). However, HVDC is currently almost completely limited to peer-to-peer connections or networks with peers situated closely to each other. This contribution introduces the flatness-based design of a feed-forward...

The control of linear time-invariant systems with incommensurate lumped and distributed delays is addressed. Using a module-theoretic point of view where these systems are modules over the ring of entire functions in ℝ(s)[e− τ s ] necessary and sufficient conditions for the freeness of these modules are presented. If these conditions hold a module...

State feedback design for linear parabolic systems with in-doma general Robin boundary conditions is considered. To this end the system is equivalent to a boundary controlled system. By means of the well establis transformation this latter system is feedback equivalent to a stable parabolic the contribution previous results concerning systems with...

The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays as representation of a coupled system of transport processes and ordinary differential equations. These time-delay systems can be represented by modules over a rin...

State feedback design for a hybrid system consisting of a spatially one-dimensional second order hyperbolic distributed parameter systems with spatially dependent coefficients and a finite dimensional linear system is considered. The approach relies on the flatness based parametrization of the solutions which is obtained by integration along the ch...

For the well-known buck converter, we replace the inductor and capacitor by a transmission line. In other words, the lumped reactive elements are substituted by a distributed element. This results in a completely different type of the model. Instead of ordinary differential equations as for the classical buck converter, we obtain a set of partial d...

Zusammenfassung Im Beitrag wird eine Methode zur Bestimmung der Parameter in linearen verteiltparametrischen Systemen vorgestellt. Der Ansatz basiert auf der Herleitung eines linearen Systems von Faltungsgleichungen aus der gegebenen Randwertaufgabe und der anschließenden Elimination nicht gemessener Systemgrößen aus diesem Gleichungssystem. Dies f...

Observer design for a class of distributed parameter systems based on the so called hyperbolic observer canonical form (o.c.f.) is considered. The method relies on the tight relation between hyperbolic d.p.s. and functional differential equations (f.d.e.). Based on an input-output description given in form of a f.d.e. and a parametrization of the o...

Parameter identification in infinite-dimensional systems with lumped measurements is considered. The proposed method is based on a convolutional input-output relation of the underlying system of partial differential equations. The derivation of this input-output relation is presented in a framework involving (ultra-)distributions. The unknown param...

A method is presented that allows for the identification of parameters in systems described by linear partial differential equations with spatially dependent coefficients. The approach uses operational calculus to generate equations that involve only convolution products of known (boundary) measurements and the system parameters. In particular, a h...

Identification of physical parameters in systems modelled by linear partial differential equations (p.d.e.) from lumped measurements is considered. The problem is solved by means of an alternative formulation of the boundary value problem as convolutional system. The approach allows for the identification even in the presence of non-homogeneous ini...

Zusammenfassung Vorgestellt wird eine Methode zur Identifikation von Parameter eines linearen, verteiltparametrischen Modells für das schwere Seil unter ausschließlicher Verwendung gemessener Randgrößen. Die Methode basiert auf der Operatordarstellung der Lösung des zugehörigen Randwertproblems. Aus dieser erhält man durch sukzessives Falten der ge...

Zusammenfassung Der Beitrag behandelt den Entwurf von Zustandsrückführungen für hyperbolische Systeme mit örtlich verteilten Parametern in einer Ortsdimension. Grundlage für den Entwurf sind hyperbolische Regelungs- und Beobachterformen. Die Transformation in diese speziellen Zustandsdarstellungen wird mit Hilfe flachheitsbasierter Methoden berechn...

Linear systems with lumped and distributed delays can be represented by modules over an appropriate ring of entire functions. While in the case of commensurate delays spectral controllability is sufficient for the existence of a basis of this module, in the incommensurate case addressed here additional conditions are required. Exploiting the relati...

Der Vortrag beschäftigt sich mit dem flachheitsbasierten Entwurf von Zustandsreglern für lineare Systeme mit örtlich verteilten Parametern in einer unabhängigen Ortsvaria-blen. Im Mittelpunkt stehen dabei Modelle, die mit Hilfe hyperbolischer partieller Diffe-rentialgleichungen beschrieben werden. Einige wesentliche Grundideen der vorgestellten Ans...

Flatness based analysis and closed loop control design for networks of hyperbolic p.d.e.'s is considered. To this end a state space description is assigned to the flatness based parametrization of the input trajectories. Stabilization of this system by state feedback is discussed. By means of a state transformation which directly follows from the p...

For linear delay systems with incommensurate (lumped) delays necessary and sufficient conditions for the freeness of the system over the ring of entire functions in are given. In contrast to the commensurate case the ring does not have the Bézout property. Therefore, additional criteria are needed involving also special properties of pure delay sys...

A flatness based approach to the analysis of state controllability of systems described by one or more boundary coupled 1D hyperbolic second order equations is analyzed on the basis of a nontrivial example. Introducing a state which corresponds to the parametrization of the solution trajectories by a so called flat output and establishing the state...

An efficient and well-established technology for power transmission across long distances is high voltage direct current transmission (HVDC). However, HVDC is up to now almost completely limited to peer-to-peer connections or networks with peers situated closely to each other. This contribution introduces the flatness-based design of a feedforward...

Invariant tracking control design for control systems in state rep-resentation with classical Lie point symmetry is considered. The relevance of the invariance aspect is motivated by an exemplary control design for the kine-matic car. Introducing the perpendicular distance between the position of the rear axle midpoint and the reference trajectory...

A flatness based approach to the analysis of state controllability of systems described by one or more boundary coupled 1D hyperbolic second order equations is proposed. To this end, the controllability problem is reduced to an interpolation problem for the trajectory of a so called flat output. The associated state transformations to the flat outp...

A flatness-based feed-forward control design approach for an open channel flow modelled by the shallow water equations is discussed. The control input consists of the adjustable height of opening of a delimiting sluice gate. In order to compute the trajectory of the control input, the physical boundaries containing the control input are neglected a...

Stable trajectory tracking by boundary control is discussed for a string with a mass at its free end. Based on the known fact that the ring of operators used to describe the system is a Bézout ring it is shown that predictions are not required for stabilization if distributed delays are admitted. The method is rather general for systems of boundary...

Planar tree-like structures consisting of rigid links with rotational joints are considered. These models can be used to describe the dynamics of planar biped robots, in particular during the single support phase. Another simple structure of this type is the so-called acrobot. In both cases, the base joint is unactuated while motors are available a...

Zusammenfassung Für örtlich eindimensionale semilineare hyperbolische Systeme werden die Trajektorienplanung und der Steuerungsentwurf betrachtet. Eine “flachheitsbasierte” Methode wird exemplarisch anhand eines durch Transportgleichungen beschriebenen Rohrreaktors untersucht, der gegebenenfalls über ein als Wärmetauscher fungierendes zweites Rohr...

Zusammenfassung Es werden lineare verteiltparametrische Modelle betrachtet, die sich durch die Zusammenschaltung einzelner Randwertaufgaben ergeben, in denen die partiellen Differentialgleichungen von zweiter Ordnung sind. Im Laplace-Bildbereich können diese Modelle durch lineare Gleichungssysteme beschrieben werden, deren Koeffizienten einem spezi...

We discuss controllability of systems that are initially given by boundary coupled PDEs of second order. These systems may be described by modules over particular rings of distributions and ultradistributions with compact support arising from the solution of the Cauchy problem of the PDE under consideration with data on the time axis. We show that...

One dimensional boundary value problems with lumped controls are considered. Such systems can be modeled as modules over a ring of Beurling ultradistributions with compact support. This ring appears naturally from a corresponding Cauchy problem. The heat equation with different boundary conditions serves for illustration.

Trajectory planning and open loop control design for semi-linear hyperbolic systems in one space dimension is considered. A “flatness based” method is introduced on an example of a convection dominated tubular reactor with heat exchanger. More generally, the method applies to boundary value problems that can be translated into Cauchy problems w.r.t...