Frank Woittennek

Controllability of Networks of Spatially One-Dimensional Second Order PDEs—An Algebraic Approach

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 those rings are Bezout domains. This property is utilized in order to derive algebraic and trajectory related controllability results.

Motion planning and open loop control design for linear distributed parameter systems with lumped controls

Motion planning and open loop boundary control schemes for linear spatially one dimensional distributed parameter systems with lumped control are discussed. Using Mikusińskis operational calculus the models are formulated as ordinary (operational) boundary value problems. Their solutions are parameterized by introducing a so-called basic variable as an appropriate free parameter. Particular classes of models considered lead to series representations involving derivatives of the basic variable of arbitrary order or to convolution operators which can be interpreted as distributed delays and advances. Examples of bending motions on a ring-shaped plate and a heat exchanger illustrate the results.

An algebraic approach to parameter identification in linear infinite dimensional systems

An algebraic approach to the identification of parameters in linear infinite dimensional systems is proposed. It is based on operational calculus. First, the method is derived for a system with delayed input and homogeneous initial conditions. A similar approach is applicable to systems described by linear partial differential equations. This is discussed for second order p.d.e., in particular for the one dimensional heat equation.

Controller Canonical Forms and Flatness Based State Feedback for 1D Hyperbolic Systems

Abstract 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 parametrization of the trajectories of the state variables, this feedback can be given in the original coordinates.

Boundary Value Problems and Convolutional Systems over Rings of Ultradistributions

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.

Flachheitsbasierte Randsteuerung von elastischen Balken mit Piezoaktuatoren (Flatness based Boundary Control of Piezoelectric Benders)

Für elastische Balken mit Piezoaktuatoren werden flachheitsbasierte Randsteuerungen entworfen, die eine Positionierung in endlicher Einstellzeit gestatten. Dabei werden sowohl Euler-Bernoulli-Balken als auch Timoshenko-Balken untersucht. Steuerungen für Balken mit mehreren Piezoaktuatoren werden durch Superposition berechnet. Die Methoden werden durch die Ergebnisse von Simulationen und eines Experiments illustriert.

Motion planning and feedback control of a planar robotic unicycle model

Abstract Open and closed loop control design for the planar motion of a unicycle model consisting of a double pendulum mounted on a rolling wheel is considered. The motion planning problem is solved by prescribing trajectories to the two pendulum angles, the wheel angle is then obtained by integrating twice. A feedforward control trajectory directly follows from this parametrization. A feedback stabilizing the planned motion is designed after linearization of the relevant subsystem about the planned trajectories. Simulation results show the usefulness of the result.

On flatness and controllability of simple hyperbolic distributed parameter systems

Abstract 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 output coordinates are obtained directly from the flatness based parametrization of the solution trajectories. The method is introduced on the basis of simple examples of different complexity for which exact controllability is obtained at least in dense subspaces of the state space.

Feed-Forward Control of an HVDC Power Transmission Network

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 control of tree-like, i.e. cycle-free, HVDC transmission networks comprising two or more converter stations. The resulting control concept allows a flexible determination of the power distribution within the network. Furthermore, effects like power losses and delays due to wave propagation, which are related especially to long transmission lines, can be easily taken into account. Numerical simulations for an example network are included to prove the value of the results.

Flatness-Based Control for a Non-Linear Spatially Distributed Model of a Drilling System

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 simulations illustrate the efficiency of the established control laws.