arXiv subjects

Frank Woittennek

Publications and source records attributed to Frank Woittennek.

11 recordsLinked to original sources

arXiv2026

On the controller form for linear hyperbolic MIMO systems with dynamic boundary conditions

This contribution develops an algebraic approach to obtain a controller form for a class of linear hyperbolic MIMO systems, bidirectionally coupled with a linear ODE system at the unactuated boundary. After a short summary of established controller forms for SISO and MIMO ODE as well as SISO hyperbolic PDE systems, it is shown that the approach to state a controller form for SISO systems cannot easily be transferred to the MIMO case as it already fails for a very simple example. Next, a generalised hyperbolic controller form with different variants is proposed and a new flatness-based scheme to compute said form is presented. Therein, the system is treated in an algebraic setting where quasipolynomials are used to express the predictions and delays in the system. The proposed algorithm is then applied to the motivating example.

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arXiv2026

On observer forms for hyperbolic PDEs with boundary dynamics

A hyperbolic observer canonical form (HOCF) for linear hyperbolic PDEs with boundary dynamics is presented. The transformation to the HOCF is based on a general procedure that uses so-called observability coordinates as an intermediate step. These coordinates are defined from an input-output relation given by a neutral functional differential equation (FDE), which, in the autonomous case, reduces to an autonomous FDE for the output. The HOCF coordinates are directly linked to this FDE, while the state transformation between the original coordinates and the observability coordinates is obtained by restricting the observability map to the interval corresponding to the maximal time shift appearing in the FDE. The proposed approach is illustrated on a string-mass-spring example.

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arXiv2025

Calculation of time-optimal motion primitives for systems exhibiting oscillatory internal dynamics

An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments, which are the time-optimal solution to an optimization problem. To achieve the shortest overall transition time, it is advantageous to recompute these segments for different acceleration levels within the motion planning procedure. This publication presents a numerical calculation method enabling fast and reliable calculation. This is achieved by explicitly evaluating the optimality conditions that arise for the problem, and further by reducing the evaluation of these conditions to a line-search problem on a bounded interval. This reduction guarantees, that a valid solution if found after a fixed number of computational steps, making the calculation time constant and predictable. Furthermore, the algorithm does not rely on optimisation algorithms, which allowed its implementation on a laboratory system for measurements with the purpose of validating the approach.

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arXiv2025

On trajectory design from motion primitives for near time-optimal transitions for systems with oscillating internal dynamics

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 segment. Within this contribution, the focus is put on the composition of the overall trajectories, assuming the required motion primitives to be readily available. Since the scheme considered is not time-optimal, even decreasing particular constraints can reduce the overall transition time, which is analysed in detail. This observation implies that replanning of the underlying jerk segments is required as an integral part of the motion planning scheme, further insight into which has been analysed in a complementary contribution. Although the proposed scheme is not time-optimal, it allows for significantly shorter transition times than established methods, such as zero-vibration shaping, while requiring significantly lower computational power than a fully time-optimal scheme.

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arXiv2023

Control of distributed-parameter systems using normal forms: An introduction

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 controller makes use of the hyperbolic controller canonical form that follows from a parametrization of the system's solutions. A backstepping design exploits the strict-feedback form of the system to recursively stabilize and transform the subsystems.

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arXiv2022

Late lumping of observer-based state feedback for boundary control systems

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 of the feedback gain, resp. observer output injection gain, into a bounded and an unbounded part. Based on a perturbation result, the spectrum-determined growth condition is established, for the closed loop.

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arXiv2022

Late lumping of transformation-based feedback laws for boundary control systems

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 the unbounded part is assumed to allow for an exact realization. Based on spectral results, the convergence of the closed-loop dynamics to the desired dynamics is established. By duality, similar results apply to the approximation of the observer output-injection gains for systems with boundary observation. The proposed design and approximation steps are demonstrated and illustrated based on a hyperbolic infinite-dimensional system.

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arXiv2020

Control of the Vertical Gradient Freeze crystal growth process via backstepping

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-varying extent of crystal and melt during growth. In addition, a different approach for the numerical approximation of the backstepping transformations kernel is presented.

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arXiv2020

On delay-partial-differential and delay-differential thermal models for variable pipe flow

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 of this model with a serial connection of a pure delay or transport system and another partial differential equation (PDE), subsequently called delay-partial-differential equation (DPDE)-model. The means for obtaining the proposed model comprise operational calculus in the Laplace domain as well as classical theory of characteristics. The finite-dimensional approximation of the DPDE-model leads to a delay-differential equation (DDE)-system, which can be seen as a generalization of commonly used DDE-models consisting of a first-order low-pass filter subject to an input delay. The proposed model is compared to several alternative models in simulations and experimental studies.

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arXiv2019

Towards model based control of the Vertical Gradient Freeze crystal growth process

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 solid and liquid domains during growth. After discussing the special needs of the process, collocated as well as flatness-based state feedback designs are carried out. To render the setup complete, an observer design is performed, using a flatness-based approximation of the original distributed parameter system. The quality of the provided approximations as well as the performance of the open and closed loop control setups is analysed in several simulations.

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arXiv2008

Controllability of networks of one-dimensional second order p.d.e. - An algebraic approach

We discuss controllability of systems that are initially given by boundary coupled p.d.e. of second order. Those systems may be described by modules over a certain subring R of the ring of Mikusinski operators with compact support. We show that the ring R is a Bezout domain. This property is utilized in order to derive algebraic and trajectory related controllability results.

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