Torsten Knüppel

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.

Control Design for Quasi-Linear Hyperbolic Systems With an Application to the Heavy Rope

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 is led back to a Cauchy problem w.r.t. space. Second, the solution of this Cauchy problem is discussed for the quasi-linear hyperbolic case using the method of characteristics. This includes the detailed presentation of a numerical integration scheme. The proposed concept is illustrated by means of a quasi-linear model of the heavy rope and, thus, generalizes results for related finite-dimensional and linear infinite-dimensional models of this system.

Flatness-based Control of Torsional-Axial Coupled Drilling Vibrations

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 the suppression of harmful dynamics. The closed loop control design ensures the stability of the error dynamics. Moreover, numerical simulations illustrate the efficiency of the established control laws.

Flatness-based trajectory planning for the shallow water equations

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 and the problem is reduced to an initial value problem w.r.t. the spatial coordinate. The solution to this problem can be obtained with the method of characteristics.

Flatness based control design for a nonlinear heavy chain model

Abstract Flatness based trajectory generation and control design for the spatially distributed nonlinear model of a planar heavy chain with freely movable suspension point is presented. By means of the method of characteristics it is shown, that the solution of the governing equations can be parametrized by the trajectory of the uncontrolled end of the chain using time-delays and advances.

Backstepping design for parabolic systems with in-domain actuation and Robin boundary conditions

Abstract 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 well established backstepping transformation this latter system is feedback equivalent to a stable parabolic equation. Within the contribution previous results concerning systems with Neumann boundary conditions are generalized by means of functional analytic methods. Existence of the involved transformations is discussed by means of the Fredholm theory while a late lumping approach is proposed for the numerical implementation.

Algebraic identification of heavy rope parameters1

Abstract An algebraic approach to the identification of parameters for a heavy rope model is proposed. It is based on operational calculus. The parameters are calculated solely from the measurements of the lower and the upper deflection of the rope. Two different sets of boundary conditions are discussed.

Algebraische Methodenzur Parameteridentifikation für das schwere Seil

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 gemessenen Trajektorien ein System algebraischer Gleichungen in den gesuchten Parametern. Simulationsergebnisse illustrieren den Ansatz. Abstract A method is presented that allows for the identification of parameters in a linear infinite-dimensional model for the heavy rope using only boundary measurements. The approach relies on an operational representation of the solution of the corresponding boundary value problem. A system of algebraic equations in the parameters is generated by repeated convolution of the measured trajectories. Simulations illustrate the results.

Zur Folgeregelung mehrachsiger Fahrzeuge

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 alternativer Ansatz für den Reglerentwurf beschrieben. Dabei wird die Rückwärtsfahrt mit Hilfe einer statischen Zustandsrückführung auf die Vorwärtsfahrt zurückgeführt. Für diese wird im Anschluss eine Folgeregelung mit Hilfe einfacher Eingangs-Ausgangs-Linearisierungs-Techniken entworfen. Die Leistungsfähigkeit der vorgeschlagenen Regelungsansätze wird auf der Basis von Simulationsstudien und experimentellen Ergebnissen gezeigt.

Modellbasierte Berechnung der Kontaktkräfte an einem elastischen Tastsensor

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 wird untersucht und ein Algorithmus zur Berechnung der Kräfte diskutiert.