Gernot Grabmair

Energy-based nonlinear control of hydraulically actuated mechanical systems

This contribution is devoted to a nonlinear energy based controller design for plants consisting of a mechanical 1-DOF load system coupled to a general hydraulic actuator. A systematic controller design which maintains the Port Hamiltonian structure of the plant is demonstrated for the case of a double-ended piston with only one servovalve. The developed controller shows good robustness properties and is able to inject additional damping into the load system without velocity measurement. Finally, the performance of the control law is demonstrated by application to a special industrial plant.

Anatomic Parameters of the Long Process of Incus for Stapes Surgery

Hypothesis The purpose of this study is to offer new anatomic data about the long process of incus (LPI) for stapes surgery. Background Anatomic study of 50 human macerated incudes to measure different parameters of cross sections of the LPI. Methods Step-by-step cutting of the LPI perpendicular to its axis starting from its free end next to the lenticular process. The layer thickness was 0.5 mm. The cutting surfaces were documented with Canon EOS 20D camera, and a standard software tool (MATLAB) was used for automated statistical analysis. Results The LPI had a maximum diameter of 1.15 mm and a minimum diameter of 0.52 mm at the level of 1.5 mm far from the tip of the long process, which is the most common site for stapes prosthesis attachment. Concerning each cross section, having a long and a short diameter, the average long diameter is 0.9011 mm, and the short diameter is 0.6507 mm. Conclusion Our anatomic study revealed wide variations of diameters and shape of the LPI. Best possible crimping of stapes prosthesis depends not only on the shape and diameters of the LPI but also on the vertical surface of the LPI as well. To prevent incus necrosis due to compression of the feeding blood vessels, the maximum contact surface of the loop of stapes prosthesis should be about 1.9 mm in length.

Model based control design - A free tool-chain

In this study we present a new free tool-chain for model based control design for mechatronic plants applicable to small embedded systems based among other software on the open simulator Scilab-XCos. After a very short introduction of model based design terms this article focuses on the code generator and the other programs of the tool-chain. The design concept is demonstrated by an adaptive self tuning control (STC) of the cart and pendulum system in gantry crane configuration in simulation and on a real laboratory experiment.

Active Vibration Rejection in Steel Rolling Mills

Abstract This contribution is concerned with vibration rejection by nonlinear control techniques in steel industry, particularly in rolling mill plants. The high quality requirements of rolled products, especially in relation to the thickness tolerances, mean a challenging task also from a control point of view. The key part of this contribution deals with so-called wrapper rolls as well as chatter vibration phenomena. With regard to the control design a mathematical model based on physical considerations is introduced where the essential nonlinearities of the system are taken into account. For the purpose of vibration rejection two nonlinear control concepts based on energy considerations and the theory of differential flatness are presented.

Application of Vibration Control in Steel Industries

In steel industry, the high quality requirements of rolled products, in particular the restrictive thickness tolerances, mean a challenging task also from a control point of view. One of the key problems in this context are vibrations of the rolling plant. Therefore, this contribution is concerned with the active rejection of two common vibration problems, namely vibrations of so-called wrapper rolls and the chatter phenomenon. A mathematical model based on physical considerations taking into account the essential nonlinearities of the plant provides the basis for the controller design. For vibration rejection two nonlinear control concepts based on energy considerations and the theory of differential flatness are presented.

Some Applications of Differential Geometry in Mechanics

Classical mechanics is not only one of the most successful scientific disciplines, it stands also at the beginning of modern physics. Furthermore, it demonstrates the deep connection between physics and geometry. Therefore, the development of differential geometry was pushed by ideas from mechanics. The goal of this contribution is to show the geometric interpretation of certain mechanical ideas like the time-space manifold or the metric on the spatial manifold and geodesics. The covariant derivative, derived from a special connection, allows us to represent the famous equations of point mechanics in a coordinate free manner. Based on this approach we extend these geometric ideas such that we are able to discuss concepts required for continuum mechanics. Here new geometric concepts like the covariant differential are introduced, which allow to transfer several ideas from point mechanics to continuum mechanics.

Flachheitsbasierte Folgeregelung des Labormodells ball on the wheel

ZusammenfassungFür dynamische Systeme, welche die Struktureigenschaft der differenziellen Flachheit zeigen und damit eine finite, vollständige und freie differentielle Parametrierung durch den so genannten flachen Ausgang erlauben, bietet die moderne Regelungstheorie einen systematischen Zugang zur Lösung des Trajektorienfolgeregelungs-Problems. Dieser Beitrag ist der flachheitsbasierten Folgeregelung des instabilen, unteraktuierten, nichtlinearen mechanischen Systems Ball on the Wheel gewidmet. Dieses System, dessen flacher Ausgang mit einer klaren physikalischen Interpretation behaftet ist, wurde als Laborexperiment zur Illustration der Möglichkeiten nichtlinearer Regelungstheorie, die Forschung und Lehre begleitend, konzipiert.AbstractBy virtue of the structural property of differential flatness, which allows for a finite, complete and free differential parametrization of a flat system by means of the so-called flat output, the trajectory tracking problem can be solved in a systematic way by invoking modern control theory. This paper is concerned with the flatness based trajectory tracking control of the unstable, underactuated, nonlinear mechanical system Ball on the Wheel. This system exhibiting a flat output with a clear physical interpretation was designed as an experimental setup for illustrating the potential of nonlinear control theory accompanying research and education.

Automatisierungstechnik in der Mechatronik — zwei Beispiele aus der Stahlindustrie

ZusammenfassungDie Mechatronik, einst als wissenschaftliches und industrielles Experiment begonnen, hat sich zu einer etablierten Wissenschaft mit einem weiten industriellen Anwendungsfeld entwickelt. Unverändert geblieben ist der Anspruch, aus der integrativen Verbindung von Elektrotechnik, Maschinenbau und Automatisierungstechnik ein Wissensgebiet zu schaffen, das einen neuen Zugang zu wissenschaftlichen und industriellen Problemen bietet. Am Beispiel zweier Systeme der Stahlindustrie, eines hydraulischen Aktuators und an S-Rollen-Systemen, wird gezeigt, wie mit Hilfe linearer und nichtlinearer Regelungen das Verhalten der Systeme wesentlich verbessert werden kann. Der Entwurf der Regelung basiert im nicht-linearen Fall dabel auf der Theorie der PCHD-Systeme (port controlled Hamiltonian systems with dissipation) und im linearen Fall auf einer partiellen Eingangs-Ausgangs-Entkopplung, kombiniert mit einemH2-Entwurf. Die Güte der so entworfenen Systeme wird durch Messungen an realen Anlagen und durch Simulationsstudien nachgewiesen. Diese Regelungen sind natürlich auch bei anderen Anlagen einsetzbar. Darüber hinaus sind die vorgestellten Konzepte auch auf ähnliche oder nur verwandte industrielle Probleme leicht übertragbar.AbstractMechatronics, once started as a scientific and industrial experiment, has shown to be a well established scientific discipline with a broad industrial area of applications. Unchanged is the claim of Mechatronics to create a scientific discipline, which offers a new approach to industrial and scientific problems by a synergetic integration of electrical and mechanical engineering with control. Two examples from the field of steel manufacturing systems, namely a hydraulic actuator and a bridle roll device, are chosen in order to demonstrate how one can improve the system performance by linear and nonlinear control. The theory of PCH-systems (port controlled Hamiltonian systems) is used in the nonlinear case, and a combination of partial input-output decoupling and H2-design is applied to the linear plant. The measurements of the hydraulic actuator and the simulations of the bridle roll system demonstrate the performance of the closed loop. Of course, the presented controllers can easily be used for similar plants. Furthermore, the presented ideas are transferable to similar or related problems in a straightforward manner.

Input design and online system identification based on Poisson moment functions for system outputs with quantization noise

We study optimal input design and bias-compensating parameter estimation methods for continuous-time models applied on a mechanical laboratory experiment. Within this task we compare two online estimation methods that are based on Poisson moment functions with focus on quantized system outputs due to an angular encoder: The standard recursive least-squares (RLS) approach and a bias-compensating recursive least-squares (BCRLS) approach. The rationale is to achieve acceptable estimation results in the presence of white noise, caused by low-budget encoders with low resolution. The input design and parameter estimation approaches are assessed and compared, experimentally, resorting to measurements taken from a laboratory cart system.

Model-Based Nonlinear Control of 2-WMR

A solid low-level movement control is essential for a successful contest robot. For two-wheeled mobile robots (WMR) numerous control approaches can be found in literature. In this contribution it is shown how the low-level control of a WMR can be systematically developed by model based design techniques. The resulting controller is able to asymptotically track given motion profiles for any reference point fixed to the robot chassis by a small extension of the well known look-ahead control.