Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Robust state estimation for the control of flexible robotic manipulators

In this thesis, a novel robust estimation strategy for observing the system state variables of robotic manipulators with distributed flexibility is established. Motivation for the derived approach stems from the observation that lightweight, high speed, and large workspace robotic manipulators often suffer performance degradation because of inherent structural compliance. This flexibility often results in persistent residual vibration, which must be damped before useful work can resume. Inherent flexibility in robotic manipulators, then, increases cycle times and shortens the operational lives of the robots. Traditional compensation techniques, those which are commonly used for the control of rigid manipulators, can only approach a fraction of the open-loop system bandwidth without inducing significant excitation of the resonant dynamics. To improve the performance of these systems, the structural flexibility cannot simply be ignored, as it is when the links are significantly stiff and approximate rigid bodies. One thus needs a model to design a suitable compensator for the vibration, but any model developed to correct this problem will contain parametric error. And in the case of very lightly damped systems, like flexible robotic manipulators, this error can lead to instability of the control system for even small errors in system parameters. This work presents a systematic solution for the problem of robust state estimation for flexible manipulators in the presence of parametric modeling error. The solution includes: 1) a modeling strategy, 2) sensor selection and placement, and 3) a novel, multiple model estimator. Modeling of the FLASHMan flexible gantry manipulator is accomplished using a developed hybrid transfer matrix / assumed modes method (TMM/AMM) approach to determine an accurate low-order state space representation of the system dynamics. This model is utilized in a genetic algorithm optimization in determining the placement of MEMs accelerometers for robust estimation and observability of the system’s flexible state variables. The initial estimation method applied to the task of determining robust state estimates under conditions of parametric modeling error was of a sliding mode observer type. Evaluation of the method through analysis, simulations and experiments showed that the state estimates produced were inadequate. This led to the development of a novel, multiple model adaptive estimator. This estimator utilizes a bank of similarly designed sub-estimators and a selection algorithm to choose the true value from a given set of possible system parameter values as well as the correct state vector estimate. Simulation and experimental results are presented which demonstrate the applicability and effectiveness of the derived method for the task of state variable estimation for flexible robotic manipulators.Ph.D

On the Influence of Piecewise Defined Contact Geometries on Friction Dampers

Diese Arbeit betrachtet Dämpfer, die sich nicht auf eine Schwingungsreduktionsstrategie beschränken, sondern mehrere kombinieren, um optimale Ergebnisse zu erzielen. Die Möglichkeiten herkömmlicher Reibungsdämpfer werden durch stetige, stückweise definierten Kontaktgeometrien erweitert. Dies führt zu Reibungsdämpfern, die ihr Verhalten je nach Amplitude der Schwingungen ändern. Der passive, abgestimmte Keildämpfer wird entworfen und untersucht. Dieser Dämpfer bringt Dämpfung bei hohen Schwingungsamplituden in System ein und nutzt Tilgung bei niedrigen Schwingungsamplituden aus. Es werden numerische und analytische Untersuchungen durchgeführt. Um das qualitative Verhalten des Dämpfers zu validieren, wird ein Dämpferprototyp konstruiert und erprobt. Zudem wurde auch eine aktive Variante des abgestimmten Keildämpfers betrachtet. Es werden zwei Regelstrategien entworfen, die adaptive Mehrmodellregelung und die langsame, frequenzbasierte Regelung. Diese werden mit einer State-of-the-Art- Regelungsstrategie in transienten, quasistationären und Anwendungsszenarien verglichen. Die Untersuchungen zum passiven, abgestimmten Keildämpfer zeigen, dass Dämpfung und Tilgung entkoppelt werden. Eine Optimierung der Dämpferparameter ergibt im Frequenzgang eine Reduktion der Maximalamplitude von 87.47% unter Beibehaltung der Tilgung. Die Experimente validieren den Entkopplungseffekt sowie den qualitativen Einfluss der Parameter. Die aktiven Systeme erreichen mit Amplitudenabsenkungen von 91.11% das beste Ergebnis

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area