Abstract
Input shaping is a well-established approach for suppressing oscillations in systems with flexible modes. When applying input shaping, it is common to assume the system to be at rest initially, i. e., the initial conditions of the oscillatory part of the system have to be at zero. In this paper, we propose a method that allows relaxing the aforementioned assumption for a large class of input signals. The approach relies on the standard input shaper structure but re-parameterizes the shaper such that non-zero initial conditions are cancelled out by the inputs, resulting in zero residual oscillation. Natural physical limitations of the concept are discussed and the application to overhead cranes is presented. The method is validated both in simulation as well as in experiments using a small scale crane. In addition, a simplified trajectory generator is presented that tailors a standard seven-segment jerk-limited motion profile such that zero residual vibrations are achieved without any dedicated input shaping.
Zusammenfassung
Input Shaping ist ein etablierter Ansatz zur Unterdrückung von Oszillationen in schwingungsfähigen Systemen. Typischerweise wird bei der Anwendung von Input Shaping angenommen, dass sich der schwingungsfähige Teil des Systems zu Beginn in einer Ruhelage befindet. In diesem Beitrag wird eine Methode vorgestellt, die eine Relaxierung der vorgenannten Annahme für eine große Klasse von Eingangssignalen ermöglicht. Der Ansatz beruht darauf, den Input Shaper derart zu parametrieren, dass die Anfangsbedingungen des schwingungsfähigen Systemteils durch die gefilterten Eingangssignale aufgehoben werden. Physikalisch bedingte Grenzen des Ansatzes werden diskutiert und die Anwendung wird anhand einer Verladebrücke sowohl in einer Simulationsumgebung als auch in einem Experiment demonstriert. Darüber hinaus wird ein Trajektoriengenerator vorgestellt, der ein ruckbegrenztes Bewegungsprofil so parametriert, dass sich auch ohne Anwendung eines Input Shapers keine bleibenden Schwingungen im System ergeben.
Dedicated to the 60th birthday of Prof. Dr.-Ing. Jürgen Adamy.
About the authors
Arne Wahrburg obtained his Dipl.-Ing. and Dr.-Ing. in Electrical Engineering from TU Darmstadt in 2010 and 2013, respectively. He received the VDI/VDE GMA Eugen-Hartmann-Award in 2015 and the Best Paper Award at the International Symposium on Robotics in 2020. Since 2013, he has been with ABB Corporate Research Germany and is currently a Senior Principal Scientist. His topics of interest include Robot and Motion Control as well as Robot Learning.
Janne Jurvanen graduated in Electrical Engineering from Tampere University of Technology in 1999. Since then he has been with ABB Drives in different software R&D and product maintenance roles and is currently technical software owner of ACS880 drives in Drives Products. His topic of interest include drive applications with demanding control, especially in area of motion control.
Matias Niemelä obtained his B. Sc. (Eng.) and M. Sc. (Eng.) degrees in Electrical Engineering and Automation from Aalto University in 2015 and 2018, respectively. Since 2013, he has been with ABB Drives Finland and is currently a Senior Software Design Engineer. His main topics of interest are Motion Control Applications controlled with Electric Drives.
Mikael Holmberg graduated Ing. in Electrical Power Technology from today named Novia University of Applied Sciences in 1986. Since 1995, he has been with ABB Drives Finland in different roles with AC-drives from service engineer/product manager and is currently a Senior Segment Sales Manager for Cranes & Marine winch applications.
Acknowledgment
The authors would like to thank Hannes Bergkvist and August Ramle for developing SensorMatrix at Lund University and making the app available.
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