Abstract
This article addresses the automatic optimization of driving speeds in conveying systems. Electric drives in existing conveying systems are usually accelerated and decelerated according to predetermined movement profiles. Such an approach is inflexible for conveying applications with changing constraints and, in many cases, not optimal with respect to energy efficiency. In the present work, a method for automatic computation of energy efficient movement profiles is proposed. The proposed method is based on accurate models for electric drives and several types of conveying applications such as roll conveyors, belt conveyors and vertical conveyors. Furthermore, joint energy efficiency optimization for two drives, which are attached to an intermediate circuit, is investigated. Thereby, additional constraints on the energy flow between the drives are imposed in order to reduce load peaks and energy feedback into the grid. The resulting optimization problem is a mixed integer quadratic program (MIQP), which can be solved in a few milliseconds. Experimental results show that energy losses of electric drives are cut down by using the obtained non-trivial movement profiles instead of standard trapezoid movement profiles. The additional constraints on the energy flow between two drives lead to further significant improvements with respect to the overall energy losses.
Zusammenfassung
Der Beitrag adressiert die energie-effiziente Ansteuerung der elektrischen Antriebe in Förderanwendungen. Elektrische Antriebe in Förderanwendungen werden in der Regel entsprechend vordefinierter Bewegungsprofile beschleunigt und abgebremst. Ein solcher Ansatz ist für Förderanwendungen mit wechselnden Randbedingungen unflexibel und in vielen Fällen nicht energie effizient. In der vorgestellten Arbeit wird daher eine Methode zur automatischen Optimierung der Bewegungsprofile vorgeschlagen. Die vorgeschlagene Methode basiert auf genauen Modellen der elektrischen Antriebe und verschiedener Arten von Förderanwendungen wie Rollenförderern, Bandförderern und Vertikalförderern. Weiterhin wird die gemeinsame Optimierung für zwei Antriebe untersucht, die an einen Zwischenkreis angeschlossen sind. Dabei werden Randbedingungen bzgl. des Energieflusses zwischen den beiden Antrieben berücksichtigt, die es ermöglichen, Lastspitzen und Rückspeisungen in das Netz zu reduzieren. Insgesamt ergibt sich ein gemischt-ganzzahliges Optimierungsproblem, welches in wenigen Millisekunden gelöst werden kann. Experimentelle Untersuchungen zeigen, dass die Verwendung der optimierten, nicht-trivialen Bewegungsprofile anstelle trapezförmiger Bewegungsprofile zu einer signifikanten Reduktion des Energieverbrauchs führt. Insbesondere durch die zusätzlichen Randbedingungen bzgl. des Energieflusses zwischen den beiden Antrieben ergeben sich deutliche Einsparungen.
About the authors
Stefan Windmann has been a postdoctoral researcher at Fraunhofer IOSB-INA in Lemgo since 2012. He studied electrical engineering and technical computer sciences at the University of Paderborn, where he finished his PhD in 2008. From 2008 to 2012, he worked as software developer in the industry. Currently, he is working in the fields of embedded software engineering, information retrieval in production systems and the optimization and diagnosis of industrial automation systems.
Oliver Niggemann received his PhD in Computer Science from the University of Paderborn. For 7 years he worked in various positions in industry, both in development and in leading management positions. In 2008, he accepted a professorship for technical computer science at the University of Applied Sciences OWL in Lemgo, Germany. He is an executive board member of the Institute of Industrial IT (inIT). Since 2009, he is also the deputy director of the Fraunhofer IOSB-INA in Lemgo. He heads the graduate school Intelligent Systems for Automation (ISA) and he is the scientific director of the Graduate Center GZ.OWL in Lemgo. His research interests comprise methods and applications for Artificial Intelligence in production systems.
Heiko Stichweh was born in Stadtoldendorf, Germany, in 1974. He received his graduate engineers degree from Clausthal University of Technology in 2000. He started working at the Institute of Electrical Power Engineering and Energy Systems in the same year, while writing his doctoral thesis. He received a doctor’s degree in control of electrical drive systems in 2004. From 2004 until 2005, he worked as an employee in the Development Department for Low Voltage Servo Drives of Lenze GmbH & Co KG Kleinantriebe. From 2006–2011, he developed motor control of frequency inverters at Lenze Drives GmbH. Since 2011, he has been the disciplinary head of the Innovation Department of Lenze SE.
Appendix A Logic and magnitudes in MIQP
Logic and magnitudes are expressed in MIQP as follows [23]:
1. Alternative restriction groups/equivalences
with continuous variables
where
are used, where
2. Propositional formulas with atomic formulas
3. Magnitudes
4. The signs
Eq. (39) can be written as
with
5. The motor modes Q (
with integer variables
Appendix B Conveying applications
The three conveying applications considered in section 2.2 are detailed in this appendix. The operating principles of the three conveying applications are shown in Fig. 7.
Operating principles of the conveying applications: a) belt conveyor b) roll conveyor c) vertical conveyor.
The belt conveyor employs a drive roll with radius
where
to cause acceleration a of a ware with mass
is required, where J denotes the overall inertia of the rolls in the respective application:
with inertia
Additionally, torque
with friction factors
is required. Transformation of (44) and (49) leads to the roll conveyor coefficients in Table 2.
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