Mechatronic systems design methods, models, concepts

Tai Lieu Chat Luong Mechatronic Systems Design Klaus Janschek Mechatronic Systems Design Methods, Models, Concepts Translation by Kristof Richmond 123 Prof Dr techn Klaus Janschek Technische Universitaet Dresden Electrical and Computer Engineering Institute of Automation Dresden Germany klaus.janschek@tu-dresden.de Dr Kristof Richmond Iowa City, Iowa USA kristof@frontierastronautics.com ISBN 978-3-642-17530-5 e-ISBN 978-3-642-17531-2 DOI 10.1007/978-3-642-17531-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011937832 c 2012 Springer-Verlag Berlin Heidelberg  This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) – For Ruth and in memory of Martin Beck – Preface This is the translated English edition of the book “Systementwurf mechatronischer Systeme” published by Springer in January 2010 For the motivation, background and concept of presentation, the obliging reader is referred to the preface of the German edition, which follows Already in the course of preparing the German book and studying the vast literature in this subject area, I recognized that there still exists some room on the international mechatronics stage for the material presented in this monograph Moreover, the many positive comments of colleagues and students on the German edition encouraged me to think of starting a second round with an English edition From the very beginning, it was clear to me that such a project could only be successful with translation support from a native speaker having broad and excellent knowledge of engineering, and particularly mechatronics Luckily, a previous stay at the Stanford Aerospace Robotics Lab brought me into contact with the best possible partner for this purpose: Dr Kristof Richmond As a fully bilingual native speaker, a highly qualified Stanford graduate, and an intelligent, critical, and altogether most clever scientific partner, he combines all of the talents which I did not really expect to find in one person The joint work on this English edition was therefore extremely smooth, mutually enriching, and, in the age of internet and Skype, never bounded by the cross-Atlantic separation between Germany and Iowa A big thanks to Kristof for this great job This English edition covers the contents of the German edition with some minor improvements in presentation, with updated English textbook bibliography, and it gave us the chance to remove errata found in the German edition For the acknowledgements in putting together this mass of material, the reader is again referred to the subsequent preface of the German edition Nevertheless, I must acknowledge two people in the context of this English edition My first thanks go to my beloved wife Ruth, who has also supported and accompanied this second mountain climbing expedition with a fantastic and ever-encouraging mood (though fortunately, this was a VIII Preface much lower summit than the previous one, cf preface to the German edition) My thanks and commemoration go also to Martin Beck, who tragically died in February 2011 just before finishing his PhD As one of my most talented PhD students and closest co-worker in my mechatronics courses, he provided major contributions in the critical proofreading of the original material, sound and always critical technical and scientific discussions, and numerous recommendations for improved didactic presentation His spirit will also remain between the lines of this English edition Last, but not least, all the aforementioned efforts would not have resulted in the present book without the valuable support, trust, and the excellent service of the Springer publishing team represented by Eva Hestermann-Beyerle Dresden, June 2011 Klaus Janschek Preface – German Edition Motivation Why another book on mechatronics? And moreover, why such a comprehensive volume with so much descriptive text? I had answered the first question for myself at the beginning of this project with the justification of “re-working my apprenticeship”, whence I derived the motivation for its realization—whose extent could not be guessed at the time The second question only presented itself in the course of composition, and was answered in cases of doubt by making decisions in favor of more text following the paradigm “everything need not be hidden between the lines and in the formulae” Now, to the story of “the apprenticeship” This began with me as an electrical engineering student at the Graz University of Technology (TU Graz), from which I obtained a very serviceable foundation in mathematics and the natural sciences—as should after all be expected of a university course of study in engineering A major and then a doctorate in control theory subsequently uncovered to me a view of “systems” and systemsoriented solutions My subsequent apprenticeship as a development engineer in mechanical engineering and in aerospace led me to application areas which had played practically no role in my studies: complex heterogeneous systems, which today would be called “mechatronic systems” That my entry into this domain was still quite successful is probably due to two things: the broad foundation provided by my university education, and a systems-oriented approach to solving problems Alongside fascinating experiences involving challenging new applications, these years of apprenticeship produced an important realization: “You must learn to bring the numerous approaches conveyed to you by your education into suitable combination with each other!” Finding the correct path to take is, of course, always left to each individual engineer, but the way will be eased by helpful, experienced mentors (of which I was lucky to have a good number) Throughout this process, the thought of 4.7 Measurement and Actuation Locations FN yO GO ,N (s ) actuator location P FN (t ) k1 k2 m1 kN mN substructure kO kN yO (t ) sensor location substructure kN kO mO yP y1 259 kN mN yN O Fig 4.19 Multiple-mass oscillator with force actuation and position measurement (here absolute, or inertial, quantities) Transfer function Here, the transfer function between the force application at Body N and the displacement from the rest position of Body O is of interest: ơư ưư X đư  ¬­ s ž ­­ žž1 žŸ X ®­ m G O , N (s )  measurement, actuation $ \y O t ^ $ \FN t ^  žžŸ žž1 k 1  K O ,N N j 1 s zeros (4.68) zk 2 poles pj As previously mentioned in Sec 4.6, the transfer functions for different measurement and actuation locations only differ in their static gain and the placement of the zeros The location and number of zeros—and thus the choice of measurement and actuation locations—have a fundamental effect on response characteristics, and they equally fundamentally determine achievable controller performance For this reason, it is worth examining this behavior more closely, using the example of the multiple-mass oscillator in Fig 4.19 4.7.2 Zeros of a multiple-mass oscillator Equations of motion in the complex domain LAPLACE transformation of the equations of motion accounting for the special forms of the mass and stiffness matrices (4.36) results in 260 Functional Realization: Multibody Dynamics  M  ¡ s k2 ¡ % ¡ ¡ kM ¡ ¡ ¡ ¡ ¡ ¢  s k M M M % kN ¯  Y s ¯   ¯ ° ¡ ° ¡ ° ° ¡ # ° ¡ # ° ° ¡ ° ¡ ° ° ¡ ° ¡ ° ° ¸ ¡YM s °  ¡FM s ° , ° ¡ ° ¡ ° ° ¡ # ° ¡ # ° ° ¡ ° ¡ °  s ° Y ¡ N s ° ¡ ° M N ± ± ¢ ± ¢ (4.69)  s M where  s  m s k k M for i  1, 2, , N i i i i (4.70) The transfer function between actuation location N and measurement location O can be derived from (4.69), giving YO s 1 -ON s ,  s det M O N  1 s ¯  G O ,N (s )    ¡ M °± ON FN t ¢ (4.71) where -ON (s ) is the minor (subdeterminant) of the submatrix obtained by  (s ) Due to the special removing the O th row and N th column from M  structure of M(s ) , it holds for -ON (s ) that -ON s  det ī1 s ¸ det ī2 s ¸ det ī s ,    ¡M1 s ¡ (1 s  ¡ ¡ ¡ ! ¡¢ ¯ ±    ¡M O s ¡ (3 s  ¡ ¡ ¡ ! ¡¢  k ¯ ¡ N ° ¡ ° (2 s  ¡ % °, ¡ °  k ¡ O °± ¢ ! ° k2 ° °, % ° °  kN1 M N1 s ° (4.72) ¯ ! ° kO ° ° % °  kN M N s °° ± Physical interpretation of zeros The zeros of GO ,N (s ) and -ON (s ) are the eigenfrequencies of two spring-mass subsystems: the first between masses m1 and m N1 given stationary mass m N (substructure ī1(s ) in Fig 4.20), and the second between masses mO