Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2012 | OriginalPaper | Buchkapitel

10. MPC Implementation for Vibration Control

verfasst von : Gergely Takács, Boris Rohal’-Ilkiv

Erschienen in: Model Predictive Vibration Control

Verlag: Springer London

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This chapter is devoted to the implementation of model predictive control (MPC) algorithms in active vibration control (AVC) applications. Even though the main area of interest is AVC, the software implementation tasks presented here are valid for any other engineering application of MPC, thus the material may be recommended to anyone interested in practical issues with MPC software deployment. Three different MPC strategies are discussed, each having its own advantages and disadvantages: the well known infinite horizon cost dual-mode quadratic programming based MPC (QPMPC), optimal and suboptimal explicit pre-computed multi-parametric programming based MPC (MPMPC) and the efficient but suboptimal Newton–Raphson MPC (NRMPC). The offline portion of the algorithms is implemented in the Matlab m-file scripting language, while the real-time controllers are realized in Simulink and subsequently transferred to the xPC Target rapid control software prototyping platform. The practical approach utilized here is focused at simplicity. An off-the shelf quadratic solver called qpOASES is used for the online implementation of QPMPC, while the MPMPC algorithm is implemented using the MPT Toolbox. As the implementation of NRMPC to physical systems is unique to this book, the most attention is devoted to the code developed for the use of Newton–Raphson MPC in the vibration damping of lightly damped structures.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Applications of Model Predictive Vibration Control
Nächstes Kapitel Simulation Study of Model Predictive Vibration Control
Fußnoten
2
Van den Broeck et al. used a computer with a Mobile Pentium 2 GHz processor with 2 GB of RAM.
 
3
See more on the topic of Sect.​ 9.​7.​3.​
 
4
The illustration in Fig. 10.4 shows the variable naming conventions familiar from earlier chapters. The code implementation in Appendix B uses the following notation for variables: \({\mathbf{H}={\rm Hqp}}{,}\) \({\mathbf{G}}={\rm F}{,}\) \({\mathbf{B}}_x={\rm BxQP}{,}\) \({\mathbf{b}}_0={\rm b0QP}\) and \({\mathbf{A}}_c={\rm AcQP}{.}\)
 
5
The particular solver module featured in Fig. 10.4 is qpOAES_QProblem, which is recommended for problem formulations assuming nominal systems and fixed constraints. In case a sequential quadratic programming problem is required by the MPC formulation (e.g. in adaptive systems), the resulting optimization task can be solved more efficiently by using the sequential qpOAES_SQProblem module of qpOASES [16]. The timing analysis featured in Sect.​ 12.​5 utilizes the sequential qpOASES solver, but with constant parameter and constraint matrices.
 
6
Software package and extended documentation is available at: http://​control.​ee.​ethz.​ch/​~mpt/​.
 
7
Also known as R2007b.
 
8
Also known as R2006a.
 
9
At the time of writing the book manuscript and according to the literature research performed by the authors.
 
10
See 12.​7.​2.​6 for details.
 
11
Remember that these are in general vectors, the boldface type is reserved for the vector of predicted inputs \({\mathbf{u}}_k\) to simplify notation.
 
12
There is an additional tolerance value. \({\mathbf{L}}\) is supposed to be positive definite, although sometimes may contain negative elements too.
 
13
Matlab is in fact based on BLAS and LAPACK.
 
Literatur
1.
2.
Arnold E, Neupert J, Sawodny O, Schneider K (2007) Trajectory tracking for boom cranes based on nonlinear control and optimal trajectory generation. In: IEEE international conference on control applications CCA, pp 1444–1449. doi:10.​1109/​CCA.​2007.​4389439
3.
4.
Baocang D (2009) Modern predictive control, 1st edn. Chapman and Hall / CRC, Boca RatonCrossRef
5.
6.
7.
Camacho EF, Bordons C (2007) Model predictive control. 2nd edn. Springer, London
8.
9.
Chapra SC (2004) Applied numerical methods with MATLAB for engineers and scientists. 1st edn. McGraw-Hill Science, New York
10.
Chen H, Allgöver F (1998) A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34(10):1205–1217MathSciNetMATHCrossRef
11.
12.
Dongarra J (2002) Basic linear algebra subprograms technical forum standard. Int J High Perform Appl Supercomput 16:1–111CrossRef
13.
Eure KW (1998) Adaptive predictive feedback techniques for vibration control. Doctoral dissertation, Virginia Polytechnic Institute and State University, Blacksburg
14.
Ferreau HJ (2006) An online active set strategy for fast solution of parametric quadratic programs with applications to predictive engine control. Master thesis, University of Heidelberg
15.
16.
Ferreau HJ (2011) qpOASES User’s Manual. Optimization in engineering center (OPTEC) and department of electrical engineering, K. U. Leuven
17.
18.
Ferreau HJ, Bock HG, Diehl M (2008) An online active set strategy to overcome the limitations of explicit MPC. Int J Robust Nonlinear Control 18(8):816–830MathSciNetCrossRef
19.
Fletcher R (2000) Practical methods of optimization. Wiley, New York
20.
21.
Hassan M, Dubay R, Li C, Wang R (2007) Active vibration control of a flexible one-link manipulator using a multivariable predictive controller. Mechatronics 17(1):311–323CrossRef
22.
Huang K, Yu F, Zhang Y (2010) Model predictive controller design for a developed electromagnetic suspension actuator based on experimental data. In: WASE international conference on information engineering (ICIE) 4:152–156. doi:10.​1109/​ICIE.​2010.​327
23.
Woo HK, Soo HH (2005) Receding horizon control: model predictive control for state models. 1st edn. Springer, London
24.
Imsland L, Rossiter JA (2005) Time varying terminal control. In: 16th IFAC world congress in Prague, p TP/19
25.
26.
Inman DJ (2007) Engineering vibrations, 3rd edn. Prentice Hall, NJ
27.
Kok J, van Heck J, Huisman R, Muijderman J, Veldpaus F (1997) Active and semi-active control of suspension systems for commercial vehicles based on preview. In: Proceedings of the 1997 American control conference 5:2992–2996. doi:10.​1109/​ACC.​1997.​612006
28.
29.
30.
31.
Kvasnica M (2009) Real-time model predictive control via multi-parametric programming: Theory and tools, 1st edn. VDM Verlag, Saarbrücken
32.
Kvasnica M (2011) Selected Topics on constrained and nonlinear control. workbook, STU Bratislava—NTNU Trondheim, Chap Multi-Parametric Toolbox, pp. 101–170
33.
33.
Kvasnica M, Grieder P, Baotic M, Morari M. (2004) Multi-parametric toolbox (MPT). In: Alur R, Pappas GJ (eds) Hybrid systems: computation and control, Lecture notes in computer science, Springer Berlin / Heidelberg, 2993:121–124
35.
36.
Kvasnica M, Rauová I, Fikar M (2010) Automatic code generation for real-time implementation of model predictive control. In: Proceedings of the 2010 IEEE international symposium on computer-aided control system design, Yokohama pp 993–998
37.
Kvasnica M, Fikar M, Čirka Ľ, Herceg M (2011) Selected Topics on constrained and nonlinear control. Textbook, STU Bratislava—NTNU Trondheim, Chap Complexity reduction in explicit Model predictive control, pp 241–288
38.
Kvasnica M, Rauová I, Fikar M (2011) Real-time implementation of model predictive control using automatic code generation. In: Selected topics on constrained and nonlinear control. Preprints, STU Bratislava—NTNU Trondheim, pp 311–316
39.
40.
Lofberg J (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD conference, Taipei
41.
42.
Maciejowski JM (2000) Predictive control with constraints, 1st edn. Prentice Hall, New Jersey
43.
Mayne DQ, Rawlings JB, Rao CV, Scokaert POM (2000) Constrained model predictive control: Stability and optimality. Automatica 36(6):789–814MathSciNetMATHCrossRef
44.
Mehra R, Amin J, Hedrick K, Osorio C, Gopalasamy S (1997) Active suspension using preview information and model predictive control. In: Proceedings of the 1997 IEEE international conference on control applications, pp 860–865, doi:10.​1109/​CCA.​1997.​627769
45.
46.
47.
Morger A (2010) Synthesis, design and control of a tendon-driven robot platform for vestibular stimulation during sleep. Master’s thesis, ETH Zurich
48.
Nesterov Y, Nemirovskii A (1994) Interior-point polynomial methods in convex programming, Studies in Applied Mathematics, vol 13. SIAM, PennsylvaniaCrossRef
49.
Niederberger D (2005) Hybrid systems: computation and control, vol 3414, Springer / Heidelberg, Berlin, Design of optimal autonomous switching circuits to suppress mechanical Vibration, pp 511–525
50.
Ping H, Ju Z (2008) Explicit model predictive control system and its application in active vibration control of mechanical system of elevator. In: Control and decision conference, CCDC . Chinese, pp 3738–3742. doi:10.​1109/​CCDC.​2008.​4598029
51.
Pistikopoulos EN, Georgiadis MC, Dua V (eds) (2007) Multi-parametric model-based control, vol 2, 1st edn. Wiley
52.
Pistikopoulos EN, Georgiadis MC, Dua V (eds) (2007) Multi-parametric programming, vol 1, 1st edn. Wiley
53.
54.
Polóni T, Takács G, Kvasnica M, Rohal’-Ilkiv B (2009) System identification and explicit control of cantilever lateral vibrations. In: Proceedings of the 17th international conference on process control, Štrbské Pleso
55.
Rauter G, Zitzewitz JV, Duschau-Wicke A, Vallery H, Riener R (2010) A tendon-based parallel robot applied to motor learning in sports. In: Proceedings of the IEEE international conference on biomedical robotics and biomechatronics
56.
Richelot J, Bordeneuve-Guibe J, Pommier-Budinger V (2004) Active control of a clamped beam equipped with piezoelectric actuator and sensor using generalized predictive control. In: 2004 IEEE international symposium on industrial electronics, vol. 1, pp 583–588 vol. 1. doi:10.​1109/​ISIE.​2004.​1571872
57.
Rossiter JA (2003) Model-based predictive control: a practical approach, 1st edn. CRC Press, Boca Raton
58.
Shi P, Liu B, Hou D (2008) Torsional vibration suppression of drive system based on DMC method. In: 7th World Congress on intelligent control and automation. WCICA, pp 4789–4792. doi:10.​1109/​WCICA.​2008.​4593699
59.
Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization methods and software—special issue on interior point methods 11–12:625–653
60.
61.
Takács G (2008) Efficient model predictive control applied on active vibration control. Written report for PhD qualification exam, Slovak Technical University, Faculty of mechanical engineering, Bratislava
62.
Takács G, Rohal’-Ilkiv B (2008) Model predictive control in vibration attenuation. In: Proceedings of the 2nd international conference education research and innovation, Bratislava
63.
Takács G, Rohal’-Ilkiv B (2009) Implementation of the Newton-Raphson MPC algorithm in active vibration control applications. In: Mace BR, Ferguson NS, Rustighi E (eds) Proceedings of the 3rd international conference on noise and vibration: emerging methods, Oxford
64.
Takács G, Rohal’-Ilkiv B (2009) MPC with guaranteed stability and constraint feasibility on flexible vibrating active structures: a comparative study. In: Hu H (ed) Proceedings of the 11th IASTED international conference on control and applications, Cambridge
65.
Takács G, Rohal’-Ilkiv B (2009) Newton-Raphson based efficient model predictive control applied on active vibrating structures. In: Proceedings of the European control conference, Budapest
66.
Takács G, Rohal’-Ilkiv B (2009) Newton–Raphson MPC controlled active vibration attenuation. In: Hangos KM (ed) Proceedings of the 28th IASTED international conference on modeling, identification and control, Innsbruck
67.
The Mathworks (2007) Matlab signal processing blockset v6.6 (R2007b). Software. The MathWorks Inc., Natick
68.
69.
Van den Broeck L, Diehl M, Swevers J (2009) Time optimal MPC for mechatronic applications. In: Proceedings of the 48th IEEE conference on decision and control, Shangai, pp 8040–8045
70.
Van den Broeck L, Swevers J, Diehl M (2009) Performant design of an input shaping prefilter via embedded optimization. In: Proceedings of the 2009 American control conference, St. Louis, pp 166–171
71.
72.
Wang L (2009) Model predictive control system design and implementation using MATLAB, 1st edn. Springer, London
73.
Wills A, Bates D, Fleming A, Ninness B, Moheimani R (2005) Application of MPC to an active structure using sampling rates up to 25 kHz. In: 44th IEEE conference on decision and control, 2005 and 2005 European control conference. CDC-ECC ’05, pp 3176–3181. doi:10.​1109/​CDC.​2005.​1582650
74.
Wills AG, Bates D, Fleming AJ, Ninness B, Moheimani SOR (2008) Model predictive control applied to constraint handling in active noise and vibration control. IEEE Trans Control Syst Technol 16(1):3–12CrossRef
75.
Yan G, Sun B, Lü Y (2007) Semi-active model predictive control for 3rd generation benchmark problem using smart dampers. Earthquake engineering and engineering vibration 6:307–315. doi:10.​1007/​s11803-007-0645-2
76.
Yim W (1996) Modified nonlinear predictive control of elastic manipulators. In: Proceedings of the 1996 IEEE international conference on robotics and automation, vol. 3, pp 2097–2102. doi:10.​1109/​ROBOT.​1996.​506180
77.
78.
Zmeu K, Shipitko E (2005) Predictive controller design with offline model learning for flexible beam control. In: Proceedings of the 2005 international conference on Physics and control, pp 345–350. doi:10.​1109/​PHYCON.​2005.​1514005
Metadaten
Titel
MPC Implementation for Vibration Control
verfasst von
Gergely Takács
Boris Rohal’-Ilkiv
Copyright-Jahr
2012
Verlag
Springer London
Buch
Model Predictive Vibration Control

Print ISBN: 978-1-4471-2332-3

Electronic ISBN: 978-1-4471-2333-0

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-1-4471-2333-0_10

Neuer Inhalt

    Bildnachweise