Top

Published in:

2012 | OriginalPaper | Chapter

11. Simulation Study of Model Predictive Vibration Control

Authors : Gergely Takács, Boris Rohal’-Ilkiv

Published in: Model Predictive Vibration Control

Publisher: Springer London

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This chapter presents the results of simulations performed with various computationally efficient model predictive control (MPC) strategies applied to the state space model of an active vibration control (AVC) demonstration device. A numerical study analyzing the minimal prediction horizon necessary to steer system state into equilibrium for the AVC demonstrator model suggests very long horizons, even for relatively small outside disturbances. Because infinite horizon cost dual-mode quadratic programming based MPC (QPMPC) with stability guarantees is assumed for this test, the feasibility of the online implementation with several hundred steps long horizon is unlikely due to excessive computation times. Through the computation of offline optimization times, number of regions and controller sizes, it is demonstrated here that the computational requirements of multi-parametric programming based MPC (MPMPC) also render it as an unlikely candidate for the AVC of lightly damped systems. From the viewpoint of computational complexity, Newton–Raphson MPC (NRMPC) is certainly a good choice for AVC, however, not without drawbacks. As the simulation results presented here suggest, invariance of the target set and therefore constraints can be violated due to numerical imprecision at the offline computational stage. Moreover, the suboptimality of this approach becomes troubling with increasing problem dimensionality. As the numerical tests demonstrate, the offline computational drawbacks can be partly remedied by performance bounds and proper solver settings, while the optimality is somewhat influenced by a suitable input penalty choice. The chapter is finished with a simulation comparison of the QPMPC, MPMPC and NRMPC algorithms, which shows input and output sequences in agreement with theoretical expectations.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now

previous chapter MPC Implementation for Vibration Control

next chapter Experimental Model Predictive Vibration Control

Simulations show that the intersection (target set) size shrinks with increasing prediction horizon, although in this case with a visually indistinguishable rate—thus not shown on the figure.

AMD Athlon X2 DualCore 4400+ @ 2.00 GHz, 2.93 GB of RAM.

Coincident with the intersection of the augmented ellipsoid with original state-space .

For detailed mathematical description please refer to [11] or the relevant section in this work: See: Sect. 8.1.3

See B.3.3 for details.

See 12.1 for an experiment with different input penalty values \({\mathbf{R}}.\)

This is a quite significant suboptimality especially that [29] states that for randomly generated examples, the error never rose above 2% and remained under 1% for 97% of the examples.

See Sect. 8.1.2 for more details.

Amer Y, Bauomy H (2009) Vibration reduction in a 2DOF twin-tail system to parametric excitations. Commun Nonlinear Sci Numer Simul 14(2):560–573. doi:10.1016/j.cnsns.2007.10.005, http://www.sciencedirect.com/science/article/B6X3D-4PYP723-2/2/b9d5375168fadb0b4e67857e92948bfc

Bandopadhya D, Bhogadi D, Bhattacharya B, Dutta A (2006) Active vibration suppression of a flexible link using ionic polymer metal composite. In: 2006 IEEE conference on robotics, automation and mechatronics, pp 1–6. doi: 10.1109/RAMECH.2006.252638

Baocang D (2009) Modern predictive control, 1st edn. Chapman and Hall / CRC, Boca RatonCrossRef

Bartlett P, Eaton S, Gore J, Metheringham W, Jenner A (2001) High-power, low frequency magnetostrictive actuation for anti-vibration applications. Sens Actuators A 91(1–2):133–136. (Third European conference on magnetic sensors & actuators). doi: 10.1016/S0924-4247(01)00475-7, http://www.sciencedirect.com/science/article/B6THG-4313YT1-14/2/851ac15043a568a17313eef3042d685f

Bemporad A, Morari M, Dua V, Pistikopoulos EN (2002) The explicit linear quadratic regulator for constrained systems. Automatica 38(1):3–20. doi: 10.1016/S0005-1098(01)00174-1, http://www.sciencedirect.com/science/article/B6V21-44B8B5J-2/2/2a3176155886f92d43afdf1dccd128a6

Benaroya H, Nagurka ML (2010) Mechanical vibration: analysis, uncertainities and control, 3rd edn. CRC Press, Taylor & Francis Group, Boca Raton

Bittanti S, Cuzzola FA (2002) Periodic active control of vibrations in helicopters: a gain-scheduled multi-objective approach. Control Eng Pract 10(10):1043–1057. doi:10.1016/S0967-0661(02)00052-7, http://www.sciencedirect.com/science/article/B6V2H-45KSPJJ-3/2/9647861ce849d131c7d4b90cdb964751

Boscariol P, Gasparetto A, Zanotto V (2010) Model predictive control of a flexible links mechanism. J Intell Rob Syst 58:125–147. doi:10.1007/s10846-009-9347-5

Braghin F, Cinquemani S, Resta F (2010) A model of magnetostrictive actuators for active vibration control. Sens Actuators A (in press). doi:10.1016/j.sna.2010.10.019, http://www.sciencedirect.com/science/article/B6THG-51F25N5-4/2/f5cf46980d38877c74a3c4d34fbd894d

10.

Cannon M (2005) Model predictive control, lecture notes. Michaelmas Term 2005 (4 Lectures), Course code 4ME44. University of Oxford, Oxford

11.

Cannon M, Kouvaritakis B (2005) Optimizing prediction dynamics for robust MPC. IEEE Trans Autom Control 50(11):1892–1897. doi:10.1109/TAC.2005.858679 MathSciNetCrossRef

12.

Chen H, Allgöver F (1998) A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34(10):1205–1217MathSciNetMATHCrossRef

13.

Cychowski M, Szabat K (2010) Efficient real-time model predictive control of the drive system with elastic transmission. IET Control Theory Appl 4(1):37–49. doi: 10.1049/iet-cta.2008.0358 MathSciNetCrossRef

14.

Eissa M, Bauomy H, Amer Y (2007) Active control of an aircraft tail subject to harmonic excitation. Acta Mech Sin 23:451–462. doi:10.1007/s10409-007-0077-2

15.

El-Badawy AA, Nayfeh AH (2001) Control of a directly excited structural dynamic model of an F-15 tail section. J Franklin Inst 338(2–3):133–147. doi:10.1016/S0016-0032(00)00075-2, http://www.sciencedirect.com/science/article/B6V04-42HNMDV-3/2/e3bf6f797834c8e8638324be88fb78f7

16.

Eure KW (1998) Adaptive predictive feedback techniques for vibration control. Doctoral dissertation, Virginia Polytechnic Institute and State University, Blacksburg

17.

Fuller CR, Elliott SJ, Nelson PA (1996) Active control of vibration, 1st edn. Academic Press, San Francisco

18.

Geyer T, Torrisi FD, Morari M (2008) Optimal complexity reduction of polyhedral piecewise affine systems. Automatica 44(7):1728–1740. doi: 10.1016/j.automatica.2007.11.027, http://www.sciencedirect.com/science/article/pii/S0005109807004906

19.

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

20.

Hu Q (2009) A composite control scheme for attitude maneuvering and elastic mode stabilization of flexible spacecraft with measurable output feedback. Aerosp Sci Technol 13(2–3):81–91. doi: 10.1016/j.ast.2007.06.007, http://www.sciencedirect.com/science/article/B6VK2-4P96269-2/2/5fbc47249fdd3f1963c5ba856f071c55

21.

Huang K, Yu F, Zhang Y (2010) Model predictive controller design for a developed electromagnetic suspension actuator based on experimental data. In: 2010 WASE international conference on information engineering (ICIE), vol 4, pp 152–156. doi:10.1109/ICIE.2010.327

22.

Imsland L, Bar N, Foss BA (2005) More efficient predictive control. Automatica 41(8):1395–1403. doi:10.1016/j.automatica.2005.03.010, http://www.sciencedirect.com/science/article/B6V21-4G7NT35-1/2/52a9590bfe1ccc2a9561165c3fbdf872

23.

Inman DJ (2007) Engineering vibrations, 3rd edn. Pearson International Education (Prentice Hall), Upper Saddle River

24.

Johansen T, Grancharova A (2003) Approximate explicit constrained linear model predictive control via orthogonal search tree. IEEE Trans Autom Control 48(5):810–815. doi: 10.1016/j.cnsns.2007.10.005

25.

Johansen TA, Jackson W, Schreiber R, Tøndel P (2007) Hardware synthesis of explicit model predictive controllers. IEEE Trans Control Syst Technol 15(1):191–197CrossRef

26.

Kang B, Mills JK (2005) Vibration control of a planar parallel manipulator using piezoelectric actuators. J Intell Rob Syst 42:51–70. doi:10.1007/s10846-004-3028-1

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, vol 5, pp 2992–2996. doi: 10.1109/ACC.1997.612006

28.

Kouvaritakis B, Rossiter J, Schuurmans J (2000) Efficient robust predictive control. IEEE Trans Autom Control 45(8):1545–1549. doi:10.1109/9.871769 MathSciNetMATHCrossRef

29.

Kouvaritakis B, Cannon M, Rossiter J (2002) Who needs QP for linear MPC anyway? Automatica 38:879–884. doi:10.1016/S0005-1098(01)00263-1, http://www.sciencedirect.com/science/article/pii/S0005109801002631 MathSciNetMATHCrossRef

30.

Krishen K (2009) Space applications for ionic polymer-metal composite sensors, actuators, and artificial muscles. Acta Astronaut 64(11–12):1160–1166. doi:10.1016/j.actaastro.2009.01.008, http://www.sciencedirect.com/science/article/B6V1N-4VM2K65-3/2/f8b0b2d64f274154a5eb59da52fbf524

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) Multi-parametric toolbox (MPT). In: Selected topics on constrained and nonlinear control, STU Bratislava–NTNU Trondheim, pp 101–170

33.

Kvasnica M, Grieder P, Baotić M (2004) Multi-parametric toolbox (MPT). http://control.ee.ethz.ch/

34.

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, vol 2993, Springer, Berlin / Heidelberg, pp 121–124

35.

Kvasnica M, Grieder P, Baotic M, Christophersen FJ (2006) Multi-parametric toolbox (MPT). Extended documentation, Zürich. http://control.ee.ethz.ch/~mpt/docs/

36.

Kvasnica M, Christophersen FJ, Herceg M, Fikar M (2008) Polynomial approximation of closed-form MPC for piecewise affine systems. In: Proceedings of the 17th world congress of the international federation of automatic control, Seoul, pp 3877–3882

37.

Kvasnica M, Fikar M, Čirka L’, Herceg M (2011) Complexity reduction in explicit model predictive control. In: Selected topics on constrained and nonlinear control, STU Bratislava–NTNU Trondheim, Bratislava 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.

Kwak MK, Heo S (2007) Active vibration control of smart grid structure by multiinput and multioutput positive position feedback controller. J Sound Vib 304(1–2):230–245. doi: 10.1016/j.jsv.2007.02.021, http://www.sciencedirect.com/science/article/B6WM3-4NH6N96-2/2/ca7b43602b9d052e388f4b2a28f1ebae

40.

Lau K, Zhou L, Tao X (2002) Control of natural frequencies of a clamped–clamped composite beam with embedded shape memory alloy wires. Compos Struct 58(1):39–47. doi:10.1016/S0263-8223(02)00042-9, http://www.sciencedirect.com/science/article/B6TWP-45XTP9W-N/2/07b9a065ac866d8869a4240deb918851

41.

Li S, Kouvaritakis B, Cannon M (2010) Improvements in the efficiency of linear MPC. Automatica 46(1):226–229. doi:10.1016/j.automatica.2009.10.010, http://www.sciencedirect.com/science/article/B6V21-4XGCHXB-3/2/20a93fa6dd4fb88469638ac3bc2fe729

42.

Lin LC, Lee TE (1997) Integrated PID-type learning and fuzzy control for flexible-joint manipulators. J Intell Rob Sys 18:47–66. doi:10.1023/A:1007942528058

43.

Lu H, Meng G (2006) An experimental and analytical investigation of the dynamic characteristics of a flexible sandwich plate filled with electrorheological fluid. Int J Adv Manuf Technol 28:1049–1055. doi:10.1007/s00170-004-2433-8

44.

Luo T, Hu Y (2002) Vibration suppression techniques for optical inter-satellite communications. In: IEEE 2002 international conference on communications, circuits and systems and west sino expositions, vol. 1, pp 585–589. doi:10.1109/ICCCAS.2002.1180687

45.

Maciejowski JM (2000) Predictive control with constraints, 1st edn. Prentice Hall, Upper Saddle River

46.

Malinauskas A (2001) Chemical deposition of conducting polymers. Polymer 42(9):3957–3972. doi: 10.1016/S0032-3861(00)00800-4, http://www.sciencedirect.com/science/article/B6TXW-42C0RR9-1/2/e8084cbb0f228b86a5cc9d061a340e22

47.

Mayne DQ, Rawlings JB, Rao CV, Scokaert POM (2000) Constrained model predictive control: stability and optimality. Automatica 36(6):789–814MathSciNetMATHCrossRef

48.

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

49.

Moon SJ, Lim CW, Kim BH, Park Y (2007) Structural vibration control using linear magnetostrictive actuators. J Sound Vib 302(4–5):875–891. doi: 10.1016/j.jsv.2006.12.023, http://www.sciencedirect.com/science/article/B6WM3-4N2M6HH-5/2/417522adfca8640acfa76e890ae0533c

50.

Moon SM, Cole DG, Clark RL (2006) Real-time implementation of adaptive feedback and feedforward generalized predictive control algorithm. J Sound Vib 294(1–2):82–96. doi:10.1016/j.jsv.2005.10.017, http://www.sciencedirect.com/science/article/B6WM3-4HYMY76-1/2/50d98047187533ebe9d3ea8310446e77

51.

Neat G, Melody J, Lurie B (1998) Vibration attenuation approach for spaceborne optical interferometers. IEEE Trans Control Syst Technol 6(6):689–700. doi: 10.1109/87.726529 CrossRef

52.

Pistikopoulos EN, Georgiadis MC, Dua V (eds) (2007) Multi-parametric model-based control, vol. 2, 1st edn. Wiley-VCH Verlag GmbH & Co., Weinheim

53.

Pistikopoulos EN, Georgiadis MC, Dua V (eds) (2007) Multi-parametric programming, vol 1, 1st edn. Wiley-VCH Verlag GmbH & Co., Weinheim

54.

Pólik I (2005) Addendum to the SeDuMi user guide version 1.1. Technical report, Advanced Optimization Lab, McMaster University, Hamilton. http://sedumi.ie.lehigh.edu/

55.

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

56.

Pradhan S (2005) Vibration suppression of FGM shells using embedded magnetostrictive layers. Int J Solids Struct 42(9–10):2465–2488. doi:10.1016/j.ijsolstr.2004.09.049, http://www.sciencedirect.com/science/article/B6VJS-4F6SSGN-1/2/b6f9e2e6ffc65bfc0c4af5083e37df0b

57.

Preumont A (2002) Vibration control of active structures, 2nd edn. Kluwer Academic Publishers, Dordrecht

58.

Rajoria H, Jalili N (2005) Passive vibration damping enhancement using carbon nanotube-epoxy reinforced composites. Compos Sci Technol 65(14):2079–2093. doi:10.1016/j.compscitech.2005.05.015, http://www.sciencedirect.com/science/article/B6TWT-4GHBPN0-5/2/a67d954050aac7829a56e3e4302c8ef6

59.

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. doi: 10.1109/ISIE.2004.1571872

60.

Rossiter JA (2003) Model-based predictive control: a practical approach, 1st edn. CRC Press, Boca Raton

61.

Shan J, Liu HT, Sun D (2005) Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF). Mechatronics 15(4):487–503. doi:10.1016/j.mechatronics.2004.10.003, http://www.sciencedirect.com/science/article/B6V43-4DR87K7-4/2/2dd311fdd61308e1415cd45c1edc3076

62.

Sturm JF (2001) SeDuMi 1.05 R5 user’s guide. Technical report, Department of Economics, Tilburg University, Tilburg. http://sedumi.ie.lehigh.edu/

63.

Sun D, Mills JK, Shan J, Tso SK (2004) A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement. Mechatronics 14(4):381–401. doi:10.1016/S0957-4158(03)00066-7, http://www.sciencedirect.com/science/article/B6V43-49DN5K4-1/2/fa21df547f182ad568cefb2ddf3a6352

64.

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

65.

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 eleventh IASTED international conference on control and applications, Cambridge

66.

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

67.

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

68.

Tøndel P, Johansen TA, Bemporad A (2003) Evaluation of piecewise affine control via binary search tree. Automatica 39(5):945–950. doi: 10.1016/S0005-1098(02)00308-4, http://www.sciencedirect.com/science/article/pii/S0005109802003084

69.

Tzou H, Chai W (2007) Design and testing of a hybrid polymeric electrostrictive/piezoelectric beam with bang-bang control. Mech Syst Signal Process 21(1):417–429. doi: 10.1016/j.ymssp.2005.10.008, http://www.sciencedirect.com/science/article/B6WN1-4HR75KY-1/2/73701e5908a2ea598fa7bec1ce093563

70.

Wang L (2009) Model predictive control system design and implementation using MATLAB, 1st edn. Springer, London

71.

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

72.

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

73.

Wilson DG, Robinett RD, Parker GG, Starr GP (2002) Augmented sliding mode control for flexible link manipulators. J Intell Rob Syst 34:415–430. doi:10.1023/A:1019635709331

74.

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

75.

Zhang QZ, Gan WS (2004) A model predictive algorithm for active noise control with online secondary path modelling. J Sound Vib 270(4–5):1056–1066. doi: 10.1016/S0022-460X(03)00516-9, http://www.sciencedirect.com/science/article/B6WM3-49D6XFX-4/2/805d0549ca0e60339bb5e2c798de7264

76.

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

Title: Simulation Study of Model Predictive Vibration Control
Authors: Gergely Takács
Boris Rohal’-Ilkiv
Publisher: Springer London
Book: Model Predictive Vibration Control
Print ISBN: 978-1-4471-2332-3

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

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-1-4471-2333-0_11

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"