Model predictive control algorithms for active vibration control: a study on timing,performance and implementation properties

Abstract

The dynamic properties of vibration control systems pose unique requirements and challenges on the implementation of model predictive control (MPC) algorithms with stability and feasibility guarantees. This article presents a comprehensive experimental comparison of computation timing and damping performance for various MPC methods; analyzing their offline and online properties in active vibration control and their impact on practical implementability. Optimal and sub-optimal MPC algorithms providing guaranteed stability and constraint feasibility have been applied to the real-time active vibration attenuation of a lightly damped mechanical test structure. Based on the experiments presented in this paper, the standard and sequential quadratic programming-based, optimal and sub-optimal minimum time multi-parametric programming-based and the sub-optimal Newton–Raphson’s algorithm-based MPC methods demonstrate closely comparable vibration attenuation performance. The offline and online timing analysis indicates that the underlying difference between the investigated MPC algorithms lies mainly in practical implementability difficulties caused by inherent algorithm efficiency, rendering certain variants of MPC more suitable for vibration control than others.

Keywords

Model predictive control vibration control model-based control optimal control timing computational efficiency algorithm stability constraint feasibility implementation

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References

Bossi

Rottenbacher

Mimmi

Magni

(2011) Multivariable predictive control for vibrating structures: An application. Control Engineering Practice 19: 1087–1098. DOI: 10.1016/j.conengprac.2011.05.003.

Canale

Milanese

Novara

(2006) Semi-active suspension control using fast model-predictive techniques. IEEE Transactions on Control Systems Technology 14: 1034–1046. DOI: 10.1109/TCST.2006.880196.

Cannon

Kouvaritakis

(2005) Optimizing prediction dynamics for robust MPC. IEEE Transactions on Automatic Control 50: 1892–1597.

Chen

Allgöver

(1998) A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34: 1205–1217.

Dongarra

(2002) Basic linear algebra subprograms technical forum standard. International Journal of High Performance Applications and Supercomputing 16: 1–111.

Faylor C, Vinschen C, Chamberlain S, Okhapkin S, Giacinti P and Taylor IL (2009) Cygwin. http://www.cygwin.com/.

Ferreau HJ (2006) An Online Active Set Strategy for Fast Solution of Parametric Quadratic Programs with Applications to Predictive Engine Control. Master’s thesis, University of Heidelberg.

Ferreau

Bock

Diehl

(2008) An online active set strategy to overcome the limitations of explicit MPC. International Journal of Robust and Nonlinear Control 18: 816–830.

Ferreau

Ortner

Langthaler

del Re

Diehl

(2007) Predictive control of a real-world diesel engine using an extended online active set strategy. Annual Reviews in Control 31: 293–301. DOI: 10.1016/j.arcontrol.2007.09.001.

10.

Franklin

Powell

Workman

(1997) Digital Control of Dynamic Systems, 3rd edn. Boston, MA: Addison-Wesley.

11.

Fuller

Elliott

Nelson

(1996) Active Control of Vibration, 1st edn. San Francisco, CA: Academic Press.

12.

Garcìa

Prett

Morari

(1989) Model predictive control: Theory and practice—a survey. Automatica 25: 335–348. DOI: 10.1016/0005-1098(89)90002-2.

13.

Hassan

Dubay

Wang

(2007) Active vibration control of a flexible one-link manipulator using a multivariable predictive controller. Mechatronics 17: 311–323.

14.

Inman

(2006) Vibration with control, Chichester: John Wiley & Sons.

15.

Jalali A and Nadimi V (2006) A survey on robust model predictive control from 1999-2006. In: International Conference on Computational Intelligence for Modelling, Control and Automation, 2006 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, p. 207. DOI: 10.1109/CIMCA.2006.29.

16.

Johansen

Jackson

Schreiber

Tøndel

(2007) Hardware synthesis of explicit model predictive controllers. IEEE Transactions on Control Systems Technology 15: 191–197.

17.

Kouvaritakis

Cannon

Rossiter

(2002) Who needs QP for linear MPC anyway? Automatica 38: 879–884.

18.

Kouvaritakis

Rossiter

Schuurmans

(2000) Efficient robust predictive control. IEEE Transactions on Automatic Control 45: 1545–1549.

19.

Kvasnica

(2009) Real-Time Model Predictive Control via Multi-Parametric Programming: Theory and Tools, 1st edn. Saarbrücken: VDM Verlag.

20.

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

21.

Ljung

(1999) System Identification: Theory for the User, 2nd edn. Upper Saddle River, NJ: PTR Prentice Hall.

22.

Lofberg J (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei, Taiwan.

23.

Maciejowski

(2000) Predictive Control with Constraints, 1st edn. Upper Saddle River, NJ: Prentice Hall.

24.

Mayne

Rawlings

Rao

Scokaert

POM

(2000) Constrained model predictive control: Stability and optimality. Automatica 36: 789–814.

25.

Niederberger D (2005) Design of optimal autonomous switching circuits to suppress mechanical vibration. Hybrid Systems: Computation and Control (Lecture Notes in Computer Science, vol. 3414). Berlin: Springer, pp. 511–525.

26.

Preumont

(2002) Vibration Control of Active Structures, 2nd edn. Dodrecht: Kluwer Academic Publishers.

27.

Qin

Badgwell

(2003) A survey of industrial model predictive control technology. Control Engineering Practice 11: 733–764. DOI: 10.1016/S0967-0661(02)00186-7.

28.

Richelot J, Bordeneuve-Guibe J and 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.

29.

Rossiter

(2003) Model-Based Predictive Control: A Practical Approach, 1st edn. Boca Raton, FL: CRC Press.

30.

Sturm

(1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11–12: 625–653.

31.

Takács

Rohal'-Ilkiv

(2012) Predictive Vibration Control: Efficient constrained MPC vibration control for lightly damped mechanical systems, 1st edn. London: SpringerDOI: 10.1007/978-1-4471-2333-0.

32.

Wills

Bates

Fleming

Ninness

Moheimani

SOR

(2008) Model predictive control applied to constraint handling in active noise and vibration control. IEEE Transactions on Control Systems Technology 16: 3–12.