This experimental study was conducted for the purpose of enhancing vibration suppression in periodically excited flexible structures by using model predictive control (MPC), an advanced optimal-control method that can be used to handle system constraints at all sampling steps. The Hildreth optimization solver was used to examine two MPC strategies, a basic MPC strategy and a repetitive MPC (RMPC) strategy, and the active vibration-control design and performance of the strategies were evaluated. The disturbance-rejection performance of the applied MPC methods was specifically investigated by using periodic input signals to excite a piezoelectric flexible beam. These comparative studies performed together with parameter analysis offer a design guideline for achieving satisfactory vibration-suppression performance and further demonstrate that the applied RMPC method can effectively suppress the vibration of a flexible-structure system.
BaiMRLinGM (1996) The development of a DSP-based active small amplitude vibration control system for flexible beams by using the LQG algorithms and intelligent materials. Journal of Sound and Vibration198(4): 411–427.
2.
BoscariolPGasparettoAZanottoV (2010) Model predictive control of a flexible links mechanism. Journal of Intelligent and Robotic Systems58(2): 125–147.
3.
BossiLRottenbacherCMimmiGMagniL (2011) Multivariable predictive control for vibrating structures: an application. Control Engineering Practice19(10): 1087–1098.
4.
CamachoEFBordonsC (2004) Model Predictive Control, London: Springer.
5.
FansonJCaughekT (1990) Positive position feedback control for large space structures. AIAA Journal28(4): 717–724.
6.
HalimDMoheimaniSOR (2001) Spatial resonant control of flexible structures - application to a piezoelectric laminate beam. IEEE Transactions on Control Systems Technology9(1): 37–53.
7.
HassanMDubayRLiCWangR (2007) Active vibration control of a flexible one-link manipulator using a multivariable predictive controller. Mechatronics17(6): 311–323.
8.
IorgaLBaruhH (2008) A review of H∞ robust control of piezoelectric smart structures. Applied Mechanics Review61(4): 040802(1–15).
9.
KhoshnoodAMMoradiHM (2014) Robust adaptive vibration control of a flexible structure. ISA Transactions. DOI: 10.1016/j.isatra.2014.03.004.
10.
Kim B and Washington GN (2008) Active vibration control of a cantilevered beam using model predictive sliding mode control. In Proceedings of 49th AIAA Structures, Structural Dynamics, and Materials Conference, Schaumburg, IL, April 7–10, pp. 2008–2038.
11.
LinCYChangCM (2013) Hybrid proportional derivative/repetitive control for active vibration control of smart piezoelectric structures. Journal of Vibration and Control19(7): 992–1003.
12.
LinCYLiuYC (2011) Precision tracking control and constraint handling of mechatronic servo systems using model predictive control. IEEE/ASME Transactions on Mechatronics17(4): 593–605.
13.
LinCYChiuWHLinJ (2014) Rejecting multiple-period disturbances: Active vibration control of a two degree-of-freedom piezoelectric flexible structure system. Journal of Vibration and Control. Epub ahead of print 10 March 2014. DOI: 10.1177/1077546314521850.
14.
LinJChaoWS (2009) Vibration suppression control of beam-cart system with piezoelectric transducers by decomposed parallel adaptive neuro-fuzzy control. Journal of Vibration and Control15(12): 1885–1906.
15.
LinJLiuWZ (2006) Experimental evaluation of a piezoelectric vibration absorber using a simplified fuzzy controller in a cantilever beam. Journal of Sound and Vibration296(3): 567–582.
16.
PanYWangJ (2012) Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Transactions on Industrial Electronics59(8): 3089–3101.
17.
PreumontA (2011) Vibration Control of Active Structures, Berlin: Springer.
18.
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 Proceedings of IEEE International Symposium on Industrial Electronics, Ajaccio, France, May 4–7, vol. 1, pp. 583–588.
19.
Takács G and Rohal’-Ilkiv B (2009) MPC with guaranteed stability and constraint feasibility on flexible vibrating active structures: a comparative study. In Proceedings of the IASTED International Conference Control and Applications, Cambridge, UK, July 13–15, pp. 278–285.
20.
TakácsGRohal’-IlkivB (2012) Model Predictive Vibration Control: Efficient Constrained MPC Vibration Control for Lightly Damped Mechanical Structures, Berlin: Springer.
WangL (2009) Model Predictive Control System Design and Implementation Using MATLAB, Berlin: Springer.
23.
WangRLGuHSongG (2014) Adaptive robust sliding mode vibration control of a flexible beam using piezoceramic sensor and actuator: an experimental study. Mathematical Problems in Engineering. 2014, Article ID 606817, 9 pp. DOI: 10.1155/2014/606817.
24.
WangYBoydS (2010) Fast model predictive control using online optimization. IEEE Transactions on Control Systems Technology18(2): 267–278.
25.
Wills AG, Bates D, Fleming A, Ninness B and Moheimani R (2005) Application of MPC to an active structure using sampling rates up to 25 kHz. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, December 12–15, pp. 3176–3181.
26.
WillsAGBatesDFlemingAJNinnessBMoheimaniSOR (2008) Model predictive control applied to constraint handling in active noise and vibration control. IEEE Transactions on Control Systems Technology16(1): 3–12.
27.
WillsAGKnaggeGNinnessB (2012) Fast linear model predictive control via custom integrated circuit architecture. IEEE Transactions on Control Systems Technology20(1): 59–71.
28.
Wills AG, Mills A and Ninness B (2011) FPGA implementation of an interior-point solution for linear model predictive control. In Proceedings of the 18th IFAC World Congress, Milano, Italy, August 28–Sept. 2, vol. 18, pp. 14527–14532.
29.
Zmeu K and Shipitko E (2005) Predictive controller design with offline model learning for flexible beam control. In Proceedings of the International Conference on Physics and Control, St. Petersburg, Russia, August 24–26, pp. 345–350.
