All Title Author
Keywords Abstract

Improving Delay-Margin of Noncollocated Vibration Control of Piezo-Actuated Flexible Beams via a Fractional-Order Controller

DOI: 10.1155/2014/809173

Full-Text   Cite this paper   Add to My Lib


Noncollocated control of flexible structures results in nonminimum-phase systems because the separation between the actuator and the sensor creates an input-output delay. The delay can deteriorate stability of closed-loop systems. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order controller. Results of real life experiments illustrate efficiency of the controller and show that the fractional-order controller has better stability robustness than the integer-order controller. 1. Introduction Flexible structures have attracted increasing attentions for many applications because of their weights and production costs. However, the flexibility leads to unwanted vibration problems. Thus, vibration control is usually needed. Over the past few decades, active vibration control has drawn more interest from researchers since it can effectively suppress the vibration [1, 2]. A large part of the active vibration control research has used piezoelectric materials for actuation and sensing. Advantages of using piezo-actuators/sensors include nanometer scale resolution, high stiffness, and fast response. Piezo-actuators have been proven to be useful in suppressing structural vibration [3, 4]. Stabilization of flexible structures can be easily done by collocating the sensors and the actuators. However, the collocated control configuration is not always feasible in practice and its performance is not always satisfactory. Thus, noncollocated control has been investigated [5, 6]. However, noncollocated control results in a nonminimum-phase closed-loop system because the separation between the actuator and the sensor creates an input-output delay, which can deteriorate stability of the closed-loop system. Fractional calculus is a 300-year-old mathematical topic [7, 8]. However, its practical applications have just recently been explored. Recently, fractional-order control has been attracting interest. It has been illustrated that fractional-order controllers yield superior performance to integer-order controllers [9, 10]. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order proportional-integral-derivative (PID) controller. The rest of the paper is organized as follows. Section 2 provides some preliminaries. Section 3 describes the piezo-actuated flexible beam that is used as an experimental test bench. Section 4 presents a finite element model of the


[1]  C. C. Fuller, Active Control of Vibration, Academic Press, 1996.
[2]  A. Preumont, Vibration Control of Active Structures, Kluwer Academic Publishers, 2004.
[3]  S. V. Gosavi and A. G. Kelkar, “Modelling, identification, and passivity-based robust control of piezo-actuated flexible beam,” Journal of Vibration and Acoustics, vol. 126, no. 2, pp. 260–271, 2004.
[4]  Z. Zhang, Y. Chen, H. Li, and H. Hua, “Simulation and experimental study on vibration and sound radiation control with piezoelectric actuators,” Shock and Vibration, vol. 18, no. 1-2, pp. 343–354, 2011.
[5]  Z. Qiu, J. Han, X. Zhang, Y. Wang, and Z. Wu, “Active vibration control of a flexible beam using a non-collocated acceleration sensor and piezoelectric patch actuator,” Journal of Sound and Vibration, vol. 326, no. 3-5, pp. 438–455, 2009.
[6]  C. Spier, J. C. Bruch, J. M. Sloss, I. S. Sadek, and S. Adali, “Effect of vibration control on the frequencies of a cantilever beam with non-collocated piezo sensor and actuator,” IET Control Theory and Applications, vol. 5, no. 15, pp. 1740–1747, 2011.
[7]  I. Podlubny, Fractional Differential Equations, Academic Press, 1999.
[8]  D. Cafagna, “Fractional calculus: a mathematical tool from the past for present engineers,” IEEE Industrial Electronics Magazine, vol. 1, no. 2, pp. 35–40, 2007.
[9]  C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Engineering Practice, vol. 16, no. 7, pp. 798–812, 2008.
[10]  T. Sangpet and S. Kuntanapreeda, “Force control of an electrohydraulic actuator using a fractional order controller,” Asian Journal of Control, vol. 15, no. 3, pp. 764–772, 2013.
[11]  B. Bandyopadhyay, T. C. Manjunath, and M. Umapathy, Modeling, Control and Implementation of Smart Structures: A FEM-State Space Approach, Spinger, Berlin, Germany, 2007.
[12]  Z. Qiu, X. Zhang, and C. Ye, “Vibration suppression of a flexible piezoelectric beam using BP neural network controller,” Acta Mechanica Solida Sinica, vol. 25, no. 4, pp. 417–428, 2012.
[13]  V. Y. Perel and A. N. Palazotto, “Finite element formulation for dynamics of delaminated composite beams with piezoelectric actuators,” International Journal of Solids and Structures, vol. 39, no. 17, pp. 4457–4483, 2002.
[14]  S. Y. Wang, “A finite element model for the static and dynamic analysis of a piezoelectric bimorph,” International Journal of Solids and Structures, vol. 41, no. 15, pp. 4075–4096, 2004.
[15]  D. L. Logan, A First Course in the Finite Element Method, Wadsworth Group, 2002.
[16]  B. M. Vinagre, I. Podlubny, A. Hernandez, and V. Feliu, “Some approximations of fractional order operators used in control theory and applications,” Fractional Calculus and Applied Analysis, vol. 3, pp. 231–248, 2000.


comments powered by Disqus

Contact Us


微信:OALib Journal