Operator-based nonlinear free vibration control of a flexible plate with sudden perturbations

Abstract

In this paper, a new nonlinear vibration control scheme using piezoelectric actuator is proposed for a flexible plate with a free vibration and sudden perturbations. First, the effect of hysteresis nonlinearity from the piezoelectric actuator is considered by Prandtl-Ishlinskii (P-I) hysteresis model. Simultaneously, a dynamic model of the flexible plate with piezoelectric actuator is considered. Then, based on the dynamic model of the flexible plate, operator-based controllers are designed to guarantee the robust stability of the nonlinear control system. In addition, for ensuring the desired vibration control performance of the flexible plate with a free vibration and sudden perturbations, operator-based compensation method is given by the proposed design scheme. In the designed compensator, the desired compensation performances of tracking and of perturbations are obtained by increasing the number of designed n-times feedback loops. Finally, both of numerical simulation and experimental result are shown to verify the effectiveness of the proposed design scheme.

Keywords

Active vibration control actuators compensation nonlinear control robust control operator theory

Get full access to this article

View all access options for this article.

References

Bailey

Hubbart

(1985) Distributed piezoelectric-polymer active vibration control of a cantilever beam. Journal of Guidance, Control and Dynamics 8(5): 605–611.

Banos

(1994) A right coprime factorization of feedback linearizable systems. In: Proceedings of the 1994 American Control Conference, Baltimore, MD, USA, 29 June–1 July 1994, pp. 1700–1701. IEEE.

Deng

(2012) Operator based robust control of MIMO aluminum plate thermal process. International Journal of Computer Application in Technology 44(4): 249–256.

Deng

(2012) Operator-based robust right coprime factorization and a nonlinear control scheme for nonlinear plant with unknown perturbations. Asian Journal of Control 14(16): 1655–1661.

Chen

Han

(1998) Robust right factorization and robust stabilization of nonlinear feedback control systems. IEEE Transactions on Automatic Control 43(10): 1505–1510.

Dimitriadis

Fuller

Rogers

(1991) Piezoelectric actuators for distributed vibration excitation of thin plates. Journal of Vibration and Acoustics 113(1): 100–107.

Deng

(2014) Operator-Based Nonlinear Control Systems Design and Applications. Wiley-IEEE Press. New Jersey: John Wiley & Sons, Inc., Hoboken.

Deng

Jiang

Inoue

(2011a) Operator based robust control for nonlinear systems with prandtl-ishlinskii hysteresis. International Journal of Systems Science 42(4): 643–652.

Deng

Wen

Inoue

(2011b) Operator-based robust nonlinear control for a Peltier actuated process. Measurement and Control: The Journal of the Institute of Measurement and Control 44(4): 116–120.

10.

Hassani

Tjahjowidodo

(2014) A survey on hysteresis modeling, identification and control. Mechanical Systems and Signal Processing 49(1–2): 209–233.

11.

Jiang

(2013) ELM-based parallel compensation control for perturbed plants with hysteresis. IEEJ Transactions on Electronics Information and Systems 133(10): 1930–1935.

12.

Jin

Deng

Wakitani

(2018) Operator based two loop nonlinear forced vibration control of a flexible plate. Electrical Engineering in Japan 203(2): 19–28.

13.

Katsurayama

Deng

Jiang

(2016) Operator-based experimental studies on nonlinear vibration control for an aircraft vertical tail with considering low-order modes. Transactions of the Institute of Measurement and Control 38(12): 1421–1433.

14.

Leissa

(1969) Vibration of plates. NASA-SP-160. Pittsburgh: U.S. Govt. Printing Office, pp. 59–60.

15.

Wang

Deng

(2013) Robust nonlinear multivariable tracking control design to a manipulator with unknown uncertainties using operator-based robust right coprime factorization. Transactions of the Institute of Measurement and Control 35(6): 788–797.

16.

Wen

Deng

Wang

(2012) Operator-based robust nonlinear control and its realization for a multi-tank process by using DCS. Transactions of the Institute of Measurement and Control 34(7): 891–902.