Robust vibration control of flexible cable-strut structure with mixed uncertainties

Abstract

The design method of μ-synthesis controller for the flexible cable-strut structure with mixed uncertainties was presented and verified by the simulation experiments. The uncertainties include model uncertainties caused by joint clearance and friction, and the uncertainties arising from the actuator range and sensor noise. Based on the structured singular value theory, the model of robust active vibration control for the flexible cable-strut structure was established. The robust performance of the external disturbance rejection is characterized by introducing a fictitious uncertainty block across the disturbance/error channels and carrying out a robust stability analysis. The controller was derived from minimizing the structured singular value. This method considers the structural characteristics of the mixed uncertainty block, so that the conservativeness of H∞ controller in dealing with the mixed uncertainty problem is avoided. The simulation results show that the method has good robustness and stability performances for the controlled system with mixed uncertainties and external disturbances.

Keywords

flexible structure robust control μ synthesis uncertainty vibration control

Get full access to this article

View all access options for this article.

References

Averseng J. , Dube JF , Crosnier B. and Motro R. ( 2005) Active control of a tensegrity plane grid. In: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, Sevilla, Spain, December 12-15, pp. 6830-6834.

Benaroya H. and Nagurka ML ( 2009) Mechanical vibration: analysis, uncertainties, and control (3th). London: CRC Press.

Chan WL , Arbelaez D. , Bossens F. and Skelton RE ( 2004) Active vibration control of a three-stage tensegrity structure . In: Proceedings of SPIE 11th Annual International Symposium on Smart Structures and Materials, San Diego, CA, 14-18 March, pp. 1-7.

Dlapa M. ( 2007) Decoupled control of two tank system via algebraic μ-Synthesis . In: Proceedings of Mediterranean Conference on Control and Automation, Athens, Greece, 27-29 July, pp. 1-6.

Doyle JC ( 1982) Analysis of feedback systems with structured uncertainties . IEE Proceedings D (Control Theory and Applications) 129(6): 242-250.

Doyle JC and Clover K. ( 1989) State-space solutions to standard H2 and H∞ control problems. IEEE Transaction on Automatic Control 34(8): 831-847.

Doyle JC , Wall JE and Stein G. ( 1982) Performance and robustness analysis for structured uncertainty . In: Proceedings of the 20th IEEE Conference on Decision and Control, Orlando, FL, 8-10 December, pp. 629-636.

Guo J. ( 2010) Dynamic characteristics analysis on the deployable structure with joint clearances. Master Dissertation, Xidian University , Xi’an, People’s Republic of China.

Mirats-Tur JM and Juan SH (2009) Tensegrity frameworks: dynamic analysis review and open problems. Mechanism and Machine Theory 44: 1-18.

10.

Raja MG and Narayanan S. ( 2007) Active control of tensegrity structures under random excitation . Journal of Smart Materials and Structures 16(3): 809-817.

11.

Song G. and Gu H. ( 2007) Active vibration suppression of a smart flexible beam using a sliding mode based controller. Journal of Vibration and Control 13(8): 1095-1107.

12.

Zhao Y. (2010) Vibration suppression of a quadrilateral plate using hybrid piezoelectric circuits. Journal of Vibration and Control 16(5): 701-720.

13.

Zhu X. , Liu J. , Huang Q. and Gao S. ( 2009) Robust H∞ control in active vibration control of piezoelectric smart structure. In: Proceedings of the Ninth International Conference on Electronic Measurement and Instruments , Beijing, People’s Republic of China, 16-19 August, pp. 694-698.