QFT Control of a Two-Link Rigid-Flexible Manipulator

Document Type: Original Article

Authors

Yazd University

Abstract

This paper evaluates a new and simple controller design method based on QFT (quantitative feedback theory) for a two-link manipulator whose first link is rigid and the second is flexible. A piezoelectric patch is attached to the surface of the flexible link for vibration suppression of it. This system is modeled as a nonlinear multi-input multi-output (MIMO) control systems whose inputs are two motor torques which are applied on the joints and a voltage which is applied on the piezoelectric patch. To control the manipulator’s end point position, motion of the manipulator is divided to two rigid and flexible parts. To control both parts, nonlinear equations of the motion is replaced by a family of uncertain linear time-invariant equivalent systems using Rafeeyan-Sobhani’s method(RS method) which results in three decoupled transfer functions established in the Laplace domain. Then the QFT method is used to design a diagonal matrix as the prefilter of the system an another diagonal matrix as the system controller. Results demonstrate the remarkable performance of the proposed controllers in reduction of residual vibration of elastic link and tracking a circular trajectory by the manipulator end point.

Keywords


S. Choura and A. S. Yigit, ²Control of a twolink rigid-flexible manipulator with a moving payload mass² , Journal of Sound and vibration, vol. 243, pp. 883-897, 2001.

T. W. Yang, W. L. Xu, and S. K. Tso, ²Dynamic modeling based on real-time reflection measurement and compensation control for flexible multi-link manipulators ² , Journal of Dynamics and Control,vol. 11, pp. 5-24, 2001.

S. K. Ider, M. K. Ozgoren, and V. Ay, ²Trajectory tracking control of robots with flexible links ² , Journal of Mechanism and Machine Theory, vol. 37, pp. 1377-1394, 2002.

Z. X. Shi, H. K. Fung, and Y. C. Li, ²Dynamic modeling of rigid-flexible manipulator for constrained motion task control² , Journal of Applied Mathematical Modeling, vol. 23, pp. 509-525, 1999.

N. C. Park, H. S. Yang, H. W. Park, and Y. P. Park, ²Position/vibration control of twodegree-of-freedom arms having one flexible link with artificial pneumatic muscle actuators ² , Journal of Robotics and Autonomous Systems, vol. 40, pp. 239-253, 2002.

R. J. Theodore, and A. Ghosl, ²Robust control of multilink flexible manipulators² , Journal of Mechanism and Machine Theory, vol. 38, pp. 367-377, 2003.

L. Tian, and C. Collins, ²A dynamic recurrent neural network-based controller for a rigidflexible manipulator system² , Journal of Mechateronics, vol. 14, pp. 471-490, 2004.

B. Subudhi, and A.S. Morris, ²Soft computing methods applied to the control of a flexible robot manipulator² , Journal of Applied Soft Computing,vol. 9, pp. 149-158, 2009.

A. N. Irani, and H. A. Talebi, ²Tip tracking of a rigid-flexible manipulator based on deflection estimation using neural network observer: A backstepping approach² , in IECON 2011 - 37th Annual Conference on IEEE Industrial Electronics Society, 2011, pp. 313 - 318.

O. Yaniv, Quantitative feedback design of linear and nonlinear control systems,Massachusetts, USA: Kluwer Academic Publishers, 1999.

S. B. Choi, S. S. Cho, H. C. Shin, and H. K. Kim, ²Quantitative feedback theory control of single-link flexible manipulator featuring piezoelectric actuator and sensor² , Journal of Smart Materials Structures,vol. 8, pp. 338- 349, 1999.

M. Sobhani, and M. Rafeeyan, ²Robust controller design for multivariable nonlinear uncertain systems² , Iranian Journal of Science & Technology, vol. 24, pp. 345-356, 2000.

C. Borgesani, Y. Chait, O. Yaniv, TheQFT frequency Domain Control Design Toolbox for Use with MATLAB, Terasoft Inc., 2003.