Modelling and H ∞ control of a single-link flexible manipulator

Abstract

The aim of this study is to investigate motion in the horizontal and the vertical planes of a single-link flexible manipulator. The manipulator is modelled including gravity terms, and it is verified experimentally that the horizontal and the vertical motions are decoupled for a cylindrically symmetrical link and payload. The mathematical model is used to design a mixed-sensitivity H^∞ contrlllerr. The sensitivity weighting function is used to obtain the required disturbance rejection properties, including zero sensitivity to a force disturbance in the steady state (i. e. integral action control). The control sensitivity weighting function is chosen to guarantee stability despite variation in the payload mass. The controller is compared experimentally with a proportional-plus-integral controller with velocity feedback and shown to give improved vibration control performance in the vertical plane.

Keywords

flexible manipulator robust control vibration control

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References

Book

W. J.

Modelling, design and control of flexible manipulator arms. PhD thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, 1974.

Cannon

R. H.

Jr. Schmitz

Initial experiments on the end-point control of a flexible one-link robot. Int. J. Robotics Res., 1984, 3 (3), 62–74.

Singh

S. N.

Control and stabilisation of a non-linear uncertain elastic robotic arm. IEEE Trans., 1988, AES-24, 148–155.

Kanoh

Tzafestas

Lee

H. G.

Kalat

Modelling and control of flexible robot arms. In Proceedings of the 25th Conference on

Decision and Control, Athens, 1996, pp. 1866–1870 (IEEE, New York).

Tokhi

Azad

A. K. M.

Modelling of a single link flexible manipulator system: Theoretical and practical investigations. Robotica, 1996, 14, 91–102.

Fraser

A. R.

Daniel

R. W.

Perturbation techniques for flexible manipulators, 1991, (Klueer, Deventer).

Theodore

R. J.

Ghosal

Comparison of the assumed modes and finite element models for flexible multi-link manipulators. Int. J. Robotics Res., 1995, 14 (2), 91–111.

Sakawa

Matsuno

Fukushima

Modelling and feedback control of a flexible arm. J. Robotic Systems, 1985, 2 (4), 453–472.

Truckenbrodt

Truncation problems in the dynamics and control of flexible mechanical systems. In Proceedings of the Eighth Triennial IFAC Congress, 1982, pp. 1909–1914.

10.

Devasia

Paden

Bayo

Vibration control of an experimental two link manipulator. In Proceedings of the American Control Conference, 1993, pp. 2093–2098.

11.

Khorrami

Jain

Non-linear control with end-point acceleration feedback for a two-link flexible manipulator: Experimental results. J. Robotic Systems, 1993, 10 (4), 505–530.

12.

de Luca

Siciliano

Regulation of flexible arms under gravity. IEEE Trans. Robotics Automn, 1993, 9 (4), 463–467.

13.

Lenz

Ozbay

Tannebaum

Turi

Morton

Frequency domain analysis and robust control design for an ideal flexible beam. Automatica, 1991, 27, 947–961.

14.

Cashmore

R. D.

Adaptive and robust control of a flexible manipulator system. PhD thesis, University of Leeds, 1993.

15.

Matsuno

Tanaka

Robust force and vibration control of a flexible arm without a force sensor. In Proceedings of the 34th IEEE Conference on

Decision and Control, 1995, pp. 2835–2840 (IEEE, New York).

16.

Estiko

Tanaka

Moran

Hayase

H∞ control of flexible arm considering motor dynamics and optimum sensor location. In Proceedings of IPEC, Yokohama, 1995, pp. 1440–1445.

17.

Landau

I. D.

Langer

Rey

Barnier

Robust control of 360° flexible arm using the combined pole placement/sensitivity function shaping method. IEEE Trans. Control Systems Technology, 1996, 4 (4), 369–383.

18.

Jovik

Lennartson

On the choice of criteria and weighting functions of an H²/H∞ design problem. In Proceedings of the 13th Triennial World Congress, 1996, pp. 373–378.

19.

Trautman

Wang

Experimental H∞ control of a single flexible link with a shoulder joint. In Proceedings of the IEEE International Conference on

Robotics and Automation, 1995, pp. 1235–1241 (IEEE, New York).

20.

Timoshenko

Young

D. H.

Weaver

Jr.

Vibration Problems in Engineering, 4th edition, 1994 (John Wiley, New York).

21.

Meirovitch

Elements of Vibration Analysis, 1986 (McGraw-Hill, New York).

22.

Zhou

Doyle

J. C.

Glover

Robust and Optimal Control, 1996 (Prentice-Hall, Englewood Cliffs, New Jersey).

23.

Sutton

R. P.

The control and modelling of a highly flexible single link robot arm. PhD thesis, The University of Leeds, 1997.