The control of a two-link manipulator with a sliding flexible link that traverses inside a rigid link is considered. Since the plant possesses time-varying dynamics that change with the position of the tip, and considerable uncertainty, a fixed controller is unsatisfactory in terms of both performance and robustness. Hence, a controller that schedules with the position is sought and implemented. An H∞ approach is adopted, and the resulting controller provides good performance and stability margins.
Balakrishnan, A.V., 1988, Control of Flexible Flight Structures, Volume dedicated to J. J. Lions, Gauthier-Villari, Paris. Balas, M.J., 1979, "Direct velocity feedback control of large space structures," AIAA Journal of Guidance and Control2(3).
2.
Balas, M.J., 1982, "Trends in large space structures control theory: Fondest hopes, wildest dreams," IEEE Transactions on Automatic Control23(3).
3.
Cannon, R.H. and Schmitz, E., 1984, "Initial experiments on the end-point control of a flexible one-link robot," The International Journal of Robotics Research3(3), 546-558.
4.
Doyle, J.C., 1981, "Guaranteed margins for LQG regulators," IEEE Transactions on Automatic Control AC-34, 831-832.
5.
Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A., 1989, "State space solutions to standard H2 and H∞ problems," IEEE Transactions on Automatic Control AC-34, 831-847.
6.
Gevarter, W.B., 1970, "Basic relations for control of flexible structures ," AIAA Journal of Guidance, Control and Dynamics8, 666-672.
7.
Hyde, R.A. and Glover, K., 1993, "The application of scheduled H∞ controllers to a VSTOL Aircraft," IEEE Transactions on Automatic Control38(7).
8.
Joshi, S.M., 1989, Control of Large Flexible Space Structures, Lecture Notes in Control and Information Sciences, Springer-Verlag, New York/Berlin.
9.
Kim, Y.K., 1988, Adaptive Control of a Robotic Manipulator With a Sliding Flexible Link, Ph.D. dissertation, University of California , Los Angeles.
10.
Kim, Y.K. and Gibson, J.1991, "A variable order adaptive controller for a manipulator with sliding flexible link", IEEE Transactions on Robotics and Automation7(6).
11.
Martin, G., 1978, On the Control of Flexible Mechanical Systems, Ph.D. thesis, Department of Aeronautics and Astronautics, Stanford University.
12.
McFarlane, D.C. and Glover, K., 1990, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions, Lecture Notes in Control and Information Sciences , Springer-Verlag, New York/ Berlin .
13.
Tahk, M. and Speyer, J.L., 1987, "Modelling of parameter vanations and asymptotic LQG synthesis ," IEEE Transactions on Automatic Control32.
14.
Vidyasagar, M., 1985, Control System Synthesis-A Factorization Approach , MIT Press, Cambridge.
15.
Zames, G., 1966, "On the input-output stability of time-varying nonlinear feedback systems, Part 1," IEEE Transactions on Automatic Control11, 465-476.