Abstract
In controlling flexible space structures one always encounters the problem that the control design is based on an inaccurate model. The inaccuracy in the models are for instance unknown damping, neglected dynamics and inaccuracy in the position of actuators and sensors. Therefore the control design must be robust.
As a simple model for such a structure we will use a partial differential equation for a one-dimensional beam with point actuators and sensors. This beam model belongs to a class of infinite-dimensional systems, which have possibly unbounded, finite-rank input and output operators. For our model we assume that both the damping as the stiffness coefficient are not exactly known.
The problem of robustly stabilizing a linear system subject to respectively additive, multiplicative and stable factor perturbations of its transfer function is considered for our flexible beam model. In particular, we will discuss the possibility of modelling the uncertainty in the parameters in our model as additive, multiplicative or stable factor perturbations.
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6. References
J. Bontsema, Dynamic stabilization of large flexible space structures, PhD-thesis, Groningen, 1989.
J. Bontsema and R.F. Curtain, Robust stabilization of a flexible beam model using a normalized coprime factorization approach, In Control of uncertain systems, Eds. D. Hinrichsen and B. Mårtensson, Proceedings of an international workshop, Bremen, Germany, June 1989, Birkhäuser, Boston, 1990.
J. Bontsema and T. van der Vaart, Comparison of robustness measures for a flexible structure. In Robust Control of Linear Systems and Nonlinear Control, Eds. M.A. Kaashoek, J.H. van Schuppen and A.C.M. Ran, proceedings MTNS-89, vol. II, Birkhäuser, Boston, 1990, pp. 583–590.
R.F. Curtain, Robust controllers for infinite-dimensional systems, (this volume).
R.F. Curtain and K. Glover, Robust stabilization of infinite dimensional systems by finite dimensional controllers, Systems and Control Letters 7, pp. 41–47. 1986.
T.T. Georgiou and M.C. Smith, Optimal robustness in the gap metric, IEEE Trans. on Autom. Control, 1990, pp. 673–686.
K. Glover, Robust stabilization of multivariable systems: relations to approximation, Int. J. Control, 43, 1986, pp. 741–766.
D.C. McFarlane and K. Glover, Robust controller design using normalized coprime factor descriptions, LNCIS 138, Springer Verlag, Berlin, 1990.
H.M. Osinga, Design of a robustly stabilizing controller for a system wth multiplicative uncertainty, MSc-thesis, Groningen, 1991.
A.A. Stoorvogel, H∞-control problem: a state space approach, Prentice Hall, New York, 1992.
J.T. van der Vaart, Comparison of robustness measures for a flexible structure, MSc-thesis, Groningen, 1989.
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Bontsema, J., Curtain, R.F., Kuiper, C.R., Osinga, H.M. (1993). Comparison of robustly stabilizing controllers for a flexible beam model with additive, multiplicative and stable factor perturbations. In: Curtain, R.F., Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems. Lecture Notes in Control and Information Sciences, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0115038
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DOI: https://doi.org/10.1007/BFb0115038
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