[en] The inverse dynamics of flexible multibody systems is formulated as a two-point boundary value problem for an index-3 differential-algebraic equation (DAE). This DAE represents the equation of motion with kinematic and trajectory constraints. For so-called nonminimum phase systems, the remaining dynamics of the inverse model is unstable. Therefore, boundary conditions are imposed not only at the initial time but also at the final time in order to obtain a bounded solution of the inverse model. The numerical solution strategy is based on a reformulation of the DAE in index-2 form and a multiple shooting algorithm, which is known for its robustness and its ability to solve unstable problems. The paper also describes the time integration and sensitivity analysis methods that are used in each shooting phase. The proposed approach does not require a reformulation of the problem in input-output normal form known from nonlinear control theory. It can deal with serial and parallel kinematic topology, minimum phase and nonminimum phase systems, and rigid and flexible mechanisms.
Disciplines :
Mechanical engineering
Author, co-author :
Bruls, Olivier ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques
Bastos, Guaraci Jr.
Seifried, Robert
Language :
English
Title :
A stable inversion method for feedforward control of constrained flexible multibody systems
Publication date :
January 2014
Journal title :
Journal of Computational and Nonlinear Dynamics
ISSN :
1555-1415
eISSN :
1555-1423
Publisher :
American Society of Mechanical Engineers, New York, United States - New York
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Bibliography
Cannon Jr., R.H., Schmitz, E., Initial experiments on the end-point control of a flexible one-link robot (1984) International Journal of Robotics Research, 3 (3), pp. 62-75
Book, W., Controlled motion in an elastic world (1993) ASME J. Dyn. Syst., Measu., Control, 115 (2 B), pp. 252-261
Da Silva, M., Bruls, O., Swevers, J., Desmet, W., Van Brussel, H., Computer-aided integrated design for machines with varying dynamics (2009) Mech. Mach. Theory, 44, pp. 1733-1745
Fliess, M., Lévine, J., Martin, P., Rouchon, P., Flatness and defect of nonlinear systems: Introductory theory and examples (1995) Int. J. Control, 61, pp. 1327-1361
Isidori, A., (1995) Nonlinear Control Systems, , 3rd ed., Springer, London
Sastry, S., (1999) Nonlinear Systems: Analysis, Stability and Control, , Springer, New York
Van Nieuwstadt, M.J., Murray, R.M., Real-time trajectory generation for differentially flat systems (1998) International Journal of Robust and Nonlinear Control, 8 (11), pp. 995-1020
Asada, H., Slotine, J.-J., (1986) Robot Analysis and Control, , Wiley-Inter-science, New York
Spong, M., Modeling and control of elastic joint robots (1987) ASME J. Dyn. Syst., Meas., Control, 109 (4), pp. 310-318
Kwon, D., Book, W., A time-domain inverse dynamic tracking control of a single-link flexible manipulator (1994) ASME J. Dyn. Syst., Meas., Control, 116 (2), pp. 193-200
Devasia, S., Bayo, E., Inverse dynamics of articulated flexible structures: Simultaneous trajectory tracking and vibration reduction (1994) J. Dyn. Control, 4 (3), pp. 299-309
Seifried, R., Held, A., Dietmann, F., Analysis of feed-forward control design approaches for flexible multibody systems (2011) J. Syst. Des. Dyn., 5 (3), pp. 429-440
Seifried, R., Burkhardt, M., Held, A., Trajectory control of serial and parallel flexible manipulators using model inversion (2013) Multibody Dynamics: Computational Methods and Applications, Computational Methods in Applied Sciences, 28. , J. Samin and P. Fisette, eds., Springer, New York
Devasia, S., Chen, D., Paden, B., Nonlinear inversion-based output tracking (1996) IEEE Transactions on Automatic Control, 41 (7), pp. 930-942. , PII S0018928696053445
Taylor, D.G., Li, S., Stable inversion of continuous-time nonlinear systems by finite-difference methods (2002) IEEE Transactions on Automatic Control, 47 (3), pp. 537-542. , DOI 10.1109/9.989157, PII S0018928602028386
Seifried, R., Two approaches for feedforward control and optimal design of underactuated multibody systems (2012) Multibody Syst. Dyn., 27 (1), pp. 75-93
Seifried, R., Integrated mechanical and control design of underactu-ated multibody systems (2012) Nonlinear Dyn., 67, pp. 1539-1557
Seifried, R., Eberhard, P., Design of feed-forward control for underactuated multibody systems with kinematic redundancy (2009) Motion and Vibration Control: Selected Papers from MOVIC 2008, , H. Ulbrich and L. Ginzinger, eds., Springer, New York
Blajer, W., Kolodziejczyk, K., A geometric approach to solving problems of control constraints: Theory and a DAE framework theory and a DAE framework (2004) Multibody Syst. Dyn., 11, pp. 343-364
Blajer, W., Kolodziejczyk, K., Control of underactuated mechanical systems with servo-constraints (2007) Nonlinear Dynamics, 50 (4), pp. 781-791. , DOI 10.1007/s11071-007-9231-4, Dynamical Systems: Theory and Applications
Seifried, R., Blajer, W., Analysis of servo-constraint problems for underactuated multibody systems (2013) Mech. Sci., 4, pp. 113-129
Bastos, G., Seifried, R., Brüls, O., Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach (2013) Multibody Syst. Dyn., 30, pp. 359-376
Morrison, D., Riley, J., Zancarano, J., Multiple shooting methods for two-point boundary value problems (1962) Commun. ACM, 5, pp. 613-614
Keller, H., (1968) Numerical Methods for Two-Point Boundary-Value Problems, , Blaisdell, Waltham, MA
Roberts, S., Shipman, J., (1972) Two-Point Boundary Value Problems: Shooting Methods, , Elsevier, New York
Chung, J., Hulbert, G.M., Time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method (1993) Journal of Applied Mechanics, Transactions ASME, 60 (2), pp. 371-375
Newmark, N., A method of computation for structural dynamics (1959) J. Eng. Mech. Div., Am. Soc. Civ. Eng., 85, pp. 67-94
Arnold, M., Bruls, O., Convergence of the generalized-α scheme for constrained mechanical systems (2007) Multibody System Dynamics, 18 (2), pp. 185-202. , DOI 10.1007/s11044-007-9084-0, Commemorating the 10th Anniversary
Arnold, M., Bruls, O., Cardona, A., Convergence analysis of generalized-α lie group integrators for constrained systems (2011) Proceedings of the Multibody Dynamics ECCOMAS Thematic Conference
Gear, C., Leimkuhler, B., Gupta, G., Automatic integration of euler-lagrange equations with constraints (1985) J. Comput. Appl. Math., 12-13, pp. 77-90
Brüls, O.E.L., Duysinx, P., Eberhard, P., Optimization of multi-body systems and their structural components (2011) Multibody Dynamics: Computational Methods and Applications, Computational Methods in Applied Sciences, 23, pp. 49-68. , W. Blajer, J. Arczewski, K. Fraczek, and M. Wojtyra, eds., Springer, New York
Wasfy, T.M., Noor, A.K., Computational strategies for flexible multibody systems (2003) Applied Mechanics Reviews, 56 (6), pp. 553-613. , DOI 10.1115/1.1590354
Bayo, E., Ledesma, R., Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics (1996) Nonlinear Dynamics, 9 (1-2), pp. 113-130
Jay, L., Negrut, D., Extensions of the HHT-method to differential-algebraic equations in mechanics (2007) Electron. Trans. Numer. Anal., 26, pp. 190-208
Géradin, M., Cardona, A., (2001) Flexible Multibody Dynamics: A Finite Element Approach, , John Wiley and Sons, Chichester, UK
Bastos, G., Seifried, R., Bruls, O., Inverse dynamics of underactuated multibody systems using a DAE optimal control approach (2011) Proceedings of the Multibody Dynamics ECCOMAS Conference
Wenger, P., Chablat, D., Kinematic analysis of a class of analytic planar 3-RPR parallel manipulators (2009) Computational Kinematics: Proceedings of the 5th International Workshop on Computational Kinematics, pp. 43-50
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