Combined DAE and Sliding Mode Control Methods for Simulation of Constrained Mechanical Systems

[+] Author and Article Information
M. D. Compere, R. G. Longoria

Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712

J. Dyn. Sys., Meas., Control 122(4), 691-698 (Feb 09, 2000) (8 pages) doi:10.1115/1.1320450 History: Received February 09, 2000
Copyright © 2000 by ASME
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Ascher,  U. M., Chin,  H., Petzold,  L. R., and Reich,  S., 1995, “Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds,” Mech. Struct, and Mach., 23, No. 2, pp. 135–157.
Ascher,  U. M., and Petzold,  L. R., 1993, “Stability of Computational Methods for Constrained Dynamics Systems,” SIAM J. Scientific Computing, 14, No. 1, pp. 95–120.
Ascher, U. M., and Petzold, L. R., 1998, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics (SIAM), Philadelphia.
Baumgarte,  J., 1972, “Stabilization of Constraints and Integrals of Motion in Dynamical Systems,” Comput. Methods Appl. Mech. Eng., 1, pp. 1–16.
Haug,  E. J., Negrut,  D., and Iancu,  M., 1997, “A State-Space-Based Implicit Integration Algorithm for Differential-Algebraic Equations of Multibody Dynamics,” Mechanics of Structures and Machines, 25, No. 3, pp. 311–334.
Stejskal, V., and Valasek, M., 1996, Kinematics and Dynamics of Machinery, Marcel Dekker, New York.
Hairer, E., and Wanner, G., 1996, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, 2nd Revised Ed., Springer, Berlin.
Rismantab-Sany,  J., and Shabana,  A. A., 1988, “Impulsive Motion of Non-Holonomic Deformable Multibody Systems, Part II: Impact Analysis,” J. Sound Vib., 127, No. 2, pp. 205–219.
Yun,  X., and Sarkar,  N., 1998, “Unified Formulation of Robotic Systems with Holonomic and Nonholonomic Constraints,” IEEE Trans. Rob. Autom., 14, No. 4, pp. 640–650.
McClamroch,  N. H., 1990, “Feedback Stabilization of Control Systems Described by a Class of Nonlinear Differential-Algebraic Equations,” Systems and Control Letters, 15, pp. 53–60.
McClamroch, N. H., 1990, “On Control Systems Described by a Class of Nonlinear Differential-Algebraic Equations: State Realizations and Local Control,” Proc. of 1990 American Control Conference, Vol. 2, pp. 1701–1706.
Chiou,  J. C., Wu,  S. D., 1998, “Constraint Violation Stabilization Using Input-Output Feedback Linearization in Multibody Dynamic Analysis,” J. Guid. Control Dyn., 21, No. 2, pp. 222–228.
Gordon, B. W., Liu, S., and Asada, H. H., 1999, “State Space Modeling of Differential-Algebraic Systems Using Singularly Perturbed Sliding Manifolds,” DSC-Vol. 67, Proceedings of the ASME Dynamic Systems and Control Division-1999, pp. 537–544.
Zhao,  F., and Utkin,  V., 1996, “Adaptive Simulation and Control of Variable-structure Control Systems in Sliding Regimes,” Automatica, 32, No. 7, pp. 1037–1042.
DeCarlo, R. A., and Drakunov, S. 1998, “A Unified Lyapunov Setting for Continuous and Discrete Time Sliding Mode Control,” Proc. of the ASME, DSC-Vol. 64, pp. 547–554.
Utkin, V. I., 1992, Sliding Modes in Control Optimization, Springer-Verlag, Berlin.
Utkin, V. I., Guldner, J., and Shi, J., 1999, Sliding Mode Control in Electromechanical Systems, Taylor and Francis, London.
Bartolini,  G., Ferrara,  A., and Utkin,  V. I., 1995, “Adaptive Sliding Mode Control in Discrete-time Systems,” Automatica, 31, No. 5, pp. 769–773.
Enright,  W. H., Jackson,  K. R., No̸rsett,  S. P., 1986, “Interpolants for Runge-Kutta Formulas,” ACM Trans. Math. Softw., 12, No. 3, pp. 193–218.
Leimkuhler, B. J., 1998, “Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations,” Ph.D. dissertation, Dept. Comp. Sci., Univ. Illinois Urbana.
Pantelides,  C. C., 1998, “The Consistent Initialization of Differential-Algebraic Systems,” SIAM J. Scientific and Statistical Computing, 9, No. 2, pp. 213–231.
Slotine, J., and Li, W., 1991, Applied Nonlinear Control, Prentice Hall, NJ.
Chin, H., 1995, “Stabilization Methods for Simulations of Constrained Multibody Dynamics,” Ph.D. thesis, Institute of Applied Mathematics, Univ. of British Columbia.


Grahic Jump Location
Time intervals of stabilization methods
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Example of how DAE post-stabilization can exceed physically realistic adjustment in x
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Compound pendulum described by an ODE
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This trace is representative of all three solutions. Note, ωn=3g/2l for small angle motion.
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This trace is representative of all three solutions.
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The states satisfy the constraints and switching surfaces very well but have physically incorrect trajectories
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Given consistent ICs, post-stabilization is used over [tinitial tfinal]
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Given inconsistent ICs, SMC’s urobust,i drives the constraints to satisfaction
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SMC forces constraints to satisfaction given inconsistent ICs




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