From orthogonal to tangential control of underactuated mechanical systems in partly specified motion - a case study illustration

• Autorzy: Blajer W. , Seifried R.
• Języki publikacji: EN

Abstrakty

EN

Underactuated mechanical systems have fewer control inputs than degrees of freedom. Their performance goal may be realization of specified in time outputs, treated as servo-constraints on the system, whose number is equal to the number of inputs. The solution to the inverse simulation problem (servo-constraint problem), that is the determination of an input control strategy that forces an underactuated system to complete the partly specified motion, is a challenging task. This is because mechanical systems may be "underactuated" in several ways and, as opposed to the passive constraint reactions which are orthogonal to the constraint manifold, the control forces may be arbitrary oriented with respect to the servo-constraint manifold. The diversity of servo-constraint problems is discussed using a simple spring-mass system mounted on a carriage, and is related to multiple issues: formulations in generalized coordinates and output-involved coordinates, orthogonal or tangential realization of servo-constraints, the arising ODE/DAE forms of the governing equations, and existence of the uncontrolled internal dynamics. Some computational issues are finally reported, with relevant simulation results for the sample case example.

Słowa kluczowe

EN

underactuated systems; inverse simulation control; servo-constraints

PL

symulacja odwrotna; serwomechanizm

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2012
• Tom: Vol. 17, no. 3
• Strony: 689--706
• Opis fizyczny: Bibliogr. 28 poz., rys., wykr.

Twórcy

autor

Blajer W.

autor

Seifried R.

• Technical University of Radom Institute of Applied Mechanics and Power Engineering ul. Krasickiego 54, 26-600 Radom, Poland,

Bibliografia

• Ascher U.M. and Petzold L.R. (1998): Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations - Philadelphia: SIAM.
• Bajodah A.H., Hodges D.H. and Chen Y.-H. (2005): Inverse dynamics of servo-constraints based on the generalized inverse. - Nonlinear Dynamics, vol.39, No.1-2, pp.179-196.
• Blajer W. (1997): Dynamics and control of mechanical systems in partly specified motion. - Journal of the Franklin Institute, vol.334B, No.3, pp.407-426.
• Blajer W. (2001): A geometrical interpretation and uniform matrix formulation of multibody system dynamics. - ZAMM, vol.81, No.4, pp.247-259.
• Blajer W., Dziewiecki K., Kołodziejczyk K. and Mazur Z. (2011): Inverse dynamics of underactuated mechanical systems: a simple case study and experimental verification. - Communications in Nonlinear Science and Numerical Simulation, vol.16, No.5, pp.2265-2272.
• Blajer W. and Kołodziejczyk K. (2004): A geometric approach to solving problems of control constraints: theory and a DAE framework. - Multibody System Dynamics, vol.11, No.4, pp.343-364.
• Blajer W. and Kołodziejczyk K. (2007a): Control of underactuated mechanical systems with servo-constraints - Nonlinear Dynamics, vol.50, No.4, pp.781-791.
• Blajer W. and Kołodziejczyk K. (2007b): A DAE formulation for the dynamic analysis and control design of cranes executing prescribed motions of payloads. - in García Orden J.C, Goicolea J.M., and Cuadrado J. (Eds.), Multibody Dynamics. Computational Methods and Applications, Series: Computational Methods in Applied Sciences, vol.4, Springer, Dordrecht, pp.91-112.
• Blajer W., Graffstein J. and Krawczyk M. (2009): Modeling of aircraft prescribed trajectory flight as an inverse simulation problem. - in Awrejcewicz J. (Ed.), Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems, Springer, Netherlands, pp.153-162.
• Blajer W. and Kołodziejczyk K. (2011): Improved DAE formulation for inverse dynamics simulation of cranes - Multibody System Dynamics, vol.25, No.2, pp.131-143.
• Brenan K.E., Campbell S.L. and Petzold L.R. (1989): Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. - Elsevier, New York, 1989.
• Chen Y.-H. (2008): Equations of motion of mechanical systems under servoconstraints: the Maggi approach. - Mechatronics, vol.18, No.4, pp.208-217.
• De Luca A. (1998): Trajectory control of flexible manipulators. - in Siciliano B. and Valavanis K.P. (Eds.), Control Problems in Robotics and Automation, Lecture Notes in Control and Information Sciences 230, Springer, London, pp.83-104.
• Fantoni I. and Lozano R. (2002): Nonlinear Control for Underactuated Mechanical Systems - London: Springer.
• Fliess M., Lévine J., Martin P., and Rouchon P.(1995): Flatness and defect of nonlinear systems: introductory theory and examples - International Journal of Control, vol.61, No.6, pp.1327-1361.
• Fumagalli A., Masarati P., Morandini M. and Mantegazza P. (2011): Control constraint realization for multibody systems - Transactions of the ASME, Journal of Computational and Nonlinear Dynamics, vol.6, No.1, 011002 (8 pages).
• Hairer E. and Wanner G. (2002): Solving Ordinary Differential Equations: Stiff and Differential-Algebraic Problems - Berlin: Springer.
• Isidori A. (1995): Nonlinear Control Systems. - London: Springer.
• Kirgetov V.I. (1967): The motion of controlled mechanical systems with prescribed constraints (servoconstraints) - Journal of Applied Mathematics and Mechanics, vol.21, No. , pp.433-466.
• O'Connor W.J. (2007): Wave-based analysis and control of lump-modeled flexible robots. - IEEE Transactions on Robotics, vol.23, No.2, pp.343-352.
• Olfati-Saber R. (2001): Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles. - PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA.
• Rouchon P. (2005): Flatness based control of oscillators. - ZAMM, vol.85, No.6, pp.411-421.
• Sara-Ramirez H. and Agrawal S.K. (2004): Differentially Flat Systems. - New York: Marcel Dekker.
• Sahinkaya M.N. (2004): Inverse dynamic analysis of multiphysics systems. - Proceedings of the IME, Journal of Systems and Control Engineering, vol.218, No.1, pp.13-26.
• Seifried R. (2012a): Integrated mechanical and control design of underactuated multibody systems. - Nonlinear Dynamics, vol.67, No.2, pp.1539-1557.
• Seifried R. (2012b): Two approaches for feedforward control and optimal design of underactuated multibody systems. - Multibody System Dynamics, vol.27, No.1, pp.75-93.
• Spong M.W. (1998): Underactuated mechanical systems - in Siciliano B. and Valavanis K.P. (Eds.), Control Problems in Robotics and Automation, Springer, London, 1998, pp. 135-150.
• Zilic T., Kasac J., Situm Z. and Essert M (2012): Simultaneous stabilization and trajectory tracking of underactuated mechanical systems with included actuators dynamics. - Multibody System Dynamics (published on line).