Mechanics, to Electronics, through Control An excursion into - PDF document

HAL Id: inria-00569427 scientifjques de niveau recherche, publiés ou non, Control. Fifty Years of Finite Freedom Mechanics. Colloquium organised in honor of Michel Jean on Vincent Acary. An excursion into Nonsmooth Dynamics: from Mechanics, to Electronics, through To cite this version: Vincent Acary Mechanics, to Electronics, through Control An excursion into Nonsmooth Dynamics: from publics ou privés. recherche français ou étrangers, des laboratoires émanant des établissements d’enseignement et de destinée au dépôt et à la difgusion de documents https://hal.inria.fr/inria-00569427 L’archive ouverte pluridisciplinaire HAL , est abroad, or from public or private research centers. teaching and research institutions in France or The documents may come from lished or not. entifjc research documents, whether they are pub- archive for the deposit and dissemination of sci- HAL is a multi-disciplinary open access Submitted on 25 Feb 2011 the occasion of his seventieth birthday, Oct 2010, Marseille, France. ฀inria-00569427฀

An excursion into Nonsmooth Dynamics Vincent Acary From Mechanics. . . to Control,. . . To Electronics. An excursion into Nonsmooth Dynamics: References from Mechanics, to Electronics, through Control Vincent Acary INRIA Rhˆ one–Alpes, Grenoble. vincent.acary@inrialpes.fr Fifty Years of Finite Freedom Mechanics. On the occasion of Michel Jean’s 70 th birthday Marseille, 25–27 October 2010

An excursion into Contents Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody From Mechanics of divided materials to multi-body and robotic systems, dynamics History and Motivations The Non smooth Lagrangian Dynamics The smooth multibody dynamics The Moreau’s sweeping process The Non smooth Lagrangian Dynamics State–of–the–art The Moreau’s sweeping process Objectives & means Academic examples. State–of–the–art Background Objectives & means Local error estimates for the Moreau’s Time–stepping Academic examples. scheme Background Any Order scheme Local error estimates for the Moreau’s Time–stepping scheme to Control,. . . Any Order scheme To Electronics. References To control (Sliding mode control Theory) To electronics (Nonsmooth modeling of switched Electrical circuits)

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme From the mechanics of divided Materials. . . Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Stack of beads with perturbation Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. 3 3 Background 2 2 1 1 Local error estimates for the (b) Zoom on the window Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References (c) Contact detection (a) FEM H8 meshing

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References Figure: von Mises stresses

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process Divided Materials and Masonry State–of–the–art Objectives & means Academic examples. MISES VALUE MISES VALUE +2.07E+01 +1.77E+04 +1.67E+05 +9.20E+04 Background +3.34E+05 +1.66E+05 +5.01E+05 +2.41E+05 +6.68E+05 +3.15E+05 Local error estimates for the +8.35E+05 +3.89E+05 +1.00E+06 +4.64E+05 +1.17E+06 +5.38E+05 Moreau’s Time–stepping +1.34E+06 +6.12E+05 +1.50E+06 +6.87E+05 +1.67E+06 +7.61E+05 scheme +1.84E+06 +8.35E+05 +2.00E+06 +9.10E+05 +2.17E+06 +9.84E+05 Any Order scheme to Control,. . . To Electronics. 3 3 3 3 References 1 1 2 2 1 1 2 2

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics FEM models with contact, friction cohesion, etc... The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means H H Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References D D 0 0 0 0 Joint work with Y. Monerie, IRSN.

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the to the dynamics of Multibody and robotic systems . . . Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody Simulation of Circuit breakers (INRIA/Schneider Electric) dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Bipedal Robot INRIA BIPOP Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Towards controlled robotic systems on granular materials Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . Simulation of the ExoMars Rover (INRIA/Trasys Space/ESA) History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art Objectives & means Academic examples. Background Local error estimates for the Moreau’s Time–stepping scheme Any Order scheme to Control,. . . To Electronics. References

An excursion into Mechanical systems with contact, impact and friction Nonsmooth Dynamics Vincent Acary From Mechanics. . . History and Motivations The smooth multibody dynamics The Non smooth Lagrangian Dynamics The Moreau’s sweeping process State–of–the–art They are all nonsmooth mechanical systems but they differ in Objectives & means Academic examples. ◮ the presence of perfect nonlinear joints, Background Local error estimates for the ◮ the presence of finite rotations, Moreau’s Time–stepping scheme ◮ the presence of Control (sensors & actuators) Any Order scheme ◮ the desired properties in design and development which influence the to Control,. . . numerical simulation and prototyping To Electronics. References