Non-Minimal Order Model of Mechanical Systems With Redundant Constraints for Simulations and Controls

PROJECT TITLE :

Non-Minimal Order Model of Mechanical Systems With Redundant Constraints for Simulations and Controls

ABSTRACT:

This technical note presents a non-minimal order dynamics model for many analysis, simulation, and control issues of constrained mechanical systems passing through singular configurations during their motion by creating use of linear projection operator. The distinct options of this model describing dynamics of the dependent coordinates are: i) The mass matrix $barM(q)$ is usually positive definite even at singular configurations; ii) matrix $dotbarM-2barC$ is skew symmetric, where all nonlinear terms are lumped into vector $barC(q,dotq)dotq$ after elimination of constraint forces. Eigenvalue analysis shows that the condition range of the constraint mass matrix can be minimized upon adequate selection of a scalar parameter referred to as “virtual mass” thereby reducing the sensitivity to round-off errors in numerical computation. It follows by derivation of two oblique projection matrices for computation of constraint forces and actuation forces. It's shown that projection-based mostly model allows feedback control of dependent coordinates that, unlike reduced-order dependent coordinates, uniquely outline spatial configuration of constrained systems.

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