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Dynamics and control of nonlinear mechanical systems and advanced mechatronic systems can be investigated more vividly and efficiently by using corresponding nonlinear position-dependent circuits that describe Lagrange's equations of motions and interactions with objects or/and task environments. Such expressions of Lagrange's equations via nonlinear circuits are indebted to lumped-parameter discretization of mechanical systems as a set of rigid bodies through equations of motion due to Newton's second law. This observation is quite analogous to validity of electric circuits that can be derived as lumped parameter versions of Maxwell's equations of electromagnetic waves. Couplings of nonlinear mechanical circuits with electrical circuits through actuator dynamics are also discussed. In such electromechanical circuits the passivity should be a generalization of impedance concept in order to cope with general nonlinear position-dependent circuits and play a crucial role in their related motion control problems. In particular, it is shown that the passivity as an input-output property gives rise to a necessary and sufficient characterization of H∞-tuning for disturbance attenuation of robotic systems, which can give another system theoretic interpretation of the energy conservation law.
Date of Publication: June 1996