Passivity-based iterative learning control for 2DOF robot manipulators with antagonistic bi-articular muscles
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This paper investigates iterative learning control based on passivity for two-degree-of-freedom (2DOF) robot manipulators with antagonistic bi-articular muscles. Firstly, a brief summary of dynamics of 2DOF robot manipulators with antagonistic bi-articular muscles is given. Next, an error dynamics of the bi-articular manipulator for iterative learning control that has an output strictly passivity property is constructed. Then, we propose an iterative learning control law for the bi-articular manipulator. The proposed torque input does not need the parameters for the accurate models. Convergence analysis of the closed-loop system is carried out based on passivity. Finally, simulation results are presented in order to confirm the effectiveness of the proposed control law.Keywords:
Passivity
Iterative Learning Control
Robot manipulator
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Passivity and dissipativity are energy-like concepts, widely used in control design, that capture the "energy" consumption of a dynamical system and therefore relate closely to the physical world. Passivity indices of a system are measures of its passivity margins and represent shortage and excess of passivity in a system. With the aid of passivity indices, one can measure how passive a system is, or how far from passivity it is. Passivity indices extend all the analysis and design methods based on passivity to nonpassive systems as well. One of the advantages of using passivity is its tight relationship to stability. Another is its compositionality, which, together with its generality, makes it possible to use passivity in a wide range of complex control systems. In the present entry, an overview of dissipativity and passivity is given. Passivity indices of a system and their relation to stability are defined, and methods to find the indices are presented.
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Passivity is an imperative concept and a widely utilized tool in the analysis and control of interconnected systems. It naturally arises in the modelling of physical systems involving passive elements and dynamics. While many theorems on passivity are known in the theory of robust control, very few converse passivity results exist. This paper establishes various versions of converse passivity theorems for nonlinear feedback systems. In particular, open-loop passivity is shown to be necessary to ensure closed-loop passivity from an input-output perspective. Moreover, the stability of the feedback interconnection of a specific system with an arbitrary passive system is shown to imply passivity of the system itself.
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This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity and very strict passivity (i.e. joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, it is discussed how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain.
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LTI system theory
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