Modeling and sensitivity analysis methodology for hybrid dynamical system

Corner, Sebastien; Sandu, Corina; Sandu, Adrian

doi:10.1016/j.nahs.2018.07.003

Cited by 10 publications

(2 citation statements)

References 24 publications

(93 reference statements)

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“…Another version of stability was analyzed in [97][98][99][100] as sensitivities to system parameters. Adapted saltation conditions were used to characterize sensitivities across hybrid events.…”

Section: Survey Of Saltation Matrix Applicationsmentioning

confidence: 99%

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

2021

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Section: Survey Of Saltation Matrix Applicationsmentioning

confidence: 99%

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

2021

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“…This gives rise to relatively complex systems of equations that require special solvers. It is also possible to simulate realistic behaviors in these systems due to recent research on multibody systems with friction [29,34,44,53], clearances [18,19,52,67], events [12,13], and even a combination of these [20]. Such behaviors further add to the complexity of the resulting system of equations.…”

Section: Introductionmentioning

confidence: 99%

Computation of Direct Sensitivities of Spatial Multibody Systems With Joint Friction

Verulkar

Sandu

Dopico

et al. 2022

Journal of Computational and Nonlinear Dynamics

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Friction exists in most mechanical systems and may have a major influence on the dynamic performance of the system. The incorporation of friction in dynamic systems has been a subject of active research for several years owing to its high non-linearity and its dependence on several parameters. Consequently, optimization of dynamic systems with friction becomes a challenging task. Gradient-based optimization of dynamical systems is a prominent technique for optimal design and requires the computation of model sensitivities with respect to the design parameters. The novel contribution of this paper is the derivation of the analytical methodology for the computation of direct sensitivities for smooth multibody systems with joint friction using the Lagrangian index-1 formulation. System dynamics have been computed using two different friction models; the Brown and McPhee, and the Gonthier et al. model. The methodology proposed to obtain model sensitivities has also been validated using the complex finite difference method. A case study has been conducted on a spatial multibody system to observe the effect of friction on the dynamics and model sensitivities, compare sensitivities with respect to different parameters and demonstrate the numerical and validation aspects. Since design parameters can have very different magnitudes and units, the sensitivities have been scaled with the parameters for comparison. Finally, a discussion has been presented on the interpretation of the case study results. Due to incorporation of joint friction, ‘jumps’ or discontinuities are observed in the model sensitivities akin to those observed for hybrid dynamical systems.

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Adjoint sensitivity analysis of hybrid multibody dynamical systems

Corner

Sandu

2020

Multibody Syst Dyn

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Sensitivity analysis of multibody systems computes the derivatives of general cost functions that depend on the system solution with respect to parameters or initial conditions. This work develops adjoint sensitivity analysis for hybrid multibody dynamic systems. Hybrid systems are characterized by trajectories that are piecewise continuous in time, with finitely-many discontinuities being caused by events such as elastic/inelastic impacts or sudden changes in constraints. The corresponding direct and adjoint sensitivity variables are also discontinuous at the time of events. The framework discussed herein uses a jump sensitivity matrix to relate the jump conditions for the direct and adjoint sensitivities before and after the time event, and provides analytical jump equations for the adjoint variables. The theoretical framework for sensitivities for hybrid systems is validated on a five-bar mechanism with non-smooth contacts.

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Modeling and sensitivity analysis methodology for hybrid dynamical system

Cited by 10 publications

References 24 publications

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Computation of Direct Sensitivities of Spatial Multibody Systems With Joint Friction

Adjoint sensitivity analysis of hybrid multibody dynamical systems

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