The aim of this work is to provide a thorough research on the implementation of some non-linear Kalman filters (KF) using multibody (MB) models and to compare their performances in terms of accuracy and computational cost. The filters considered in this study are the extended KF (EKF) in its continuous form, the unscented KF (UKF) and the spherical simplex unscented KF (SSUKF). The MB formulation taken into consideration to convert the differential algebraic equations (DAE) of the MB model into the ordinary differential equations (ODE) required by the filters is a state-space reduction method known as projection matrix-R method. Additionally, both implicit and explicit integration schemes are used to evaluate the impact of explicit integrators over implicit integrators in terms of accuracy, stability and computational cost. However, state estimation through KFs is a closed- loop estimation correcting the model drift according to the difference between the predicted measurement and the actual measurement, what limits the interest in using implicit integrators despite being commonly employed in MB simulations. Performance comparisons of all the aforemen- tioned non-linear observers have been carried out in simulation on a 5-bar linkage. The mechanism parameters have been obtained from an experimental 5-bar linkage and the sensor characteristics from off-the-shelf sensors to reproduce a realistic simulation. The results should highlight useful clues for the choice of the most suitable filters and integration schemes for the aforementioned MB formulation
This paper introduces a general and flexible design method for the inverse modal optimization of undamped vibrating systems, i.e., for the computation of mass and stiffness linear modifications ensuring the desired system eigenstructure. The technique is suitable for the design of new systems or the optimization of the existing ones and can handle several design requirements and constraints. Paramount strengths of the method are its capability to modify an arbitrary number of parameters and assigned vibration modes, as well as the possibility of dealing with mass and stiffness matrices with arbitrary topologies. To this purpose, the modification problem is formulated as a constrained inverse eigenvalue problem and then solved within the frame of convex optimization. The effectiveness of the method is assessed by applying it to two different test cases. In particular, the second investigation deals with a meaningful mechanical design application: the optimization of a system recalling an industrial vibratory feeder. The results highlight the generality of the method and its capability to ensure the achievement of the prescribed eigenstructure.
This paper tackles the problem of designing state observers for flexible link mechanisms: An investigation is made on the possibility of employing observers making use of suitable piecewise-linear truncated dynamics models. A general and novel approach is proposed, which provides an objective way of synthesizing observers preventing the instability that may arise from using reduced-order linearized models. The approach leads to the identification of the regions of the domain of the state variables where the linear approximations of the nonlinear model can be considered acceptable. To this purpose, first of all, the stability of the equilibrium points of the closed-loop system is assessed by applying the eigenvalue analysis to appropriate piecewise-linear models. Admittedly, the dynamics of such a closed-loop system is affected by the perturbation of the poles caused by spillover and by the discrepancies between the linearized models of the plant and the one of the observer. Additionally, when nodal elastic displacements and velocities are not bounded in the infinitesimal neighborhoods of the equilibrium points, the difference between the nonlinear model and the locally linearized one is expressed in terms of unstructured uncertainty and stability is assessed through H∞ robust analysis. The method is demonstrated by applying it to a closed-chain flexible link mechanism.
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