Reduced‐Order Observers for Nonlinear State Estimation in Flexible Multibody Systems

Abstract

Modern control schemes adopted in multibody systems take advantage of the knowledge of a large set of measurements of the most important state variables to improve system performances. In the case of flexible-link multibody systems, however, the direct measurement of these state variables is not usually possible or convenient. Hence, it is necessary to estimate them through accurate models and a reduced set of measurements ensuring observability. In order to cope with the large dimension of models adopted for flexible multibody systems, this paper exploits model reduction for synthesizing reduced-order nonlinear state observers. Model reduction is done through a modified Craig-Bampton strategy that handles effectively nonlinearities due to large displacements of the mechanism and through a wise selection of the most important coordinates to be retained in the model. Starting from such a reduced nonlinear model, a nonlinear state observer is developed through the extended Kalman filter (EKF). The method is applied to the numerical test case of a six-bar planar mechanism. The smaller size of the model, compared with the original one, preserves accuracy of the estimates while reducing the computational effort.

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

“…In all the cases, systems with rigid-links are considered, so there are no examples of robotic systems with flexible links or fully compliant mechanisms on which the natural motion is applied. Considering the increasing interest in these kind of systems, the effect of link flexibility for the exploitation of the natural motion should be investigated, since link flexibility affects the system motion [114]. This could be taken into account in two ways-controlling the resulting unwanted vibrations or making them part of the natural motion trajectory.…”

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

“…i ) up to the desired Taylor order, it is possible to compute all the coefficients of the Taylor series expansion in Equation (22). In such a way, the eigenvectors and eigenvalues of a FMBS are expressed as polynomial functions of the system rigid-body motion and of other possible variables of interest.…”

“…A common practice used in the literature to apply the modal analysis to FLMBSs consists of linearizing the nonlinear dynamic model about a selected configuration so that the modal parameters can be computed. In particular, if the system model is formulated by means of ODEs, the eigenvalue analysis can be straightforwardly applied to the linearized system equations [12,22]. Conversely, if the system model is formulated by means of DAEs, two different strategies are possible for computing the eingensolutions: (a) transform the motion equations from DAEs to ODEs, linearize the resulting model, and then compute the eigenpairs [5,23,24]; (b) perform a direct eigenanalysis, i.e., the eigenanalysis for the system of equations resulting from the direct linearization of the DAEs [25,26].…”

Deep learning of multibody minimal coordinates for state and input estimation with Kalman filtering

“…These methods have a broad applicability, but carry a relatively high computational cost and specific modifications to the multibody formulation are generally required to be able to handle the constraint equations. More dedicated approaches have also been explored where nonlinear reduced order modelling methods have been deployed [12,13] such that they can be more readily integrated in an estimation framework. In [12], the DAEs are reduced to ODEs in an offline phase for various configurations and during the online phase an interpolation is performed.…”