A Discrete-Time Extended Kalman Filter Approach Tailored for Multibody Models: State-Input Estimation

Abstract

Model-based force estimation is an emerging methodology in the mechatronic community given the possibility to exploit physically inspired high-fidelity models in tandem with ready-to-use cheap sensors. In this work, an inverse input load identification methodology is presented combining high-fidelity multibody models with a Kalman filter-based estimator and providing the means for an accurate and computationally efficient state-input estimation strategy. A particular challenge addressed in this work is the handling of the redundant state-description encountered in common multibody model descriptions. A novel linearization framework is proposed on the time-discretized equations in order to extract the required system model matrices for the Kalman filter. The presented framework is experimentally validated on a slider-crank mechanism. The nonlinear kinematics and dynamics are well represented through a rigid multibody model with lumped flexibilities to account for localized interaction phenomena among bodies. The proposed methodology is validated estimating the input torque delivered by a driver electro-motor together with the system states and comparing the experimental data with the estimated quantities. The results show the stability and accuracy of the estimation framework by only employing the angular motor velocity, measured by the motor encoder sensor and available in most of the commercial electro-motors.

The Dependent Coordinates in the Linearization of Constrained Multibody Systems: Handling and Elimination

“…The linearized equations of multibody systems are also computed in other works devoted to the development of Kalman filters [36][37][38] and order reduction methods [39], where the system is modeled by using the nonlinear finite elements of absolute nodal coordinate formulation and then locally linearized at a series of quasi-static equilibrium configurations. The stability of complex multibody systems is addressed by Bauchau et al [40,41], and Floquet theory [42,43] is the preferred methodology for assessing the linear stability of systems with periodic coefficients [44,45].…”

Linearization-based state-transition model for the discrete extended Kalman filter applied to multibody simulations

“…The use of multibody system dynamics, together with state-estimation algorithms, offers an approach to estimate the behavior of a mechanical system [2]. Within multibody dynamics, state-estimation algorithms have been used in estimation of vehicle dynamics [3,4], for systems with hydraulic actuators [5], and in railway applications [6].…”

Sensor Selection and State Estimation for Unobservable and Non-Linear System Models

“…As a result of increased computational power, these virtual sensing schemes have gained significant traction for the analysis of structural [7] and general mechanical systems [8,9] in recent years. Driven by the need for more accurate system information, model complexity has significantly increased up to flexible multibody-related formulations [10][11][12]. However, this comes at the cost of increased computational effort and additional issues towards observability and thus estimator stability.…”