Application of Physical Function Model to State Estimations of Nonlinear Mechanical Systems

The physical function model has been effectively used for model-based development (MBD) of automobile systems. This research demonstrates a novel application of this modeling method to the state estimation of nonlinear mechanical systems based on the Kalman filtering theory. The physical function model is a block diagram that describes each engineering field by a common rule, which focuses on the energy flow. Compared to traditional modeling approaches, this model has the flexibility to incorporate a wide range of nonlinear characteristics and the know-how accumulated by the manufacturers. Hence, it has a quite high affinity with the industrial world. The purpose of this research is to pioneer a new application of the physical function model beyond simulation analysis. In particular, physical function modeling offers a model of a system with multiple nonlinearities in the form of a time-varying linear state equation. By focusing on this feature, this study applies it to the Kalman filtering theory. The proposed approach is applicable to a wide range of nonlinearities, reduces the calculation load, and considers the background of the current MBD. Finally, verifications using an experimental apparatus, which simplifies an automotive drivetrain with backlash, demonstrate the effectiveness of the proposed approach.

[1]  Jun Hu,et al.  Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements , 2012, Autom..

[2]  Xin Su,et al.  A Localization Based on Unscented Kalman Filter and Particle Filter Localization Algorithms , 2020, IEEE Access.

[3]  Martin Vossiek,et al.  An Iterative Extended Kalman Filter for Coherent Measurements of Incoherent Network Nodes in Positioning Systems , 2020, IEEE Access.

[4]  Yong Sun,et al.  A hybrid algorithm combining EKF and RLS in synchronous estimation of road grade and vehicle׳ mass for a hybrid electric bus , 2016 .

[5]  Masao Nagamatsu,et al.  An Approach on Modeling for Functional Development of Automobile , 2000 .

[6]  Masao Nagamatsu,et al.  A New Approach on Modeling for Product Development (Expansion and Unification) , 1998 .

[7]  Masao Nagamatsu,et al.  A New Approach on Modeling for Product Development. The Basic Concept of Functional Model. , 1998 .

[8]  Salvatore Strano,et al.  Constrained nonlinear filter for vehicle sideslip angle estimation withno a priori knowledge of tyre characteristics , 2018 .

[9]  Itsuro Kajiwara,et al.  Vibration Control of Automotive Drive System With Nonlinear Gear Backlash , 2019, Journal of Dynamic Systems, Measurement, and Control.

[10]  Vijay Kumar,et al.  An impact model of mechanical backlash for control system analysis , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[11]  Yashar Shabbouei Hagh,et al.  Adaptive square-root unscented Kalman filter: An experimental study of hydraulic actuator state estimation , 2019, Mechanical Systems and Signal Processing.

[12]  Hiroyuki Sasahara,et al.  Analytical Prediction of Temperature Distribution in Cylinder Liner during Various Boring Operations , 2008 .

[13]  Per-Olof Gutman,et al.  New models for backlash and gear play , 1997 .

[14]  Takashi Ohtani,et al.  Static Stress Analysis of Link Plate of Roller Chain using Finite Element Method and Some Design Proposals for Weight Saving , 2009 .

[15]  Gianfranco Rizzo,et al.  A Computer Code for S.I. Engine Control and Powertrain Simulation , 2000 .

[16]  Bo Egardt,et al.  Backlash Estimation With Application to Automotive Powertrains , 2007, IEEE Transactions on Control Systems Technology.

[17]  Masao Nagamatsu,et al.  Modeling for Functional Expression of Rotary Apparatus , 2002 .

[18]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[19]  Bengt J H Jacobson,et al.  On Vehicle Driving Cycle Simulation , 1995 .

[20]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[21]  Fei Hu,et al.  Comparisons on Kalman-Filter-Based Dynamic State Estimation Algorithms of Power Systems , 2020, IEEE Access.

[22]  Y. Tanabe,et al.  Evaluation of variance of time history response of the system based on time-constant analysis , 2020, Transactions of the JSME (in Japanese).

[23]  J. M. Enrique,et al.  Iterative Fuzzy Modeling of Hydrogen Fuel Cells by the Extended Kalman Filter , 2020, IEEE Access.

[24]  Daniel J. Rogers,et al.  A Simple Attitude Unscented Kalman Filter: Theory and Evaluation in a Magnetometer-Only Spacecraft Scenario , 2016, IEEE Access.

[25]  Wim Desmet,et al.  Broadband Load Torque Estimation in Mechatronic Powertrains Using Nonlinear Kalman Filtering , 2018, IEEE Transactions on Industrial Electronics.

[26]  Chao Huang,et al.  Robustness Evaluation of Extended and Unscented Kalman Filter for Battery State of Charge Estimation , 2018, IEEE Access.

[27]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[28]  Masao Nagamatsu,et al.  A Modeling Approach on Modeling of Nonlinear System for Functional Development of Automobile , 2001 .

[29]  Itsuro Kajiwara,et al.  Vibration control of automotive drive system with backlash considering control period constraint , 2019, Journal of Advanced Mechanical Design, Systems, and Manufacturing.

[30]  M. Saito,et al.  MPC for a simplified transmission model with backlash using UKF , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[31]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[32]  Saad Mekhilef,et al.  Wave Excitation Force Estimation Using an Electrical-Based Extended Kalman Filter for Point Absorber Wave Energy Converters , 2020, IEEE Access.

[33]  S. Elliott,et al.  Bifurcation control of a Duffing oscillator using pole placement , 2015 .

[34]  L. A. Mcgee,et al.  Discovery of the Kalman filter as a practical tool for aerospace and industry , 1985 .

[35]  Masao Nagamatsu,et al.  Hierarchical functional model for automobile development , 1998 .

[36]  Jun Zhou,et al.  Recurrent-neural-network-based unscented Kalman filter for estimating and compensating the random drift of MEMS gyroscopes in real time , 2021 .

[37]  Chang Liu,et al.  Kalman filter-based tracking of moving objects using linear ultrasonic sensor array for road vehicles , 2018 .