Computationally efficient and stable order reduction method for a large-scale model of MEMS piezoelectric energy harvester

In this work, we present a computationally efficient model order reduction technique for a large-scale multiport model of piezoelectric energy harvester. This novel technique generates stable reduced order models. The method combines model reduction based on Krylov subspaces and a Schur complement transformation of the resulting system. We demonstrate an excellent match between the full-scale and the reduced order model during transient and harmonic simulation.

[1]  T. Hughes,et al.  Finite element method for piezoelectric vibration , 1970 .

[2]  J. Korvink,et al.  Mor4ansys: Generating compact models directly from ANSYS models , 2004 .

[3]  Michel Nakhla,et al.  Sparse and passive reduction of massively coupled large multiport interconnects , 2007, ICCAD 2007.

[4]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[5]  R. Freund Krylov-subspace methods for reduced-order modeling in circuit simulation , 2000 .

[6]  S. Ben-Yaakov,et al.  Self-Contained Resonant Rectifier for Piezoelectric Sources Under Variable Mechanical Excitation , 2011, IEEE Transactions on Power Electronics.

[7]  T. Aftab,et al.  NEW MODELLING APPROACH FOR MICRO ENERGY HARVESTING SYSTEMS BASED ON MODEL ORDER REDUCTION ENABLING TRULY SYSTEM-LEVEL SIMULATION , 2012 .

[8]  C.-C. Chen,et al.  Generating Passive Compact Models for Piezoelectric Devices , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  P. D. Mitcheson,et al.  Power-Extraction Circuits for Piezoelectric Energy Harvesters in Miniature and Low-Power Applications , 2012, IEEE Transactions on Power Electronics.

[10]  J. Korvink,et al.  Error indicators for fully automatic extraction of heat-transfer macromodels for MEMS , 2005 .

[11]  Frank Liu,et al.  Sparse and efficient reduced order modeling of linear subcircuits with large number of terminals , 2004, ICCAD 2004.

[12]  Michael Günther,et al.  Efficient extraction of thin-film thermal parameters from numerical models via parametric model order reduction , 2010 .

[13]  B. H. Stark,et al.  Review of Power Conditioning for Kinetic Energy Harvesting Systems , 2012, IEEE Transactions on Power Electronics.

[14]  B. Lohmann,et al.  Parametric Order Reduction of Proportionally Damped Second Order Systems , 2006 .

[15]  Zhaojun Bai,et al.  Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method , 2005, SIAM J. Sci. Comput..

[16]  Peter Benner,et al.  Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective , 2014, Archives of Computational Methods in Engineering.

[17]  T. Aftab,et al.  Reduced order modeling enables system level simulation of a MEMS piezoelectric energy harvester with a self-supplied SSHI-scheme , 2013, 2013 14th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE).

[18]  J. Korvink,et al.  A Fully Adaptive Scheme for Model Order Reduction Based on Moment Matching , 2015, IEEE Transactions on Components, Packaging and Manufacturing Technology.

[19]  Jan G. Korvink,et al.  A fully MEMS-compatible process for 3D high aspect ratio micro coils obtained with an automatic wire bonder , 2009 .

[20]  Wei Wang,et al.  Passive Reduced-Order Macromodeling Algorithm for Microelectromechanical Systems , 2008, Journal of Microelectromechanical Systems.

[21]  B. Lohmann,et al.  Order reduction of large scale second-order systems using Krylov subspace methods , 2006 .

[22]  Peter Benner,et al.  Model Reduction for Linear Descriptor Systems with Many Ports , 2012 .

[23]  Roland W. Freund,et al.  SPRIM: structure-preserving reduced-order interconnect macromodeling , 2004, IEEE/ACM International Conference on Computer Aided Design, 2004. ICCAD-2004..

[24]  Jacob K. White,et al.  A multiparameter moment-matching model-reduction approach for generating geometrically parameterized interconnect performance models , 2004, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[25]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[26]  Roland W. Freund SPRIM: structure-preserving reduced-order interconnect macromodeling , 2004, ICCAD 2004.

[27]  Alberto Corigliano,et al.  Numerical simulations of piezoelectric MEMS energy harvesters , 2014, 2014 15th International Conference on Thermal, Mechanical and Mulit-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE).

[28]  Mattan Kamon,et al.  A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits , 1999 .

[29]  E. Rudnyi,et al.  Using the Superposition Property for Model Reduction of Linear Systems with a Large Number of Inputs , 2008 .

[30]  S. Matova,et al.  A piezoelectric vibration harvester based on clamped-guided beams , 2012, 2012 IEEE 25th International Conference on Micro Electro Mechanical Systems (MEMS).

[31]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[32]  Sang-Gug Lee,et al.  An efficient parallel SSHI rectifier for piezoelectric energy scavenging systems , 2011, 13th International Conference on Advanced Communication Technology (ICACT2011).