Persistent Models for Complex Control Systems

We use smooth orthogonal decomposition (SOD) as a multivariate analysis method to obtain a reduced order model for an example of a complex nonlinear control system.We evaluate the robustness of the reduced order models. Our results show that SOD-based reduced control models are able to reduce the computation time of the actual system.

[1]  A. Swindlehurst,et al.  Subspace-based signal analysis using singular value decomposition , 1993, Proc. IEEE.

[2]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[3]  J. Jahanpour,et al.  Resonant Analysis of Systems Equipped with Nonlinear Displacement-Dependent (NDD) Dampers , 2016 .

[4]  Ioannis T. Georgiou,et al.  Advanced Proper Orthogonal Decomposition Tools: Using Reduced Order Models to Identify Normal Modes of Vibration and Slow Invariant Manifolds in the Dynamics of Planar Nonlinear Rods , 2005 .

[5]  Peter Benner,et al.  Two-Sided Projection Methods for Nonlinear Model Order Reduction , 2015, SIAM J. Sci. Comput..

[6]  J. Jahanpour,et al.  Forced vibration analysis of a system equipped with the nonlinear displacement-dependent (NDD) damper , 2016 .

[7]  C. Pierre,et al.  A NEW GALERKIN-BASED APPROACH FOR ACCURATE NON-LINEAR NORMAL MODES THROUGH INVARIANT MANIFOLDS , 2002 .

[8]  Faridoon Shabaninia,et al.  Application of Adaptive Fuzzy Control in the Variable Speed Wind Turbines , 2012, AICI.

[9]  David Chelidze.  Identifying Robust Subspaces for Dynamically Consistent Reduced-Order Models , 2014 .

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

[11]  J. Scherpen.  H∞ Balancing for Nonlinear Systems , 1996 .

[12]  Shahab Ilbeigi,et al.  A novel scheme for nonlinear displacement-dependent dampers , 2012 .

[13]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[14]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[15]  J. Marsden,et al.  A subspace approach to balanced truncation for model reduction of nonlinear control systems , 2002 .

[16]  Shahab Ilbeigi,et al.  A novel scheme for flexible NURBS-based C2 PH Spline Curve contour following task using Neural Network , 2014 .

[17]  Victor M. Calo,et al.  Fast multiscale reservoir simulations using POD-DEIM model reduction , 2015, ANSS 2015.

[18]  Clarence W. Rowley,et al.  Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition , 2005, Int. J. Bifurc. Chaos.

[19]  Hankel-norm model reduction for delayed fuzzy systems , 2015, The 27th Chinese Control and Decision Conference (2015 CCDC).

[20]  Wenliang Zhou,et al.  Smooth orthogonal decomposition-based vibration mode identification , 2006 .

[21]  Muruhan Rathinam,et al.  A New Look at Proper Orthogonal Decomposition , 2003, SIAM J. Numer. Anal..

[22]  G. Sell,et al.  On the computation of inertial manifolds , 1988 .

[23]  J. M. A. Scherpen,et al.  Balancing for nonlinear systems , 1993 .

[24]  Luís Miguel Silveira,et al.  Guaranteed passive balancing transformations for model order reduction , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[25]  Shahab Ilbeigi,et al.  Reduced Order Models for Systems with Disparate Spatial and Temporal Scales , 2016 .

[26]  James A. Sherwood,et al.  Vibration prediction of thin-walled composite I-beams using scaled models , 2017 .

[27]  J. A. Atwell,et al.  Reduced order controllers for Burgers' equation with a nonlinear observer , 2001 .

[28]  Shahab Ilbeigi,et al.  Model Order Reduction of Nonlinear Euler-Bernoulli Beam , 2016 .

[29]  Jacquelien M. A. Scherpen,et al.  Balanced Realization and Model Order Reduction for Nonlinear Systems Based on Singular Value Analysis , 2010, SIAM J. Control. Optim..

[30]  Terence R. Smith.  Low-dimensional Models of Plane Couette Flow using the Proper Orthogonal Decomposition , 2003 .

[31]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .