Control-oriented implementation and model order reduction of a lithium-ion battery electrochemical model

The use of electrochemical models makes it computationally intractable for online implementation as the model is subject to a complicated mathematical structure including partial-differential equations (PDE). This paper is based on the single particle model with electrolyte dynamics. Methods to solve the PDEs in the governing equations are given. Model order reduction techniques are applied to the electrochemical model to reduce the order from 350 to 14. The models solved by numerical solution, residue grouping method and balanced truncation method are compared with experimental data of a coin cell for validation. The results show that the reduced order model can decrease simulation time 75 times compared with the high order model. And the accuracy of the model is kept with 2.3% root mean square error comparing with the experiment results

Simulation Of Reduction Order Model Ltnear Parameter Varying (Lpv) Systems Using Matlab Software

The use of optimal control techniques on high-order systems producehigh-order controller. Therefore, an approximation from high-ordersystem to low-order system is needed. The approximation is known asreduction model. In this paper we study one of reduction model ofLinear Parameter Varying (LPV) i.e. method balanced truncation. Theprocedure of this method can be stated as follows:First, the quadraticstable (Q-stable) is shown for given a high-order of LPV. Second, thestate space realization ofthe high-order LPV plant is transformed to thebalanced realization. Third, the balanced realizations are truncated toobtain the reduced-order plant. Fourth, the reduced-order plant isshown similar properties with the high-order plant. Finally, the simulation is carried out for a missile autopilot by using LMI Controltoolbox and Robust Control toolbox in MATLAB software. From the simulation results we obtain that the reduction system has similarproperties with the high-order system, i.e. Q-stable and balanced

Multipoint model order reduction of delayed PEEC systems

We present a new model order reduction technique for electrically large systems with delay elements, which can be modeled by means of neutral delayed differential equations. An adaptive multipoint expansion and model order reduction of equivalent first order systems are combined in the new proposed method that preserves the neutral delayed differential formulation. An adaptive algorithm to select the expansion points is presented. The proposed model order reduction technique is validated by pertinent numerical results. A comparison with a previous model order reduction algorithm based on a single point expansion is performed to show the considerably improved modeling capability of the new proposed technique

Randomized Local Model Order Reduction

In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation (PDE) with random boundary conditions, yield an approximation that converges provably at a nearly optimal rate, and can be generated at close to optimal computational complexity. In many localized model order reduction approaches like the generalized finite element method, static condensation procedures, and the multiscale finite element method local approximation spaces can be constructed by approximating the range of a suitably defined transfer operator that acts on the space of local solutions of the PDE. Optimal local approximation spaces that yield in general an exponentially convergent approximation are given by the left singular vectors of this transfer operator [I. Babu\v{s}ka and R. Lipton 2011, K. Smetana and A. T. Patera 2016]. However, the direct calculation of these singular vectors is computationally very expensive. In this paper, we propose an adaptive randomized algorithm based on methods from randomized linear algebra [N. Halko et al. 2011], which constructs a local reduced space approximating the range of the transfer operator and thus the optimal local approximation spaces. The adaptive algorithm relies on a probabilistic a posteriori error estimator for which we prove that it is both efficient and reliable with high probability. Several numerical experiments confirm the theoretical findings.Comment: 31 pages, 14 figures, 1 table, 1 algorith

Nonlinear model order reduction via Dynamic Mode Decomposition

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix that correlates spatial features while simultaneously associating the activity with periodic temporal behavior. With this decomposition, one can obtain a fully reduced dimensional surrogate model and avoid the evaluation of the nonlinear term in the online stage. This allows for an impressive speed up of the computational cost, and, at the same time, accurate approximations of the problem. We present a suite of numerical tests to illustrate our approach and to show the effectiveness of the method in comparison to existing approaches