Model-Based State-of-Charge Estimation for a Valve-Regulated Lead-Acid Battery Using Linear Matrix Inequalities

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Zheng Shen ◽  
Christopher D. Rahn
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Models ◽  
Observer Design ◽  
State Of Charge ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Estimation Errors ◽  
Luenberger Observer ◽  
Averaged Models ◽  
Lead Acid

State-of-charge (SOC) estimation for valve-regulated lead-acid (VRLA) batteries is complicated by the switched linear nature of the underlying dynamics. A first principles nonlinear model is simplified to provide two switched linear models and linearized to produce charge, discharge, and averaged models. Luenberger and switched SOC estimators are developed based on these models and propagated using experimental data. A design methodology based on linear matrix inequalities (LMIs) is used in the switched SOC estimator design to obtain a switched Luenberger observer with guaranteed exponential stability. The results show that estimation errors are halved by including switching in the observer design.

Stabilization of Nonlinear Systems Using Quasi-Linear Models

2000 ◽  
Author(s):  
Kiriakos Kiriakidis
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Models ◽  
Nonlinear Models ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Analysis And Design ◽  
Linear Differential Inclusions ◽  
Linear Differential ◽  
Generalized Lyapunov Functions ◽  
Takagi Sugeno

Abstract Unconventional nonlinear models such as nonlinear ARMAX, Takagi-Sugeno fuzzy models, global linearizations, and linear hybrid systems are, at the highest level of abstraction, a sort of quasi-linear models, namely, Polytopic Linear Differential Inclusions (PLDIs). At present, quadratic stability has enabled, mainly via linear matrix inequalities, the analysis and design of a nonlinear system from the vertex matrices of its PLDI model. Proving stability by a globally quadratic Lyapunov function, however, entails conservatism. This paper proposes a less conservative framework by using piecewise-quadratic generalized Lyapunov functions. Further manipulation of the problem within such framework yields a set of bilinear rather than linear matrix inequalities.

POLYTOPIC OBSERVER FOR GLOBAL SYNCHRONIZATION OF SYSTEMS WITH OUTPUT MEASURABLE NONLINEARITIES

2003 ◽  
Vol 13 (03) ◽  
pp. 703-712 ◽  
Author(s):  
GILLES MILLERIOUX ◽  
JAMAL DAAFOUZ
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
Chaos Synchronization ◽  
Observer Design ◽  
Linear Matrix ◽  
Dynamical Matrix ◽  
Matrix Inequalities ◽  
Global Synchronization ◽  
Lyapunov Approach ◽  
Special Case

Chaos synchronization has been tackled by considering the problem as a special case of an observer design. The considered dynamical systems to be synchronized have measurable nonlinearities. Their dynamical matrix is described in a polytopic way. By using the notion of polyquadratic stability, the problem of the observer synthesis is turned into the resolution of a set of Linear Matrix Inequalities (LMI) which are less conservative compared to the case of an usual quadratic Lyapunov approach. This enables to enlarge the class of systems for which synchronization can take place. The resulting matrix gain of the observer is computed by interpolating vertices gains resulting from the solution of the LMI's.

Generalized dynamic observer design for quasi-LPV systems

2018 ◽  
Vol 66 (3) ◽  
pp. 225-233 ◽  
Author(s):  
A.-J. Pérez-Estrada ◽  
G.-L. Osorio-Gordillo ◽  
M. Darouach ◽  
V.-H. Olivares-Peregrino
Keyword(s):  
Linear Matrix Inequalities ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Algebraic Constraints ◽  
Dynamic Observer

Abstract This paper presents a new generalized dynamic observer (GDO) for quasi-linear parameter varying (LPV) systems. It generalises the structures of the proportional observer (PO) and proportional integral observer (PIO). The design of the GDO is derived from the solution of linear matrix inequalities (LMIs) and the solution of the algebraic constraints obtained from the estimation error analysis. The efficiency of the proposed approach is illustrated by a numerical example.

Stable and Optimal Controller Design for Takagi-Sugeno Fuzzy Model Based Control Systems via Linear Matrix Inequalities

2016 ◽  
Vol 14 (3) ◽  
pp. 31-40 ◽  
Author(s):  
M. Namazov ◽  
A. Alili
Keyword(s):  
Nonlinear System ◽  
Control Systems ◽  
Linear Matrix Inequalities ◽  
Linear Models ◽  
Fuzzy Model ◽  
Design Procedure ◽  
Optimal Performance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Takagi Sugeno

AbstractThis paper deals with a systematic design procedure that guarantees the stability and optimal performance of the nonlinear systems described by Takagi-Sugeno fuzzy models. Takagi-Sugeno fuzzy model allows us to represent a nonlinear system by linear models in different state space regions. The overall fuzzy model is obtained by fuzzy blending of these linear models. Then based on this model, linear controllers are designed for each linear model using parallel distributed compensation. Stability and optimal performance conditions for Takagi-Sugeno fuzzy control systems can be represented by a set of linear matrix inequalities which can be solved using software packages such as MATLAB’s LMI Toolbox. This design procedure is illustrated for a nonlinear system which is described by a two-rule Takagi-Sugeno fuzzy model. The fuzzy model was built in MATLAB Simulink and a code was written in LMI Toolbox to determine the controller gains subject to the proposed design approach.

State and Input Observer Design for Nonlinear Impulsive Systems via LMI Approach

2014 ◽  
Vol 950 ◽  
pp. 119-124
Author(s):  
Tian Shao ◽  
Ke Peng ◽  
Zhi Sheng Chen ◽  
Yan Jun Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Sufficient Conditions ◽  
The State ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Impulsive Systems ◽  
Lmi Approach ◽  
Quadratic Constraint

This paper addresses the observer design for simultaneously estimating the state and input of a class of impulsive systems whose nonlinear terms satisfy an incremental quadratic constraint. By employing Lyapunov theory, sufficient conditions for asymptotical and exponential estimation convergence are derived. Gain matrices of the proposed observer can be obtained by solving linear matrix inequalities (LMIs).

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers
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