scholarly journals Optimizing Regenerative Braking: A Variational Calculus Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
L. Q. English ◽  
A. Mareno ◽  
Xuan-Lin Chen
Keyword(s):  
Optimization Problem ◽  
Lagrange Equation ◽  
Variational Calculus ◽  
Regenerative Braking ◽  
Battery Charging ◽  
Air Drag ◽  
Battery Charge ◽  
Basic Physics ◽  
Integral Quantity ◽  
Charging Efficiency

We begin by analyzing, using basic physics considerations, under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over “coasting” where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we express the recovered energy as an integral quantity, and we solve the associated Euler–Lagrange equation to find the optimal braking curves that maximize this quantity in the framework of variational calculus. Using Lagrange multipliers, we also explore the effect of adding a fixed-displacement constraint.

Li-Ion Battery Charging Efficiency

2016 ◽  
Vol 74 (1) ◽  
pp. 37-43 ◽  
Author(s):  
M. Toman ◽  
R. Cipin ◽  
D. Cervinka ◽  
P. Vorel ◽  
P. Prochazka
Keyword(s):  
Li Ion Battery ◽  
Battery Charging ◽  
Li Ion ◽  
Charging Efficiency

Design of Lead-Acid Battery Intelligent Charging System

2014 ◽  
Vol 651-653 ◽  
pp. 1068-1073
Author(s):  
Yu Lin Gong ◽  
Hong Zuo Li ◽  
Ming Qiu Li ◽  
Wei Da Zhan
Keyword(s):  
Service Life ◽  
Software Design ◽  
Social Benefits ◽  
Lead Acid Battery ◽  
Negative Pulse ◽  
Battery Charging ◽  
Charging System ◽  
Pulse Charging ◽  
Charging Efficiency ◽  
Lead Acid

This paper expounds the principle of lead-acid battery intelligent charging system, design the main circuit of the intelligent charging system, the positive and negative pulse charging circuit, control circuit and software design of intelligent charging system. Experimental results show that the system USES intelligent charging method can effectively improve the charging efficiency of battery and prolong the service life of the battery, can be widely used in lead-acid battery charging system, which has a broad prospect of industrialization and social benefits.

The Intelligent Control for the Battery Charge in the Solar Lighting System

2012 ◽  
Vol 512-515 ◽  
pp. 298-302
Author(s):  
Xia Li ◽  
Zhao Xiang Zeng
Keyword(s):  
Solar Energy ◽  
Intelligent Control ◽  
Constant Voltage ◽  
Lighting System ◽  
Battery Charging ◽  
Battery Charge ◽  
Solar Battery ◽  
Solar Lighting ◽  
Tracking Technology

This paper gives the description of the scheme of solar energy lighting system. In the stated scheme, constant voltage tracking technology is used to complete the solar battery charging. The intelligent charging technology is used to implement over-current protection, over-voltage protection, and over-temperature protection.

scholarly journals DETERMINATION OF JOIN REGIONS BETWEEN CARBON NANOSTRUCTURES USING VARIATIONAL CALCULUS

2013 ◽  
Vol 54 (4) ◽  
pp. 221-247 ◽  
Author(s):  
D. BAOWAN ◽  
B. J. COX ◽  
J. M. HILL
Keyword(s):  
Carbon Nanotubes ◽  
Variational Principle ◽  
Carbon Nanostructures ◽  
Lagrange Equation ◽  
Variational Calculus ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Dimensional Plane ◽  
Continuous Models

AbstractWe review the work of the present authors to employ variational calculus to formulate continuous models for the connections between various carbon nanostructures. In formulating such a variational principle, there is some evidence that carbon nanotubes deform as in perfect elasticity, and rather like the elastica, and therefore we seek to minimize the elastic energy. The calculus of variations is utilized to minimize the curvature subject to a length constraint, to obtain an Euler–Lagrange equation, which determines the connection between two carbon nanostructures. Moreover, a numerical solution is proposed to determine the geometric parameters for the connected structures. Throughout this review, we assume that the defects on the nanostructures are axially symmetric and that the into-the-plane curvature is small in comparison to that in the two-dimensional plane, so that the problems can be considered in the two-dimensional plane. Since the curvature can be both positive and negative, depending on the gap between the two nanostructures, two distinct cases are examined, which are subsequently shown to smoothly connect to each other.

The Stationary Action Principle

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Boundary Conditions ◽  
Lagrange Equation ◽  
Variational Calculus ◽  
Action Principle ◽  
Dirichlet Boundary Conditions ◽  
Lagrange Formulation ◽  
Helmholtz Conditions ◽  
Stationary Action ◽  
The Difference ◽  
Corner Conditions

This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed include Hessian conditions, Douglas’s theorem, the Jacobi last multiplier, Helmholtz conditions, Noether-type variation and Frenet–Serret frames, as well as concepts such as on shell and off shell. Actions of non-continuous extremals are examined using Weierstrass–Erdmann corner conditions, and the action principle is written in the most general form as the Hamilton–Suslov principle. Important applications of the Euler–Lagrange formulation are highlighted, including protein folding.

scholarly journals Application of PID optimization control strategy based on particle swarm optimization (PSO) for battery charging system

2020 ◽  
Vol 15 (4) ◽  
pp. 528-535
Author(s):  
Tiezhou Wu ◽  
Cuicui Zhou ◽  
Zhe Yan ◽  
Huigang Peng ◽  
Linzhang Wu
Keyword(s):  
Particle Swarm Optimization ◽  
Control Method ◽  
Dynamic Performance ◽  
Particle Swarm ◽  
Control Effect ◽  
Swarm Optimization ◽  
Battery Charging ◽  
Charging System ◽  
Modified Particle Swarm Optimization ◽  
Charging Efficiency

Abstract The battery charging process has nonlinear and hysteresis properties. PID (Proportion Integration Differentiation) control is a conventional control method used in the battery charging process. The control effect is determined by the PID control parameters ${K}_p$,  ${K}_i$  and  ${K}_d$. The traditional PID parameter setting method is difficult to give the appropriate parameters, which affects the battery charging efficiency. In this paper, the particle swarm optimization (PSO) is used to optimize the PID parameters. Aiming at the defects of basic PSO, such as slow convergence speed, low convergence precision and easy to be premature, a modified particle swarm optimization algorithm is proposed, and the optimized PID parameters are applied to the battery charging control system. Also, the experimental results show that the battery charging process possesses better dynamic performance and the charging efficiency of the battery has increased from 86.44% to 91.47%, and the charging temperature rise has dropped by 1°C.

scholarly journals The Second Euler-Lagrange Equation of Variational Calculus on Time Scales

2011 ◽  
Vol 17 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Zbigniew Bartosiewicz ◽  
Natália Martins ◽  
Delfim F.M. Torres
Keyword(s):  
Time Scales ◽  
Lagrange Equation ◽  
Variational Calculus
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