Optimal battery charging, Part I: Minimizing time-to-charge, energy loss, and temperature rise for OCV-resistance battery model

This article addresses the optimal (minimum-time/energy) trajectory design for rapid output transitions, i.e. changing the output from one value to another, in linear systems. Furthermore, the output is required to be maintained constant (e.g. without vibration) outside the transition time interval. The output-transition problem is posed as a linear quadratic minimum-time (LQMT) optimal control problem, which avoids bang-bang controllers that result from solving the traditional time-optimal problem. Additionally, the LQMT approach allows the time-optimal requirement to be traded off with the energy requirement by selecting appropriated weighting factors. Current methods transform this LQMT output-transition problem into a state-transition problem by constraining the initial and final state of the output-transition interval. However, the choice of the initial and final states can be ad hoc and the resulting control law may not be optimal. In contrast, the proposed approach directly solves the LQMT output-transition problem by optimally choosing the initial and final states to minimize the output-transition cost. The novelty of the proposed approach is that inputs are not applied just during the output-transition time interval; rather, inputs are also applied before the beginning of and after the end of the output-transition time interval (these inputs are called pre- and post-actuation). The method is illustrated using a flexible structure model, and simulation results show substantial reduction in output-transition cost when compared with the cost of standard state-transition-based approaches, which do not use pre-and post-actuation.

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Minimum-time/energy output-transitions in linear systems

In this paper, we present a closed-form solution to the problem of optimally charging a Li-ion battery. The objective function is considered as a combination of two cost functions: time-to-charge (TTC) and energy losses (EL). For the case where cost function is a combination of TTC and EL, the optimal charging strategy is a Constant Current-Constant Voltage (CC-CV) policy with the value of the current in the CC stage being a function of the ratio of weighting on TTC and EL and of the resistance of the battery. The case where the cost function is a weighted sum of TTC, EL and a temperature rise index (TRI) is also considered and an analytical solution for the problem is derived. This analytical solution can be approximated by a CC-CV with the value of current in the CC stage being a function of ratio of weighting on TTC and EL, resistance of the battery and the effective thermal resistance. The effects of weights in the objective function on the optimal charging profile is discussed and the behavior of different kinds of commercial batteries are analyzed.

Battery charging optimization for OCV-resistance equivalent circuit model

This article addresses the optimal (minimum-time/energy) trajectory design for changing the output from one value y to another y within a finite time interval [0, t f ] called the output-transition time interval. The output should be maintained constant (at the desired value) outside the output-transition time interval. The main contribution of this article is to establish the existence of a solution to the problem when preactuation (input applied during time t t f ) are allowed. The advantage of using pre- and postactuation inputs is illustrated with an experimental dual-stage actuator system.

Minimum-Time/Energy, Output Transitions for Dual-Stage Systems

The present work deals with the linear quadratic control problem for a discrete distributed system with terminal convex constraint. Using techniques of perturbation by feedback, it is shown that the resolution of the considered problem is equivalent to that of a controllability, one so-called Extended Exact Controllability with time-varying operators. The Hilbert uniqueness method approach is then extended to this case to provide an explicit form for the optimal control. In the same framework, the inequality constraint case is examined for which a practical numerical resolution is given. Finally, the results obtained are used to treat a minimum-time reachability problem.

Linear quadratic control problem with a terminal convex constraint for discrete-time distributed systems

E. I. Verriest and F. L. Lewis have presented in (1) a new method to approximate the minimum-time control of linear continuous-time systems avoiding the Bang-Bang control. Their method relied on the optimization of a cost including time energy and precision terms. Our purpose in this article is to extend their work to discrete-time linear systems. Indeed, we consider a linear discrete-time system and a quadratic cost including time and energy term, and we look for the minimum-time and the control which minimizes the cost function and leads the system from a given initial state to a fixed final one. By selecting the magnitude of the energy term, one may balance off the requirement for minimum-time versus the one for keeping the state and inputs small over the considered interval of time. Finally we give a method to compute the minimum-time and the optimal control.

N. El Alami

Papers

On the discrete linear quadratic minimum-time problem