Abstract
Stochastic dynamic programming (SDP) is applied to the optimal control of a hybrid electric vehicle in a concerted attempt to deploy and evaluate such a controller in the real world. Practical considerations for robust implementation of the SDP algorithm are addressed, such as the choice of discount factor used and how charge sustaining characteristics of the SDP controller can be examined and adjusted. A novel cost function is used incorporating the square of battery charge (C-rate) as an indicator of electrical powertrain stress, with the aim of lessening the affliction of real-world concerns such as battery health and motor temperature, while allowing short spells of operation toward the system peak power limits where advantageous. This paper presents the simulation and chassis dynamometer results over the LA92 drive cycle, as well as the results of testing on open roads. The hybrid system is operated at several levels of aggressivity, allowing the tradeoff between fuel savings and electrical powertrain stress to be evaluated. In dynamometer testing, this approach yielded a 13% reduction in electrical powertrain stress without sacrificing any fuel savings, compared with a controller that does not consider aggressivity in its optimization.
Highlights
T HE OPTIMAL control of hybrid electric vehicle (HEV) powertrains in real-world conditions is nontrivial because the solution depends on the future use case: this determines whether there are likely to be effective opportunities for hybrid operation as well as the availability of recoverable energy.The present literature on the optimal control of hybrid vehicles advocates stochastic dynamic programming (SDP) [1]–[8], which aims to use Bellman’s principle of optimality applied to a statistical model of what the future is likely to entail, rather than deterministic dynamicManuscript received January 12, 2015; revised June 10, 2015; accepted October 4, 2015
SDP has been demonstrated as a promising algorithm for optimal hybrid vehicle control by many researchers in a simulation environment
This paper has presented a functioning controller, evaluated on a retrofit hybrid vehicle using representative real-world driving data
Summary
T HE OPTIMAL control of hybrid electric vehicle (HEV) powertrains in real-world conditions is nontrivial because the solution depends on the future use case: this determines whether there are likely to be effective opportunities for hybrid operation as well as the availability of recoverable energy. The present literature on the optimal control of hybrid vehicles advocates stochastic dynamic programming (SDP) [1]–[8], which aims to use Bellman’s principle of optimality applied to a statistical model of what the future is likely to entail, rather than deterministic dynamic. Manuscript received in final form November 1, 2015. The SDP controller would likely be out performed by a controller with perfect knowledge of the future and freedom to be time varying; it is the stationary policy that will yield the best possible result when operated indefinitely, over a drive cycle matching its probability model. In the absence of perfect knowledge of the future, this SDP controller is extremely attractive. It does require a collection of representative driving data on which to be based, which may not be available. Its implementation is not straightforward and so requires time investment during design, the control map is difficult to examine because it is multidimensional, and the embedded real-time operation may be memory intensive (though not computationally intensive)
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