Research Papers

Control of Engine-Starts for Optimal Drivability of Parallel Hybrid Electric Vehicles

[+] Author and Article Information
Dongsuk Kum

Cho Chun Shik Graduate School of Green Transportation,
Korea Advanced Institute of Science and Technology,
2116-1 Eureka Hall,
291 Daehak-ro, Yuseong-gu,
Daejeon 305-701, Republic of Korea
e-mail: dskum@kaist.ac.kr

Huei Peng

G036 Lay Automotive Laboratory,
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2133
e-mail: hpeng@umich.edu

Norman K. Bucknor

Propulsion Systems Research Laboratory,
General Motors R&D Center,
Warren, MI 48091
e-mail: norman.k.bucknor@gm.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 14, 2011; final manuscript received October 29, 2012; published online February 21, 2013. Assoc. Editor: Luis Alvarez.

J. Dyn. Sys., Meas., Control 135(2), 021020 (Feb 21, 2013) (10 pages) Paper No: DS-11-1314; doi: 10.1115/1.4023067 History: Received October 14, 2011; Revised October 29, 2012

The pretransmission parallel hybrid electric vehicle (HEV) with a single electric motor requires relatively little changes from existing powertrain configurations. This configuration, however, has a challenging drivability issue during engine-starts because the electric motor must simultaneously provide the demanded propulsion torque and start the engine. Depending on the propulsion power level, such engine-start process may require a trade-off between drivability and quick start. The goal of this study is to find theoretical performance limits and corresponding optimal control strategies that achieve the balance between these two conflicting goals. We first develop a simplified parallel HEV powertrain model to predict the engine, clutch, and vehicle dynamics. Assuming that the clutch torque can be accurately estimated and perfectly cancelled, an optimal engine-start control problem is formulated to minimize engine-start time while supplying the driver demanded torque. This nonlinear constrained optimal control problem is solved both analytically and numerically. For some special cases, the optimization problem can be solved analytically to obtain a closed-form solution. For the numerical method, dynamic programming (DP) is used, and both analytical and numerical solutions show that selecting a proper level of constant clutch pressure is the key to achieve near-optimal drivability performance. Furthermore, the DP control policy is found to be time-invariant, and thus can be implemented in the form of a full state feedback controller.

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Fig. 1

Schematic of the pretransmission parallel hybrid electric vehicle

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Fig. 2

Simplified free-body diagram of the HEV powertrain during engine-starts

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Fig. 3

Block diagram of the powertrain model for the engine-start control

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Fig. 4

Approximated friction coefficient (μ) as a function of the slip speed (Δω)

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Fig. 5

Overview of the engine torque and intake manifold pressure model

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Fig. 6

A sample cylinder pressure map of firing mode at 1000 rpm

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Fig. 8

Block diagram of the engine-start control architecture: the clutch actuator loop is neglected for the implementation of DP

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Fig. 7

Sample simulation results of the engine-start model

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Fig. 9

Conceptual engine speed trajectories of various optimal solutions

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Fig. 10

Simulation results of an example optimal solution using analytical approach

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Fig. 11

Optimal pressure commands and engine speed profiles of various DP solutions. (β = 1 × 10−6, γ = 1 × 10−6).

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Fig. 12

Trade-off between initial clutch pressure and engine-start time

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Fig. 13

Trade-off between torque reserve and engine-start time

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Fig. 16

Simulation results of the directly implemented DP control policy. (Treserve = 30 Nm, β = 1 × 10−6, γ = 1 × 10−6).

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Fig. 14

DP control policy (uk *) at various time steps k. (θcrank = 0 deg, Treserve = 30 Nm, and ωi = 1300 rpm).

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Fig. 15

Filtered DP control policy (uk * ) at θcrank = 0 deg. (Treserve = 30 Nm).




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