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Research Papers

State of Charge Estimator Design for a Gas Charged Hydraulic Accumulator

[+] Author and Article Information
Andreas Pfeffer

Automation and Control Institute,
Vienna University of Technology,
Gußhausstraße 27-29/376,
Vienna 1040, Austria
e-mail: pfeffer@acin.tuwien.ac.at

Tobias Glück

Automation and Control Institute,
Vienna University of Technology,
Gußhausstraße 27-29/376,
Vienna 1040, Austria
e-mail: glueck@acin.tuwien.ac.at

Wolfgang Kemmetmüller

Assistant Professor
Automation and Control Institute,
Vienna University of Technology,
Gußhausstraße 27-29/376,
Vienna 1040, Austria
e-mail: kemmetmueller@acin.tuwien.ac.at

Andreas Kugi

Professor
Automation and Control Institute,
Vienna University of Technology,
Gußhausstraße 27-29/376,
Vienna 1040, Austria
e-mail: kugi@acin.tuwien.ac.at

Note that henceforth the additional index m refers to the corresponding measured quantity.

The filter time constant tf is chosen based on measurements.

The mean squared error and the mean absolute errors are normalized by 1l2 and 1l, respectively.

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 24, 2014; final manuscript received December 16, 2014; published online February 4, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(6), 061014 (Jun 01, 2015) (9 pages) Paper No: DS-14-1134; doi: 10.1115/1.4029407 History: Received March 24, 2014; Revised December 16, 2014; Online February 04, 2015

The gas charged hydraulic accumulators under consideration are used as energy storage devices in automotive hydraulic hybrid systems. The knowledge of the state of charge (SOC) is of utmost importance for an efficient energy management of the hybrid drive-train. Since the direct measurement of the SOC is difficult and costly, an SOC estimator design is presented based on a mathematical model of the gas charged hydraulic accumulator. Two different SOC estimation strategies, a signal-based approach and an Extended Kalman-filter, are presented and compared with each other. The performance of the estimators is validated by means of measurement results of a test driving cycle.

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Figures

Grahic Jump Location
Fig. 1

Schematic of the gas charged hydraulic piston-type accumulator

Grahic Jump Location
Fig. 2

Comparison of the simulated model with measurement results: (a) measured piston position sp,m; (b) measured oil pressure po,m; (c) calculated inlet oil flow qo,c from actual pump data and inlet oil flow qo,ND, obtained from the measured piston position; and (d) gas temperature Tg,s of the sensor model, calculated gas temperature Tg,c using Eq. (3), measured gas temperature Tg,m, and measured ambient temperature Ta,m.

Grahic Jump Location
Fig. 3

Concept of the signal-based estimator

Grahic Jump Location
Fig. 4

Comparison of the estimator results and measurement data for nominal parameters: (a) measured gas volume Vg,m and estimated gas volumes V∧g,SB and V∧g,KF; (b) estimation errors of the two approaches; and (c) estimated oil leakage flow of the EKF Δq∧o,KF compared to the result of the numerical differentiation Δqo,ND.

Grahic Jump Location
Fig. 5

Comparison of alternative calculation methods based on an ideal adiabatic (index ad) and isothermal (index is) process with different initial conditions, based on the initial fill (index if) and on V∧g,0 (index V∧g,0): (a) measured gas volume Vg,m and estimated gas volumes V∧g,• and (b) estimation errors.

Grahic Jump Location
Fig. 6

Comparison of the estimation results of the Extended Kalman-filter with nominal ambient temperature (index KF) and with an error in the ambient temperature of −5 K (index KF,T˜a5) and −15 K (index KF,T˜a15): (a) measured gas volume Vg,m and estimated gas volumes V∧g,•; (b) estimation errors; and (c) estimated oil leakage flows Δq∧o,• compared to the results of the numerical differentiation Δqo,ND.

Grahic Jump Location
Fig. 7

Study of the influence of a reduced (simulation) gas mass of m˜g=0.95mg: (a) measured gas volume Vg,m and estimated gas volumes V∧g,•; (b) estimation errors; and (c) estimated oil leakage flow Δq∧o,KF,m˜g compared to the results of the numerical differentiation Δqo,ND,m˜g.

Grahic Jump Location
Fig. 8

Comparison of the Extended Kalman-filters with constant gas mass m˜g = 0.95mg (index KF,m˜g) and with an augmented gas mass model (index KF,m∧g), where the initial gas mass is set to m∧g,0 = 0.75mg: (a) measured gas volume Vg,m and estimated gas volumes V∧g,•; (b) estimation errors; (c) gas mass mg and estimated gas mass m∧g; and (d) estimated oil leakage flow Δq∧o,KF,m∧g and Δq∧o,KF,m˜g compared to the results of the numerical differentiation Δqo,ND,m˜g.

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