Battery state-of-charge estimator using robust H;observer

• US 8,890,484 B2
• Filed: 05/08/2012
• Issued: 11/18/2014
• Est. Priority Date: 05/08/2012
• Status: Active Grant

• Current Assignee: GM Global Technology Operations LLC (General Motors Company)
• Original Assignee: GM Global Technology Operations LLC (General Motors Company)
• Inventors: Mao, Xiaofeng, Tang, Xidong, Hu, Yiran
• Primary Examiner(s): LIN, SUN J
• Application Number:
  US13/466,374
• Publication Number:
  US 20130300377A1
• Time in Patent Office: 924 Days
• Field of Search: 320/23, 320/40, 320/59, 320/64, 320/152
• US Class Current: 320/152
• CPC Class Codes: B60L 2240/545 Temperature
• CPC Class Codes: B60L 2240/547 Voltage
• CPC Class Codes: B60L 2240/549 Current
• CPC Class Codes: B60L 2260/44 by parameter estimation
• CPC Class Codes: B60L 50/16 with provision for separate direct mechanical propulsion
• CPC Class Codes: B60L 58/12 responding to state of charge [SoC]
• CPC Class Codes: G01R 31/367 Software therefor, e.g. for battery testing using modelling or look-up tables
• CPC Class Codes: Y02T 10/70 Energy storage systems for electromobility, e.g. batteries
• CPC Class Codes: Y02T 10/7072 Electromobility specific charging systems or methods for batteries, ultracapacitors, supercapacitors or double-layer capacitors

Abstract

A battery state-of-charge (SOC) estimator uses a robust H_∞ filter design by taking into account the battery parameter uncertainties, which is due to battery age, variation, and operating conditions such as temperature and SOC level. Each of the time-varying battery parameter values and their variation rates are bounded. By utilizing the parameter variation bounds and parameter variation rate bounds into the design process and minimizing the H_∞ gain from the measured current signal to the estimation error of V_oc, the battery SOC estimator can achieve enhanced robustness to the variations of battery age, variation, and operating conditions that include temperature and SOC level.

Claims

1. A method of determining a state-of-charge for a battery while connected to a plurality of loads, the method comprising steps of:

measuring a terminal voltage of the battery;

measuring a temperature of the battery coinciding with the measured terminal voltage;

inputting the measured terminal voltage to a first linear time invariant infinity observer filter, the first linear time invariant infinity observer filter developed in an off-vehicle design process, wherein the first linear time invariant infinity observer filter minimizes a gain of an output energy signal to an input energy signal of the battery;

estimating, by a control module, an open circuit voltage in response to the measured terminal voltage input to the first linear time invariant infinity observer filter;

determining, by the control module, the state-of-charge of the battery as a function of the open circuit voltage; and

regulating the battery in response to the state-of-charge.

2. The method of claim 1 further comprising steps of:

determining whether a current sensor is available for measuring a terminal current draw of the battery;

measuring a terminal current draw of the battery coinciding with the measured terminal voltage in response to the current sensor being available;

inputting the measured terminal current draw and the measured terminal voltage to a second linear time invariant infinity observer filter in response to the current sensor being available; and

estimating the open circuit voltage as a function of the measured terminal voltage and the measured current draw by the second linear time invariant infinity observer.

3. The method of claim 2 wherein a battery system model utilizes a two-RC pair equivalent circuit model, wherein the two-RC pair equivalent circuit model is represented by the formula:

V=V_oc+IR+V_dl+V_df

where V_oc is the open circuit voltage, V_dl is a double layer voltage, V_df is a diffuse voltage, I is a terminal battery current, and R is an ohmic resistance.

4. The method of claim 3 wherein the battery system model is transformed into discrete counterparts.

5. The method of claim 4 wherein the transformed battery system model is represented by the following matrices:

6. The method of claim 5 wherein the parameters of the battery system model are bounded and are represented by the following formula:

7. The method of claim 6 further comprising a step of generating a state vector of the battery system model which is represented by the following formula:

x(k)=└

V_dl(k)V_df(k)V_oc(k)┘

where V_oc is the open circuit voltage, V_dl is a double layer voltage, V_df is a diffuse voltage, I is a terminal battery current, and R is an ohmic resistance.

8. The method of claim 7 further comprising a step of generating an augmented system model as represented by the following expression:

x(k+1)=A(θ

(k))x(k)+B(θ

(k))w(k)

y(k)=C(θ

(k))x(k)+D(θ

(k))w(k)

s(k)=C_s(θ

(k))x(k)+D_s(θ

(k))w(k)

where θ

(k) is a vector of unknown parameters represented by θ

(k)=[θ

₁(k), θ

₂(k), θ

₃(k), θ

₄(k), θ

₅(k), θ

₆(k)] , w(k) is an uncertain input signal, s(k) is a signal estimated online, y(k) is an output signal that is a function of battery parameter measurements available online, and A ,B ,C ,D are coefficients of matrices representing an output of an LTI (linear time invariant) infinity observer filter.

9. The method of claim 8 wherein elements of the first LTI infinity observer filter are represented by the following observation:

10. The method of claim 9 wherein the first LTI infinity observer filter is represented as follows:

{circumflex over (x)}(k+1)=A_f{circumflex over (x)}(k)+B_fV(k)

ŝ

(k)=C_f{circumflex over (x)}(k)+D_fV(k)

where A_f, B_f, C_f, D_fare output matrices from a filter design process of the first LTI infinity observer.

11. The method of claim 10 wherein elements of the second LTI infinity observer filter are represented by the following observation:

12. The method of claim 11 wherein the second LTI observer infinity observer filter is represented as follows:

{circumflex over (x)}(k+1)=A_f{circumflex over (x)}(k)+B_f[V(k) I(k)]^T

ŝ

(k)=C_f{circumflex over (x)}(k)+D_f[V(k) I(k)]

where A_f, B_f, C_f, D_f are output matrices from a filter design process of the second LTI infinity observer.

13. The method of claim 12 wherein a set of bound values and variation rate values for the parameters of the filter design process are selected for the first LTI infinity observer filter/the second LTI infinity observer filter based on whether an optimization goal value can achieve a predetermined upper bound of a gain that is a function of an uncertain input signal and an estimation error as represented by the following formula:

14. The method of claim 13 wherein the set of bound values, variation rate values, and the optimization goal value for the parameters of the filter design process that achieve the predetermined upper bound of the gain are determined valid if the following inequality is satisfied:

15. The method of claim 14 wherein the optimization goal value is recursively decreased and evaluated for determining whether the each decreased optimization value and associated set of bound and variation rate values satisfy the inequality, and wherein a lowest optimization value from the evaluated optimization goal values that successfully satisfies the inequality is selected for both the first and the second LTI infinity observer filter.

16. The method of claim 1 further comprising a step of outputting the state of charge of the battery to an output device for displaying the state-of-charge to a user of a vehicle.

17. The method of claim 1 wherein the regulating step comprises outputting the state-of-charge of the battery to an electronic control unit for regulating the battery terminal voltage.

18. The method of claim 1 wherein the regulating step comprises outputting the state-of-charge of the battery to an electronic control unit for improving fuel economy of a vehicle.

19. The method of claim 1 wherein the state-of-charge is derived from an open circuit voltage-state-of-charge lookup table stored in a memory of a vehicle.