CN110226097B

CN110226097B - Method for setting observer gain

Info

Publication number: CN110226097B
Application number: CN201880008457.3A
Authority: CN
Inventors: 长村谦介; 足立修一; 八田羽谦一; 川口贵弘; 井上正树
Original assignee: Calsonic Kansei Corp; Keio University
Current assignee: Keio University; Marelli Corp
Priority date: 2017-03-03
Filing date: 2018-03-02
Publication date: 2022-07-05
Anticipated expiration: 2038-03-02
Also published as: CN110226097A; JPWO2018159843A1; WO2018159843A1; JP7141620B2; DE112018001123T5

Abstract

The invention provides a charging rate estimating apparatus capable of improving the estimation accuracy of the charging rate. A charging rate estimation device (1) estimates the charging rate of a battery (4) by using an observer based on a model of the battery (4). The model is constructed based on hysteresis characteristics. The observer gain, which is a parameter of the observer, is set to reduce an estimation error of the charging rate corresponding to a modeling error of a parameter included in the model, and may be changed according to at least one of the magnitude of the current flowing through the battery (4) and the terminal voltage of the battery (4).

Description

Method for setting observer gain

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from Japanese patent application No. 2017-040080 (application 3/2017), the disclosure of which is hereby incorporated by reference in its entirety.

Technical Field

The present invention relates to a state of charge estimation device and a state of charge estimation method.

Background

There is known a device for estimating a charging rate of a battery having a hysteresis relationship between the charging rate and an open circuit voltage of the battery (for example, patent document 1, patent document 2, and the like).

(Prior art document)

(patent literature)

Patent document 1: japanese patent laid-open publication No. 2016-

Patent document 2: japanese patent laid-open publication No. 2011-33453

Disclosure of Invention

(problems to be solved by the invention)

The charge rate of the battery can be estimated from a battery model. In a battery having a hysteresis relationship between the charging rate and the open circuit voltage of the battery, a parameter representing a battery model is likely to change. Modeling errors in parameters due to changes in parameters representing a battery model can reduce the accuracy of estimating the state of charge of the battery.

However, in patent documents 1 and 2, no consideration is given to an estimation error of the charging rate corresponding to a modeling error of the parameter. For example, in paragraph 0139 of patent document 2, "the conversion operation processing …" performed by the appropriate conversion operation unit 34a is performed on all or a part of the respective parameters (i.e., Iact, Vact, Δ a, Δ V, Δ Vest, (Δ V- Δ Vest), K, Q, aest, and the like). Although the description has been made on the noise of the voltage change or the current change, the estimation error caused by the modeling error of the parameter of the battery having the hysteresis characteristic and the change of the parameter indicating the battery model having the hysteresis characteristic are not discussed.

The present invention has been made in view of the above circumstances, and an object thereof is to provide a state of charge estimation device and a state of charge estimation method that can change a parameter of an estimator according to a change in a parameter of a battery, thereby improving estimation accuracy of a state of charge of the battery.

(measures taken to solve the problems)

In order to solve the above problem, a state of charge estimation device according to a first aspect estimates a state of charge of the battery using an observer based on a battery model. The model is constructed based on hysteresis characteristics. An observer gain, which is a parameter of the observer, is set to reduce an estimation error of the state of charge corresponding to a modeling error of a parameter included in the model. The observer gain may be varied according to at least one of a magnitude of a current flowing through the battery and a terminal voltage of the battery.

In order to solve the above problem, a charging rate estimating method according to a second aspect includes a step of estimating a charging rate of the battery using an observer based on a battery model. The method of estimating the state of charge includes a step of setting an observer gain, which is a parameter of the observer, so as to reduce an estimation error of the state of charge corresponding to a modeling error of a parameter included in the model. The charging rate estimating method includes a step of changing the observer gain according to at least one of a magnitude of a current flowing through the battery and a terminal voltage of the battery. The model is constructed based on hysteresis characteristics.

(Effect of the invention)

According to the state of charge estimation device in the first aspect, the accuracy of estimating the state of charge of the battery can be improved.

According to the state of charge estimation method in accordance with the second aspect, the accuracy of estimating the state of charge of the battery can be improved.

Drawings

Fig. 1 is a functional block diagram showing a schematic configuration example of a charging rate estimating apparatus.

Fig. 2 is a diagram showing one example of the battery equivalent circuit.

Fig. 3A is an n-order Foster (Foster) type RC ladder.

FIG. 3B is an n-order couer (Cauer) type RC ladder.

Fig. 4 is a diagram showing an example of the SOC-OCV characteristic.

Fig. 5 is a diagram showing one example of the SOC-OCV characteristic with hysteresis.

Fig. 6 is a diagram showing an example of a battery equivalent circuit including hysteresis voltages.

Fig. 7 is a diagram showing an example of an equivalent circuit of the battery after replacing the walbaur impedance of fig. 6 with a foster type RC ladder circuit.

Fig. 8 is a flowchart illustrating an example of the state of charge estimation method.

Fig. 9 is a graph showing one example of the current input to the battery equivalent circuit.

Fig. 10 is a graph showing one example of the estimation result of the SOC of the battery.

Fig. 11 is a graph showing one example of the estimation error of the SOC of the battery.

Fig. 12 is a graph showing an example of RMSE of estimation error.

Detailed Description

The state-of-charge estimation device according to one embodiment of the present disclosure may be mounted on a vehicle such as an electric vehicle or a hybrid vehicle. The charging rate estimating device may estimate a charging rate of a battery of the vehicle. The vehicle is mounted with an electric motor for driving the vehicle, a battery, a controller for these, and the like. The battery discharges and supplies power to the electric motor, and during braking, regenerative charging is performed from the electric motor, or charging is performed from a ground charging facility. The charging rate estimating means may estimate the charging rate of the battery based on a charging/discharging current flowing through the battery and a terminal voltage of the battery.

[ functional Block diagrams ]

As shown in fig. 1, the state of charge estimation device 1 is connected to a battery 4 via a current sensor 2 and a voltage sensor 3. The charging rate estimation device 1 may include a current sensor 2 and a voltage sensor 3. The charging rate estimation device 1 may be connected to the power supply device 5. The state of charge estimation device 1 can input a charge/discharge current from the power supply device 5 to the battery 4. The power supply means 5 may be, for example, a current source. The charging rate estimation device 1 may include a power supply device 5.

The current sensor 2 detects a charge/discharge current to the battery 4. In the present embodiment, it is assumed that the charge/discharge current is expressed by a function u (t) at time (t). The current sensor 2 outputs the detected charge/discharge current to the state of charge estimation device 1.

The voltage sensor 3 detects a terminal voltage of the battery 4. In the present embodiment, it is assumed that the terminal voltage is expressed by a function y (t) at time (t). The voltage sensor 3 outputs the detected terminal voltage to the charging rate estimating apparatus 1.

The battery 4 may be, for example, a secondary battery. The secondary battery is also called a rechargeable battery. In the present embodiment, it is assumed that the battery 4 is a lithium ion battery. The battery 4 may be another kind of battery.

The charging rate estimating device 1 includes a control unit 10 and a storage unit 20. The control unit 10 controls each constituent unit of the state of charge estimation device 1. The control unit 10 may be constituted by a processor, a microcomputer, or the like, for example. The storage unit 20 may be formed of, for example, a semiconductor memory, a magnetic storage device, or the like. The control unit 10 may store data or information processed in the charging rate estimating device 1 in the storage unit 20.

The control unit 10 acquires the charge/discharge current and the terminal voltage of the battery 4 from the current sensor 2 and the voltage sensor 3, respectively. The control unit 10 can estimate the internal state of the battery 4 from the charge/discharge current and the terminal voltage of the battery 4.

The internal state of the battery 4 can be represented by a model including, as parameters, the open-circuit voltage of the battery 4, and the overvoltage generated inside the battery 4. The open Circuit voltage is also called ocv (open Circuit voltage). OCV is a potential difference between electrodes of the battery 4 in an electrochemically balanced state. The OCV corresponds to a terminal voltage of the battery 4 when no charge-discharge current flows in the battery 4. The overvoltage corresponds to the magnitude of the voltage drop due to the internal impedance. The internal impedance is determined according to the reaction speed of the electrochemical reaction inside the battery 4.

A model representing the internal state of the battery 4 can be approximated by a battery equivalent circuit as shown in fig. 2. The model approximated by the battery equivalent circuit is also referred to as a battery model. The input of the cell equivalent circuit corresponds to the charge and discharge current flowing through the cell 4 and is denoted as u (t). The arrow marked u (t) in fig. 2 indicates the direction of the current charging the battery 4. It is assumed that u (t) is a positive value when a current for charging the battery 4 flows. It is assumed that u (t) has a negative value when a discharge current flows from the battery 4. The output of the battery equivalent circuit corresponds to the terminal voltage of the battery 4 and is denoted by y (t). It is assumed that the terminal on the tip side of the arrow marked y (t) in fig. 2 corresponds to the positive terminal of the battery 4.

In the battery equivalent circuit, the OCV of the battery 4 is represented by a voltage source 201. The voltage output by the voltage source 201 is represented by a function ocv (t) of the time instant. Ocv (t) corresponds to a terminal voltage of battery 4 when no charge-discharge current flows in battery 4. When no charge/discharge current flows in the battery 4, u (t) may be 0. When u (t) is 0, ocv (t) is true (y) (t).

In the battery equivalent circuit of fig. 2, the internal impedance of the battery 4 is represented by a circuit in which a resistor indicated by R0 and a wattle impedance indicated by zw (p) are connected in series. The resistance indicated by R0 represents the resistance due to the migration process in the electrolyte of the battery 4. The walbau impedance represents impedance caused by a diffusion process of ions in the battery 4 or the like. The overvoltage of the battery 4 is represented as a voltage drop generated in the internal impedance of the battery 4 by the current flowing through the battery equivalent circuit.

The Valurburg impedance may be expressed, for example, as shown in FIG. 3A, with n being represented by R₁～R_nResistance shown and C₁～C_nThe parallel circuit of capacitors is shown as an n-order Foster circuit connected in series. The Valley impedance may be represented, for example, as n capacitors (C) connected in series, such as shown in FIG. 3B₁～C_n) Are respectively connected with R in parallel₁～R_nAn n-order coulter-type circuit of n resistors is shown. The Valurburg impedance may also be represented by other linear transfer function models.

The parameters of the battery equivalent circuit that approximates the battery 4 include the resistance value of the resistor that constitutes the wattle impedance, and the capacity of the capacitor. The parameters of the battery equivalent circuit may be preset. The parameters of the battery model may be stored in the control unit 10 or may be stored in the storage unit 20.

The control unit 10 estimates the internal state of the battery 4 based on the parameters of the battery equivalent circuit, the charge/discharge current flowing through the battery 4, and the terminal voltage of the battery 4. In the present embodiment, the control unit 10 estimates the charging rate and overvoltage of the battery 4 as the internal state of the battery 4. The charging rate of the battery 4 is a ratio of the charged amount to the charged capacity of the battery 4. The charging rate is also referred to as soc (state Of charge). It is assumed that the control unit 10 does not estimate the resistance value of the resistor and the capacity of the capacitor, which constitute the internal impedance of the battery 4. The control unit 10 is not limited to a configuration in which the resistance value and the capacity included in the internal impedance are not estimated. The control unit 10 may be configured to estimate a resistance value and a capacity included in the internal impedance.

The control unit 10 can estimate the OCV and the overvoltage of the battery 4. At this time, control unit 10 may estimate the SOC of battery 4 from the OCV of battery 4.

The OCV of the battery 4 can be expressed as a function of the SOC. The relationship between the SOC and OCV is referred to as SOC-OCV characteristics. The SOC-OCV characteristic can be represented by a graph shown in fig. 4, for example. The horizontal axis and the vertical axis of fig. 4 represent SOC and OCV, respectively. The SOC-OCV characteristics can be obtained in advance by experiments and the like. Control unit 10 may estimate the OCV of battery 4 from the SOC-OCV characteristic of battery 4 and the estimated value of the SOC of battery 4.

[ hysteresis characteristics ]

The SOC-OCV characteristic sometimes has a hysteresis characteristic. The SOC-OCV characteristic having the hysteresis characteristic is different at the time of charging and the time of discharging. The SOC-OCV characteristic having the hysteresis characteristic is shown in fig. 5, for example. The horizontal axis and the vertical axis of fig. 5 represent SOC and OCV, respectively. In fig. 5, a charging SOC-OCV characteristic 501 representing the SOC-OCV characteristic when the battery 4 is charged is shown by a broken line. A discharge SOC-OCV characteristic 502 indicating the SOC-OCV characteristic when the battery 4 is discharged is indicated by a one-dot chain line.

The charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502 form an SOC-OCV characteristic loop. The SOC-OCV characteristic loop formed by the charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502 is also referred to as a main loop. The main return line can be obtained by a charge-discharge experiment performed on the battery 4.

The battery 4 is not limited to being charged after being discharged until the SOC becomes 0%. For example, by discharging the battery 4 to the point a of fig. 5 and then charging it, the SOC-OCV characteristic shown on the path from the point a to the point B can be displayed. The battery 4 is not limited to being discharged after being charged until the SOC becomes 100%. For example, by charging the battery 4 to the point C of fig. 5 and then discharging it, the SOC-OCV characteristic shown on the path from the point C to the point D can be displayed. For example, a loop of the SOC-OCV characteristic smaller than that of the main loop, which is shown by a path formed by connecting points a, B, C, D, and a in this order, is also referred to as a sub loop. Unlike the primary return line, the secondary return line can be virtually infinitely present. The secondary loop is difficult to obtain by a preliminary experiment as compared with the primary loop.

The SOC-OCV characteristic 500 shown by the solid line in fig. 5 corresponds to an average value of the charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502. The SOC-OCV characteristic 500 is not limited to the average value of the charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502. The SOC-OCV characteristic 500 may be a graph included between the charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502.

The difference between the SOC-OCV characteristic 500 and the OCV between the main loops is also referred to as hysteresis voltage. Let the hysteresis voltage be denoted as h (t). The SOC-OCV characteristic having hysteresis may be represented by the following equation (1) including hysteresis voltage, rather than by a secondary loop that may exist virtually infinitely.

[ mathematical formula 1]

OCV(t)＝f_OCV(x_SOC(t))+h(t) (1)

f_OCV(. cndot.) is a function representing the SOC-OCV characteristic 500.

Since the SOC-OCV characteristic is as shown in equation (1), control unit 10 estimates the powerThe internal state of the cell 4 is estimated in conjunction with h (t), whereby the accuracy of the conversion between SOC and OCV can be improved. When the SOC-OCV characteristic is as shown in equation (1), the battery equivalent circuit is as shown in fig. 6. The battery equivalent circuit of fig. 6 is different from the battery equivalent circuit of fig. 2 in that h (t) indicating the hysteresis voltage is added to the battery equivalent circuit of fig. 6 and the output voltage of the voltage source 201 is indicated by f_OCV(x_SOC(t))。

In this embodiment, it is assumed that the wattle castle impedance is represented by a foster type circuit shown in fig. 3A. At this time, the battery equivalent circuit is as shown in fig. 7. The battery equivalent circuit of fig. 7 is different from the battery equivalent circuit of fig. 6 in Z of the battery equivalent circuit of fig. 7_w(p) alternative for Foster type circuits. v. of_k(t) represents C_kThe voltage drop produced in the capacity shown. k is an integer of 1 to n.

According to a hysteresis model proposed by Plett, which is one of models representing hysteresis, the behavior of h (t) is expressed by the following formula (2).

[ mathematical formula 2]

γ is a positive number that specifies the decay rate of the hysteresis voltage. m represents the maximum value of the hysteresis voltage. For the hysteresis model proposed by Plett, for example, the following documents can be referred to.

G.L.Plett:“Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs Part 2.Modeling and identification”,Journal of Power Sources 134(2004)262-276

X of the battery 4 at time (t)_SOC(t) can be calculated by the following formula (3). t is t₀The measurement start time is shown. The integral of the second term on the right side of equation (3) represents the amount of charge that is taken in and out of the battery 4 calculated by integrating the charge and discharge current. Fcc (full Charge capacity) represents the full Charge capacity of the battery 4.

[ mathematical formula 3]

The overvoltage is expressed by the following equation (4) based on the internal impedance of the battery 4 and the charge/discharge current of the battery 4.

[ mathematical formula 4]

ζ(t)＝G_n(p)u(t) (4)

ζ (t) represents an overvoltage. G_ζ(p) represents the internal impedance, is R₀And Z_wThe sum of (p).

When the walbauer impedance is a foster type circuit, zw (p) is as shown in the following equation (5).

[ math figure 5]

Wherein,

[ mathematical formula 6]

R_dIndicating the diffusion resistance. C_dIndicating the diffusion capacity. Y (t) corresponding to the output of the battery equivalent circuit of fig. 7 is represented by the following equation (7).

[ math figure 7]

y(t)＝f_OCV(x_SOC(t))+h(t)+G_ζ(p)u(t) (7)

The battery model represented by the battery equivalent circuit of fig. 7 is represented by an input-output system in which a charge-discharge current is input and a terminal voltage is output. Input-output systems are also referred to simply as systems. The input-output system can be expressed as a state space shown by the following equations (8) and (9).

[ mathematical formula 8]

y(t)＝f_OCV(x_soc(t))+c^Tx(t)+R₀u(t) (9)

The state space is a space in which state variables of the system are represented as coordinate axes. Equation (8) is a state equation representing the relationship between the input and the state variable. Equation (9) is an output equation representing the relationship between the state variable and the output.

A (u (t)) of the formula (8) is an (n +2) × (n +2) order matrix of the real number space, which is expressed by the following formula (10). diag is a function of the output diagonal matrix.

[ mathematical formula 9]

A (u (t)) is also called the system matrix. The system matrix represents at least a portion of the characteristics of the system. The system matrix of equation (8) depends on u (t) which represents the input to the system. Therefore, the systems represented by the formulas (8) and (9) can also be said to be parameter variable systems. The parameter variable system is also known as the pv (parameter varying) system. In other words, the model of the cell 4 represented by the cell model of fig. 7 may be represented by a PV system.

B of equation (8) and c of equation (9) represent (n +2) -order column vectors of the real space, and are expressed by equations (11) and (12) below. T denotes a transposed matrix.

[ mathematical formula 10]

c＝[0 1 … 1]^T (12)

X (t) of equations (8) and (9) is a state variable, which is expressed by equation (13) below.

[ mathematical formula 11]

x(t)＝[x_SOC(t) v₁(t) … v_n(t) h(t)]^T (13)

[ estimation of internal State of System ]

The state of charge estimation device 1 according to the present embodiment can estimate the internal state of the battery 4 by estimating a state variable in a PV system representing a model of the battery 4. The control unit 10 inputs the charge/discharge current acquired from the current sensor 2 to a model of the battery 4, and calculates an estimated value of the terminal voltage. The control unit 10 feeds back the difference between the estimated value of the terminal voltage and the actual terminal voltage to the model of the battery 4, and estimates the SOC of the battery 4 one by one.

In the present embodiment, it is assumed that the PV system representing the model of the cell 4 is a linear parameter variable system. The linear Parameter variable system is also called lpv (linear Parameter varying) system. The following description of the LPV system is not limited to a system showing a model of the battery 4.

The LPV system can be expressed as a state space shown by the following equations (14) to (18). As shown in equations (16) to (18), a as a system matrix can be expressed in a polytope. Polycythemia is a form in which functions are expressed by a first order combination. First order combining is also referred to as linear combining.

[ mathematical formula 12]

y(t)＝Cx(t) (15)

Equation (14) is a state equation representing the relationship between the input to the system and the state variables representing the internal state of the system. The formula (15) represents the state variable andan output equation from the relationship between the outputs of the system. x (t) is an nth order column vector of the real number space, representing the state variable. u (t) is n of real number space_uAn order column vector, representing the input to the system. y (t) is n of real number space_yAn order column vector, representing the output from the system. n, n_uAnd n_yThe state, the magnitude of the input signal, and the magnitude of the output signal are set according to the respective conditions. The size of the matrix denoted by a (θ (t)), B, and C is set according to the size of the respective signals.

U (t) of the inputs to the system represented by equations (14) and (15) is a vector and is described in bold. U (t) of the input to the system represented by equations (8) and (9) is a scalar and is described in a font of thin body. Hereinafter, in order to distinguish between the present invention and the detailed description thereof, u (t) indicating a vector is hereinafter denoted as u → (t). The same is true for x (t) and y (t), and x (t) and y (t) representing vectors are denoted below as x → (t) and y → (t), respectively.

In the LPV systems represented by equations (14) to (18), a positive definite matrix X is assumed to exist for positive numbers a and ρ, and a linear matrix inequality represented by the following equation (19) is established. The linear Matrix inequality is also called lmi (linear Matrix inequality). The positive definite value matrix is also referred to as a positive definite matrix.

[ mathematical formula 13]

In formula (19), I represents an identity matrix.

When the LMI shown in the formula (19) is satisfied, the free response and the input-output response in the LPV systems shown in the formulas (14) to (18) satisfy the following formulas (20) and (21).

[ mathematical formula 14]

The notation shown in | · | | | represents a norm. The norm of a signal represents the magnitude of the signal. For example, | x (t) | represents the size of x (t). I | · | purple wind₂The symbol shown represents L₂And (4) norm. L is a radical of an alcohol₂The norm is calculated as the square root of the mean square value of the components included in the signal. L is₂The norm is one of the norms. Expressed as L in the formula (21)₂Is represented by the symbol L₂A space. In the formula (21), u → is L₂The basis of the space.

It can be found as a theorem that the equations (20) and (21) are satisfied when the equation (19) is satisfied. The theorems shown in equations (19) to (21) are also referred to as a first theorem.

The state-of-charge estimation device 1 according to the present embodiment estimates a state variable of a system and an output from the system. An error may occur between the estimated value and the actual value. The error occurring between the estimated value and the true value is also referred to as estimation error. External disturbances may be imposed in the input to the system. Due to external disturbances applied to the input, estimation errors of the state variables and the output may become large.

Assuming that external disturbance is applied to the input of the system and noise is included in the output of the system, the system is represented by the following equations (22) to (24).

[ mathematical formula 15]

y(t)＝C₁x(t)+D₁₁u(t)+D₁₂w(t) (23)

z(t)＝C₂x(t)+D₂₁u(t) (24)

Like the equations (14) and (15), x → (t), u → (t), and y → (t) represent state variables of the system, inputs to the system, and outputs from the system, respectively. z (t) is n of real number space_zAnd the order column vector represents the evaluation output of the system. The evaluation output of the system includes the data from the systemOf the outputs of the systems, an output to be evaluated is of particular interest. The evaluation may be performed on the external interference suppression performance or the quick response property or the like. Z (t), which will be referred to as vector, is denoted as z → (t). v (t) is n of real number space_vAn order column vector representing the external disturbance applied to the input to the system. w (t) is n of real number space_wThe order column vector represents the noise contained in the output from the system. W (t), which will be referred to as a vector, is denoted as w → (t). n is_zAnd n_wThe evaluation output and the magnitude of the external disturbance signal are set according to each other. A (θ (t)) is obtained by equations (16) to (18). Is represented as B₁、B₂、C₁、C₂、D₁₁、D₁₂And D₂₁The size of the coefficient matrix of (a) is set according to the state variable, the input, the output, the evaluation output, and the size of the signal of the external disturbance.

Equation (22) is a state equation representing the relationship between the input to the system to which the external disturbance is applied and the state variable representing the internal state of the system. Equation (23) is an output equation representing the state variables and the relationship between the inputs to the system and the outputs from the system. Equation (24) is an evaluation output equation representing the relationship between the state variable and the evaluation output of the system.

In equations (22) to (24), equations (25) to (27) can be derived by replacing the state variable, the output, and the evaluation output with the estimated values, respectively. The estimates of the state variables, outputs, and evaluation outputs are represented by the notation ^ above x, y, and z, respectively.

[ mathematical formula 16]

Hereinafter, terms labeled with a sign ^ above x → (t), y → (t), and z → (t) are also denoted by x → (t), y → (t), and z → (t).

The estimation errors of the state variables, the outputs, and the evaluation outputs are expressed by the following equations (28), (29), and (30), respectively. The estimation errors of the state variables, the outputs, and the evaluation outputs are represented by symbols → (t), y → (t), and z → (t) respectively.

[ mathematical formula 17]

Hereinafter, items marked with signs "→ (t) above x → (t), y → (t), and z → (t) are also denoted by x → (t), y → (t), and z → (t).

By applying equations (22) and (25) to the equation obtained by differentiating both sides of equation (28) at time (t), equation (31) below can be derived.

[ mathematical formula 18]

In equation (29), when a (θ (t)) is stable, the estimation error of the state variable can converge with the passage of time. In other words, whether the estimation error converges can be determined according to whether the system matrix is stable.

As an equation including the state variables, the outputs, and the estimated values of the evaluation outputs, the following equation (30) may be assumed instead of equation (25).

[ math figure 19]

L is an n × ny order matrix.

The third term on the right side of equation (32) represents the output estimation error fed back to the state equation. By applying equations (23) and (26) to item 3 on the right of equation (32), the following equation (33) can be derived.

[ mathematical formula 20]

By applying the equations (22), (32) and (33) to the equation obtained by differentiating both sides of the equation (28) at the time (t), the following equation (34) can be derived.

[ mathematical formula 21]

In the formula (34), L may be set in order to stabilize a (θ (t)) -LC. In other words, L that allows the estimation error to converge may be set regardless of whether the system matrix is stable.

The formula consisting of formulas (32), (26), and (27) is also referred to as an observer for the system. The observer is also referred to as a state estimator. The observer is a mechanism that estimates a state variable that cannot be directly observed based on input and output when at least a part of the state variable cannot be directly observed. An observer for a system representing a model is also referred to as a model-based observer. L of equation (32) is also referred to as observer gain. The setting or determination of L is also referred to as the design of the observer gain.

Each element of L indicating the observer gain may be a constant value or may be changed according to the magnitude of the current flowing through the battery 4. Each element of L may be changed not only according to the magnitude of the current flowing through the battery 4 but also according to other parameters such as a state variable of the battery 4. An observer, also called a gain scheduling observer, that optimizes control performance by changing the observer gain according to changes in the state of the battery 4.

As a parameter of the gain scheduling observer, an observer gain that is changed in accordance with a parameter of the battery 4 is also referred to as a variable observer gain. Like a (θ (t)) representing the system matrix, the variable observer gain as a function of θ (t) can be represented by a polytope. L (θ (t)) representing the variable observer gain can be shown as the following equation (35).

[ mathematical formula 22]

In order to make the estimation error at each time of estimating the state of the battery 4 smaller, the variable observer gain may be changed in accordance with the parameter of the battery 4. On the other hand, the observer gain may be designed to be constant so that the estimation error does not become extremely large even when the parameter of the battery 4 changes. When the observer gain is constant, the burden of designing the observer gain in the state of charge estimating device 1 can be reduced as compared with the case of designing the variable observer gain. When the observer gain is designed to be variable, the estimation error in the state of charge estimating device 1 can be further reduced as compared with the case where the observer gain is constant.

Where v (t) and w (t) are collectively expressed by η (t) as shown in the following formula (36).

[ mathematical formula 23]

n(t)＝[v(t) w(t)]^T (36)

Gerr, which represents a deviation system with η (t) as an input and z →to (t) as an output, is expressed by the following equations (37) and (38). Equation (37) represents the estimated error of the state variable, and is derived by subtracting both sides of equation (22) and equation (32) and applying equation (33). The formula (38) represents the estimation error of the evaluation output, and is derived by subtracting the two sides of the formula (24) and the formula (27).

[ mathematical formula 24]

Among these, in the formula (37), the following formulas (39) and (40) hold.

[ mathematical formula 25]

A_e(θ(t))＝A(θ(t))-L(θ(t))C₁ (39)

B_c(0(t))＝[B₂-L(0(t))D₁₂] (40)

The observer gain may be designed to have a degree of attenuation performance representing a speed of attenuation of an estimation error of a state variable existing in an initial state of the system or a performance of reducing an influence of an external disturbance on the estimation error of the evaluation output.

The external disturbances represented by η (t) include disturbances applied to the input to the system represented by v (t), and noise contained in the output from the system represented by w (t). The observer gain can be designed to simultaneously reduce the effects of disturbances applied to the system input and the effects of noise contained in the output from the system.

η (t) may be constructed by weighting v (t) and w (t) by weighting parameters, as shown in equation (41).

[ mathematical formula 26]

η(t)＝[v(t) λw(t)]^T (41)

λ denotes a weighting parameter. At λ < 1, the observer gain can be designed to easily reduce the effect of disturbances applied to the input to the system. At λ > 1, the observer gain can be designed to easily reduce the influence of noise contained in the output from the system.

The observer gain can be designed by various methods. For example, assume that there are positive definite value matrices X and Y for positive numbers a and ρ, and that LMI shown in the following equation (42) holds.

[ mathematical formula 27]

Assuming that when L (θ (t)) representing the observer gain is represented by a polytope shown in formula (35), the observer gain is designed based on the following formula (43).

[ mathematical formula 28]

L_i＝X^-1Y_i,i∈{1，…，L} (43)

When the LMI shown in the formula (42) is established and the observer gain is designed based on the formula (43), the free response to the deviation system shown in the formulas (37) to (40) satisfies the following formula (44).

[ mathematical formula 29]

The initial state of the system is a state of the system when time (t) is 0. x → (0) represent estimation errors of the state variables existing in the initial state of the system. The estimation error of the state variable existing in the initial state of the system is also referred to as an initial value error of the state estimation value. a represents the speed at which the initial value error of the state estimation value decays, also referred to as the degree of decay. b is a coefficient that can be determined appropriately. Equation (44) indicates that the magnitude of the estimated error of the state variable can be attenuated below a certain speed.

When the LMI shown in the formula (42) is established and the observer gain is designed based on the formula (43), the input/output response to the deviation system shown in the formulas (37) to (40) satisfies the following formula (45).

[ mathematical formula 30]

ρ is a coefficient that can be appropriately determined and indicates the degree of influence of external disturbance on the evaluation output. Equation (45) indicates that the evaluation output can be reduced below a certain ratio with respect to external disturbances and noise.

The theorem derived based on the first theorem can result in satisfying equations (44) and (45) when equation (42) holds and the observer gain is designed based on equation (43). The theorems expressed by expressions (42) to (45) are also referred to as a second theorem.

[ design of observer for Battery model ]

The state-of-charge estimation device 1 according to the present embodiment can attenuate an estimation error of a state variable of a system at a speed equal to or higher than a specific speed by appropriately designing an observer for the system. The state of charge estimation device 1 according to the present embodiment can reduce the influence of external disturbance on the estimation error of the evaluation output by appropriately designing the observer for the system.

The system corresponding to the model of the battery 4 can be expressed by equations (8) to (13). In the case where the hysteresis model is included in the model of the battery 4, an external disturbance caused by uncertainty of the parameters of the hysteresis model may be applied to the input to the system. For example, m and γ included in the formula (2) as parameters of the hysteresis model may have modeling errors with respect to the true values. It can be assumed that the nominal values of m and γ are parameters of the hysteresis model. The nominal values of m and γ are values assumed to be m and γ, respectively. When the nominal values are assumed as parameters of the hysteresis model, the following equations (46), (47) and (48) can be derived from equations (8) and (9) representing the system.

[ mathematical formula 31]

y(t)＝f_OCV(x_SOC(t))+c^Tx(t)+R₀u(t)+w(t) (47)

z(t)＝C_zx(t) (48)

V (t) of equation (46) represents external disturbances caused by uncertainty of the parameters of the hysteresis model. v (t) is represented by the following formula (49).

[ mathematical formula 32]

v(t)＝[Δmγ+Δγ{m-sgn(u(t))h(t)}]u(t) (49)

sgn (·) represents a sign function. The sign function is a function that outputs 1 in the case where the input value is a positive value, outputs-1 in the case where the input value is a negative value, and outputs 0 in the case where the input value is 0. Δ m represents the difference between the true value of m and the nominal value. Δ γ represents the difference between the true value and the nominal value of γ.

U (t), y (t), v (t), and w (t) in the equations (46) and (47) respectively represent scalars and are distinguished from u → (t), y → (t), v → (t), and w → (t).

F of the formula (46) is expressed by the following formula (50).

[ mathematical formula 33]

f＝[0 … 0 1]^T (50)

f is the (n +2) order column vector of the real space. When f is expressed by the formula (50), the component of v (t) expressing the external interference is applied to only h (t) among the components included in x (t) according to the formulas (13) and (46).

Cz of the formula (48) is expressed by the following formula (51).

[ mathematical formula 34]

C_zIs a 2 x (n +2) order matrix of the real number space.

In this case, the evaluation output is expressed by the following formula (52).

[ math figure 35]

z(t)＝[x_SOC(t) αh(t)]^T (52)

Since the evaluation output includes the SOC of the battery 4, the estimation accuracy of the SOC can be evaluated. Since the evaluation output includes the parameters of the hysteresis model, the influence of the uncertainty of the model of the hysteresis voltage can be evaluated. By multiplying α as a coefficient by a parameter of the hysteresis model, the estimation accuracy of SOC and the uncertainty of the model can be weighted and evaluated.

C_zThe formula (51) is not limited to the example, and may be a matrix including other elements. C_zOther state variables that can be set for the battery 4 are included in the evaluation output.

Equations (46) and (47) represent the system of the battery 4 in consideration of the errors of the parameters of the hysteresis model. For the systems shown in equations (46) and (47), an observer shown by the following equations (53), (54), and (55) may be constructed.

[ mathematical formula 36]

x → (t) and y ^ (t) respectively represent estimated values of x → (t) and y (t). The estimated value of SOC is represented by the label ^ above SOC. The term labeled above SOC with the label ^ is also denoted SOC ^. L (u (t)) is a (n +2) -order column vector of the real space, representing the observer gain.

Assuming that the estimation error of SOC is sufficiently small, fcv () is linearized, and the following equation (56) can be derived.

[ mathematical formula 37]

β is a positive number that can be determined appropriately.

From the equations (28), (30), (33) and (46) to (56), the following equations (57) and (58) can be derived which represent the deviation system with η (t) as input and z to (t) as output.

[ mathematical formula 38]

Among these, in the formula (57), the following formulas (59) and (60) hold.

[ math figure 39]

A_c(u(t))＝A(u(t))-L(u(t))c_l ^T (59)

B_c(u(t))＝[ -L(u(t))] (60)

c_lThis is expressed by the following formula (61).

[ mathematical formula 40]

c_l＝[β 1 … 1]^T (61)

c_lIs an (n +2) -order column vector of the real number space.

Deviation system (G) shown in equations (37) and (38)_err) Is the LPV system for which the system matrix depends on u (t).

At G_errBIBO (Bounded Input Bounded Output) is stable, and G is Bounded Input Bounded Output_errWhen the input/output gain of (2) is sufficiently small, the estimation error of SOC can be reduced regardless of the input of η (t). BIBO stabilization means that when the input to the system is finite, the output from the system is also finite.

BIBO stabilization, and G_errThe input-output gain of (1) is sufficiently small, and can be considered as a limit represented by the following equations (62) and (63).

[ math figure 41]

Equation (62) represents the estimation error of the state variable in the initial state of the system, G_errThe free response of (c) should satisfy the formula of the attenuation limit. a is a radical G_errIs a positive number of degrees of attenuation of the free response. b is a coefficient that can be determined appropriately. Equation (62) is an equation corresponding to equation (44).

Formula (63) is for G_errL of₂L that the gain should satisfy₂The formula of the gain limit. L is₂The gain limitation corresponds to interference suppression performance that prevents degradation of estimation accuracy due to the influence of external interference. G is to be_errL of₂Gain is defined as G_errL of the evaluation output signal₂Norm and G_errL of the input signal₂Upper bound of the ratio of norms. ρ is a given G_errL of₂A positive number of ranges of the upper bound of the gain. G_errL of₂The gain is a ratio of the magnitude of the evaluation output to an error of a parameter included in the model represented by the system.

In the present embodiment, the observer gain may be designed to satisfy both the constraints shown in equations (62) and (63). In other words, the observer gain may be set to satisfy a specific constraint condition. Specific limiting conditions include attenuation limit and L₂And (4) limiting the gain.

For example, a of the equation (62) may be set such that the estimation error of the SOC of the battery 4 converges within a certain time. In the case where the estimation error with a set to SOC converges within a certain time, ρ may be minimized to satisfy equation (63).

The magnitude of the charge-discharge current of the battery 4 is expressed as | u (t) |. In the case where the maximum value and the minimum value of | u (t) | are known, the system matrix of the system representing the model of the battery 4 can be represented by a manifold shown by the following equations (64) to (67).

[ mathematical formula 42]

A(u(t))＝θ₁(u(t))A(u_min)+θ₂(u(t))A(u_max) (64)

θ₁(u(t))+θ₂(u(t))＝1，θ₁，θ₂≥0 (67)

u_minIs the minimum value of | u (t) |. u. of_maxIs the maximum value of | u (t) |. Theta₁(u (t)) and θ₂(u (t)) is a parameter of polytope.

The system matrix constitutes at least a part of the parameters of the observer represented by equations (53) and (54). By representing the system matrix in a polytope, at least a portion of the parameters of the observer can be represented in a polytope.

Assume that a (u (t)) is expressed in a polytope, that a positive definite matrix X and a matrix Y exist for positive numbers a and ρ, and that LMI shown in the following formula (68) holds.

[ math figure 43]

In the formula (67), the following formula (69) holds.

[ math figure 44]

Ξ_i＝X(A_i+al)-Y_ic_l ^T，B′_ei＝[Xf-Y_i]，i∈{1，2} (69)

Wherein the variable observer gain is set as a function of u (t). In this case, L (u (t)) is expressed by a polycycle shape shown by the following formulas (70) and (65) to (67), similarly to a (u (t)) representing the system matrix.

[ mathematical formula 45]

L(u(t))＝θ₁(u(t))L₁+θ₂(u(t))L₂ (70)

According to the second theorem, G is designed by the following formula (71)_errWhile satisfying the observer gains of equations (62) and (63).

[ mathematical formula 46]

L_i＝X^-1Y_i，i∈{1，2} (71)

The positive definite value matrix X and matrix Y can be calculated such that LMI shown in equation (67) holds and ρ is minimized_i. Based on the positive definite value matrix X and matrix Y calculated in this way_iIt is possible to design a film having a smaller L as shown in the following equations (72) and (73)₂Observer gain of gain.

[ math figure 47]

The observer gain shown in equation (72) may vary according to u (t). That is, the observer gain shown in equation (72) is a variable observer gain. L of formula (73)_iMay be pre-calculated. That is, the state of charge estimating device 1 can change the observer gain using only the value of u (t).

In the battery model of the battery 4, G_errL of₂The gain is a ratio of the magnitude of the estimation error of the state of charge of the battery 4 to the influence of the error of the parameter included in the battery model. By designing to have a smaller L₂The observer gain of the gain can reduce an estimation error of the charging rate of the battery 4 corresponding to an error of a parameter included in the battery model. Designing the observer gain to have a smaller L₂The observer of the gain is also called a robust observer.

The state of charge estimating device 1 according to the present embodiment estimates the SOC of the battery 4 using an observer based on a model of the battery 4 including hysteresis characteristics. By using the observer, even when there is an error in the parameter of the model of the battery 4 due to the influence of the hysteresis characteristic or the like, the estimation accuracy of the SOC of the battery 4 can be improved. In addition, the calculation load of the state of charge estimation device 1 can be reduced compared to the case where the error of the parameter is reduced by successive estimation of the parameter of the battery model.

By setting the observer gain so as to reduce the estimation error of the SOC corresponding to the error of the parameter included in the model of the battery 4, the estimation accuracy of the SOC of the battery 4 can be improved.

By setting the observer gain to the variable observer gain in accordance with the magnitude of the current input to the battery 4, even when the state of the battery 4 changes, the estimation accuracy of the SOC of the battery 4 in each state can be improved. In other words, since the observer gain is a function indicating the magnitude u (t) of the current, SOC can be estimated using an observer optimized from the value of u (t). On the other hand, when the observer gain is constant, the SOC is estimated using the same observer regardless of the value of u (t). In this case, u (t) with higher estimation accuracy of SOC and u (t) with lower estimation accuracy of SOC coexist. That is, when the SOC is optimized over the entire range of values where u (t) can be taken, the SOC estimation accuracy may be locally lowered at a specific value of u (t). By using the variable observer gain, the estimation accuracy of SOC is difficult to decrease regardless of the value of u (t).

By setting the observation gain to satisfy a specific constraint condition, the estimation accuracy of the SOC of the battery 4 can be improved.

By expressing the system matrix, which is a part of the parameters included in the observer, in a polytope as in the equations (64) to (67), the observer gain can be easily calculated. In addition, even if the observer gain satisfies a specific LMI, the observer gain can be easily calculated.

Since the specific LMI that the observer gain satisfies includes the degree of attenuation a as a parameter, the influence of the error of the parameter on the estimated value of the SOC can be further reduced.

[ method of estimating charging Rate ]

The state of charge estimation device 1 according to the present embodiment can estimate the SOC of the battery 4 by the state of charge estimation method shown in fig. 8.

The control unit 10 acquires parameters of the battery model of the battery 4 (step S1). The control unit 10 may acquire parameters of the battery model from the storage unit 20 or an external device.

The control unit 10 acquires an input of a system indicated by a battery model of the battery 4 (step S2). The input to the system corresponds to the current input to the battery 4. The control section 10 may acquire an output of the system. The output of the system corresponds to the terminal voltage of the battery 4.

The control unit 10 designs an observer of the system for the battery 4 (step S3). The control section 10 may design an observer according to the current input to the battery 4. The control section 10 may design the observer from the parameters of the battery model, equations (70) and (71), and the like.

Control unit 10 estimates the SOC of battery 4 (step S4). The control portion 10 may estimate the SOC of the battery 4 from the acquired observer. This can improve the estimation accuracy of the SOC of the battery 4. The control unit 10 may return to step S2 to continue the process, or may end the process of the flowchart of fig. 8.

[ example of Charge Rate estimation result ]

The SOC of the battery 4 can be estimated by an observer including an observer gain designed according to the equations (70) and (71) and the like. Next, an example of the estimation result of the SOC will be described with reference to fig. 9, 10, and 11.

In order to estimate the SOC, a current that varies with time as shown in fig. 9 is input to a system represented by a battery model of the battery 4. Fig. 9 shows a time variation of the current when the battery 4 is mounted on an electric vehicle and a running test is performed, as an example of the time variation of the current.

The observer used in the SOC estimation of embodiment 1 includes a constant observer gain and is designed as G_errWhile satisfying equations (62) and (63). In other words, the observer used in the SOC estimation of embodiment 1 is an observer that takes into account both the attenuation degree limit and L₂The gain limit is designed. On the other hand, as the SOC estimation in the comparative example, the one including a constant was usedObserver gain and design as G_errThe observer satisfying the formula (62) estimates the SOC. L is not considered as an observer used in the estimation of SOC according to the comparative example₂The gain limit is designed only in consideration of the attenuation limit.

As shown in fig. 10, the SOC of the battery 4 is estimated using the observers designed in the example 1 and the comparative example, respectively. In fig. 10, the horizontal axis and the vertical axis represent time and SOC, respectively. The true value of the SOC is represented by the dashed line. The true value of the SOC is a value calculated by integrating the input current to the battery 4 or the like. The estimated value of SOC in example 1 is shown by a solid line. The estimated value of SOC in the comparative example is indicated by a dashed-dotted line. The estimated value of SOC in example 1 is closer to the true value of SOC than the estimated value of SOC in comparative example.

As shown in fig. 11, the estimation error of the SOC using the observer of embodiment 1 is smaller than the estimation error of the SOC using the observer of the comparative example. The estimation error of the SOC is a difference between the estimated value of the SOC and the true value of the SOC. In fig. 11, the horizontal axis and the vertical axis represent the time and the SOC estimation error, respectively.

RMSE (root mean Square Error) of the estimated Error of the SOC illustrated in fig. 11 is calculated. As a result, when Δ m indicating the uncertainty of the parameter of the hysteresis model is 0, the RMSE of the estimation error of the SOC using the observer according to embodiment 1 is smaller than the RMSE of the estimation error of the SOC using the observer according to the comparative example. That is, in comparison with the case where the observer is designed in consideration of only the attenuation degree limit, the attenuation degree limit and L are included by consideration₂By designing the observer under a specific constraint condition of gain limitation, the estimation accuracy of SOC can be improved.

The observer used in the SOC estimation of embodiment 2 includes a variable observer gain, which is designed as G_errWhile satisfying equations (62) and (63). Not only the RMSE of the estimation error of SOC when Δ m indicating the uncertainty of the parameters of the hysteresis model is 0, but also the RMSE of the estimation error of SOC when Δ m is larger than 0 or when Δ m is smaller than 0 can be calculated. Such asAs shown in fig. 12, the RMSE of examples 1 and 2 was smaller than that of the comparative example regardless of the value of Δ m. The RMSE of example 2 was as high as that of example 1 when the absolute value of Δ m was close to 0, and was lower than that of example 1 when the absolute value of Δ m was large. By making the observer gain variable, the estimation accuracy of SOC can be improved even when the state of the battery 4 changes, as compared with the case where the observer gain is constant.

As shown in fig. 12, when the absolute value of Δ m is large, RMSE of the SOC estimation error tends to increase. The observer gain can be designed to simultaneously reduce the influence of external disturbances applied to the input of the system, represented by v (t), and the influence of noise contained in the output from the system, represented by w (t). As shown in equation (41), by weighting v (t) and w (t) with the weighting parameters, a balance can be set between the magnitude of RMSE when Δ m is close to 0 and the magnitude of RMSE when the absolute value of Δ m is large. For example, the observer gain may be set so that the RMSE becomes smaller when the absolute value of Δ m is larger, instead of increasing the RMSE when Δ m approaches 0.

In the description of the present embodiment, the variable observer gain is a function representing u (t) which is an input to the system. u (t) may include the magnitude of the current flowing through the battery 4. The variable observer gain may also be a function of y (t) representing the output to the system. y (t) may include the terminal voltage of the battery 4.

Although the embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various changes or modifications based on the present disclosure. Therefore, it should be noted that these variations or modifications are included in the scope of the present disclosure. For example, functions and the like included in each component, each step, and the like may be rearranged in a logically inconstant manner, and a plurality of components, steps, and the like may be combined into one or divided.

(description of reference numerals)

1: a state of charge estimating device; 2: a current sensor; 3: a voltage sensor; 4: a battery; 5: a power supply device;

10: a control unit; 20: a storage unit; 201: a voltage source; 500: SOC-OCV characteristics;

501: a charging SOC-OCV characteristic; 502: discharge SOC-OCV characteristics

Claims

1. A method of setting an observer gain, which is a parameter of an observer for estimating a charging rate of a battery having a hysteresis characteristic, set for an input-output system representing a model of the battery, comprising:

the observer is configured to: a step of determining a relationship between a state variable of a charging rate of the battery included as an element and the observer gain, and reflecting a function representing an open-circuit voltage of the battery with the charging rate of the battery as a variable and the state variable on an output of the observer; and

a step of sequentially setting the observer gain so that the observer gain satisfies a constraint condition with respect to an estimation error of the state of charge corresponding to disturbance caused by uncertainty of a parameter related to the hysteresis characteristic included in the model, and sequentially setting the observer gain so that the observer gain is optimized in accordance with a magnitude of a current flowing through the battery, based on a weighting of an influence of disturbance applied to an input of a system and an influence of noise included in an output from the system, which are parameters of the model,

wherein the limitation condition includes an attenuation degree limitation that is a limitation satisfied by a free response of the system represented by the estimation error of the disturbance and the state of charge for an estimation error of the state variable in an initial state of the system, and a gain limitation for limiting a ratio of a magnitude of the evaluation output to an error of a parameter included in a model represented by the input-output system.

2. The method for setting the observer gain according to claim 1,

at least a part of the parameters contained in the observer gain are represented in a polytope,

the constraints are expressed in a prescribed linear matrix inequality.