JP6869697B2 - How to set the observer gain - Google Patents

Description

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

A device for estimating the charge rate of a battery having hysteresis in the relationship between the charge rate of the battery and the open circuit voltage is known (for example, Patent Document 1 and the like).

Japanese Unexamined Patent Publication No. 2016-90322

The charge rate of the battery can be estimated based on the battery model. In a battery having a hysteresis in the relationship between the battery charge rate and the open circuit voltage, the parameters representing the battery model are variable. Parameter errors due to changes in the parameters representing the battery model can reduce the accuracy of estimating the charge rate of the battery.

An object of the present invention made in view of such circumstances is to provide a charge rate estimation device and a charge rate estimation method capable of improving the estimation accuracy of the battery charge rate.

In order to solve the above problem, the charge rate estimation device according to the first aspect estimates the charge rate of the battery by using an observer based on the battery model. The model includes hysteresis characteristics. The observer includes an observer gain as a parameter. The observer gain is set to reduce the estimation error of the charge rate according to the modeling error of the parameter relating to the hysteresis characteristic included in the model.

In order to solve the above problems, the charge rate estimation method according to the second aspect includes a step of estimating the charge rate of the battery by using an observer based on the battery model. The model includes hysteresis characteristics. The observer includes an observer gain as a parameter. The charging rate estimation method further includes a step of setting the observer gain so as to reduce the charging rate estimation error according to the modeling error of the parameter relating to the hysteresis characteristic included in the model.

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

According to the charge rate estimation method according to the second aspect, the accuracy of estimating the charge rate of the battery can be improved.

It is a functional block diagram which shows the schematic configuration example of the charge rate estimation device. It is a figure which shows an example of the battery equivalent circuit. It is an nth-order RC ladder circuit ((A) Foster type (B) Cowell type). It is a figure which shows an example of the SOC-OCV characteristic. It is a figure which shows an example of the SOC-OCV characteristic which has hysteresis. It is a figure which shows the example of the battery equivalent circuit including the hysteresis voltage. It is a figure which shows the example of the battery equivalent circuit which replaced the Warburg impedance of FIG. 6 with a Foster type RC ladder circuit. It is a flowchart which shows an example of the charge rate estimation method. It is a graph which shows an example of the input current with respect to a battery equivalent circuit. It is a graph which shows an example of the estimation result of SOC of a battery. It is a graph which shows an example of the estimation error of SOC of a battery.

The charge rate estimation device according to the embodiment of the present disclosure may be mounted on a vehicle such as an electric vehicle or a hybrid electric vehicle. The charge rate estimation device may estimate the charge rate of the vehicle battery. The vehicle is equipped with an electric motor for driving the vehicle, a battery, a controller for these, and the like. The battery is discharged to supply electric power to the electric motor, regeneratively charged from the electric motor during braking, and charged from the ground charging facility. The charge rate estimation device may estimate the charge rate of the battery based on the charge / discharge current flowing through the battery and the terminal voltage of the battery.

[Functional block]
As shown in FIG. 1, the charge rate estimation device 1 is connected to the battery 4 via the current sensor 2 and the voltage sensor 3. The charge rate estimation device 1 may include a current sensor 2 or a voltage sensor 3. The charge rate estimation device 1 may be connected to the power supply device 5. The charge rate estimation device 1 may input a charge / discharge current from the power supply device 5 to the battery 4. The power supply device 5 may be, for example, a current source. The charge rate estimation device 1 may include a power supply device 5.

The current sensor 2 detects the charge / discharge current for the battery 4. In this embodiment, it is assumed that the charge / discharge current is represented by u (t), which is a function of time (t). The current sensor 2 outputs the detected charge / discharge current to the charge rate estimation device 1.

The voltage sensor 3 detects the terminal voltage of the battery 4. In this embodiment, it is assumed that the terminal voltage is represented by y (t), which is a function of time (t). The voltage sensor 3 outputs the detected terminal voltage to the charge rate estimation device 1.

The battery 4 may be, for example, a secondary battery. The secondary battery is also called a rechargeable battery. The battery 4 is assumed to be a lithium ion battery in this embodiment. The battery 4 may be another type of battery.

The charge rate estimation device 1 includes a control unit 10 and a storage unit 20. The control unit 10 controls each component of the charge rate estimation device 1. The control unit 10 may be composed of, for example, a processor, a microcomputer, or the like. The storage unit 20 may be composed of, for example, a semiconductor memory, a magnetic storage device, or the like. The control unit 10 may store the data or information handled by the charge rate estimation 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 may estimate the internal state of the battery 4 based on 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 that includes the open circuit voltage of the battery 4 and the overvoltage generated inside the battery 4 as parameters. The open circuit voltage is also referred to as OCV (Open Circuit Voltage). OCV is the potential difference between the electrodes in the electrochemical equilibrium state of the battery 4. The OCV corresponds to the terminal voltage of the battery 4 when the charge / discharge current does not flow through the battery 4. The overvoltage corresponds to the magnitude of the voltage drop caused by the internal impedance. The internal impedance is determined according to the reaction rate of the electrochemical reaction inside the battery 4.

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

The OCV of the battery 4 is represented by the voltage source 201 in the battery equivalent circuit. The voltage output by the voltage source 201 is represented by OCV (t), which is a function of time. OCV (t) corresponds to the terminal voltage of the battery 4 when the charge / discharge current does not flow through the battery 4. When the charge / discharge current does not flow through the battery 4, it can be said that u (t) = 0. When u (t) = 0, OCV (t) = y (t) holds.

In the battery equivalent circuit of FIG. 2, the internal impedance of the battery 4 is represented as a circuit in which a resistor represented by _{R 0} and _{a Warburg impedance represented by Z w (p) are connected in series.} The _{resistance represented by R 0} represents the resistance caused by the migration process or the like in the electrolytic solution of the battery 4. The Warburg impedance represents an impedance caused by an ion diffusion process or the like in the battery 4. The overvoltage of the battery 4 is expressed as a voltage drop generated by the internal impedance of the battery 4 due to the current flowing through the battery equivalent circuit.

Warburg impedance, for example 3 shown in (A), R ₁ ~R parallel circuit of the capacitor, shown as resistor and C ₁ -C _n, shown as _n is the n serially connected n-order Foster type circuit May be expressed as. The Warburg impedance is such that each of the n resistors shown as R _{1 to} R _{n is parallel to each of the n capacitors (C 1 to} C _n ) connected in series, as shown in FIG. 3 (B). It may be represented as an n-th order Cowell type circuit connected to. The Warburg impedance may be represented using other linear transfer function models.

The parameters of the battery equivalent circuit that approximates the battery 4 include the resistance value of the resistor constituting the Warburg impedance and the capacitance 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 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 charge rate and the overvoltage of the battery 4 as the internal state of the battery 4. The charge rate of the battery 4 is the ratio of the charge amount to the charge capacity of the battery 4. The charge rate is also called SOC (State Of Charge). It is assumed that the control unit 10 does not estimate the resistance value of the resistor constituting the internal impedance of the battery 4 and the capacity of the capacitor. The control unit 10 is not limited to a configuration in which the resistance value and capacitance included in the internal impedance are not estimated. The control unit 10 may be configured to estimate the resistance value and capacitance included in the internal impedance.

The control unit 10 may estimate the OCV and overvoltage of the battery 4. In this case, the control unit 10 can estimate the SOC of the battery 4 based on the OCV of the battery 4.

The OCV of battery 4 can be expressed as a function of SOC. The relationship between SOC and OCV is called the SOC-OCV characteristic. The SOC-OCV characteristics can be represented, for example, by the graph shown in FIG. The horizontal axis and the vertical axis of FIG. 4 indicate SOC and OCV, respectively. The SOC-OCV characteristics can be determined in advance by experiments or the like. The control unit 10 can estimate the OCV of the battery 4 based on the SOC-OCV characteristic of the battery 4 and the estimated value of the SOC of the battery 4.

[Hysteresis characteristics]
The SOC-OCV characteristic may have a hysteresis characteristic. The SOC-OCV characteristics having hysteresis characteristics differ between the characteristics at the time of charging and the characteristics at the time of discharging. The SOC-OCV characteristic having a hysteresis characteristic is shown, for example, as shown in FIG. The horizontal axis and the vertical axis of FIG. 5 indicate SOC and OCV, respectively. In FIG. 5, the charging SOC-OCV characteristic 501, which indicates the SOC-OCV characteristic when the battery 4 is charged, is indicated by a broken line. The discharge SOC-OCV characteristic 502, which indicates the SOC-OCV characteristic when the battery 4 is discharged, is indicated by a alternate long and short dash line.

The charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502 form a loop of SOC-OCV characteristics. The loop of the SOC-OCV characteristic formed by the charging SOC-OCV characteristic 501 and the discharging SOC-OCV characteristic 502 is also referred to as a major loop. The major loop can be obtained by charging / discharging experiments on the battery 4.

The battery 4 is not always charged after being discharged until the SOC reaches 0%. For example, the battery 4 can exhibit the SOC-OCV characteristics shown in the path from the point A to the point B by being charged after being discharged to the point A in FIG. The battery 4 is not always charged and then discharged until the SOC reaches 100%. For example, the battery 4 can exhibit the SOC-OCV characteristics shown in the path from the point C to the point D by being charged to the point C in FIG. 5 and then discharged. For example, a loop with SOC-OCV characteristics smaller than a major loop, which is indicated by a path connected in the order of points A, B, C, D, and A, is also called a minor loop. Minor loops, unlike major loops, can exist virtually infinitely. Minor loops are less likely to be obtained by prior experimentation than major loops.

The SOC-OCV characteristic 500 shown by the solid line in FIG. 5 corresponds to the 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.

ｆ_ＯＣＶ（・）は、ＳＯＣ−ＯＣＶ特性５００を表す関数である。 The difference in OCV between the SOC-OCV characteristic 500 and the major loop is also referred to as a hysteresis voltage. Hysteresis voltage is assumed to be expressed as h (t). The SOC-OCV characteristic having hysteresis can be represented by the following equation (1) including the hysteresis voltage instead of being represented by a minor loop that can exist virtually infinitely.

f _OCV (.) Is a function representing the SOC-OCV characteristic 500.

Since the SOC-OCV characteristics are expressed as in the equation (1), the control unit 10 also estimates h (t) when estimating the internal state of the battery 4, and thus between the SOC and the OCV. The accuracy of conversion of can be improved. When the SOC-OCV characteristic is expressed as in the equation (1), the battery equivalent circuit is expressed as in FIG. The battery equivalent circuit of FIG. 6 is the battery of FIG. 2 in that h (t) representing the hysteresis voltage is added and the output voltage of the voltage source 201 _{is represented by f OCV} (SOC (t)). Different from the equivalent circuit.

In this embodiment, it is assumed that the Warburg impedance is represented by the Foster type circuit shown in FIG. 3 (A). In this case, the battery equivalent circuit is represented as shown in FIG. The battery equivalent circuit of FIG. 7 differs from the battery equivalent circuit of FIG. 6 in _{that Z w (p) is replaced with a foster type circuit.} v _k (t) represents the voltage drop that occurs with the capacitance shown as _{C k.} k is an integer of 1 to n.

γは、ヒステリシスモデルの電圧降下の速さを表す。ｍは、ヒステリシス電圧の最大値を表す。Plettによるヒステリシスモデルについては、例えば、以下の文献が参照されうる。
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 According to the hysteresis model by Plett, which is one of the models representing the hysteresis phenomenon, the behavior of h (t) is expressed by the following equation (2).

γ represents the speed of voltage drop of the hysteresis model. m represents the maximum value of the hysteresis voltage. For the hysteresis model by Plett, for example, the following documents may be referred to.
GL 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

The SOC (t) of the battery 4 at the time (t) can be calculated by the following equation (3). t ₀ represents the measurement start time. The integral of the second term on the right side of the equation (3) represents the amount of electric charge entering and exiting the battery 4 calculated by integrating the charge / discharge currents.

η（ｔ）は、過電圧を表す。Ｇ_η（ｐ）は、内部インピーダンスを表し、Ｒ_０とＺ_ｗ（ｐ）との和である。 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.

η (t) represents an overvoltage. G _η (p) represents the internal impedance and is the sum of _{R 0} and Z _{w (p).}

ただし、

である。Ｒ_ｄは、拡散抵抗を表す。Ｃ_ｄは、拡散容量を表す。 When the Warburg impedance is a Foster type circuit, Z _w (p) is expressed by the following equation (5).

However,

Is. R _d represents the diffusion resistance. C _d represents the diffusion capacity.

The y (t) corresponding to the output of the battery equivalent circuit of FIG. 7 is represented by the following equation (7).

The battery model represented by the battery equivalent circuit of FIG. 7 is represented by an input / output system that takes charge / discharge current as an input and terminal voltage as an output. The input / output system is also simply called a system. The input / output system can be represented as a state space represented by the following equations (8) and (9).

The state space is a space represented by the state variables of the system as coordinate axes. Equation (8) is an equation of state that expresses the relationship between the input and the state variable. Equation (9) is an output equation that expresses the relationship between the state variable and the output.

Ａ（ｕ（ｔ））は、システム行列ともいう。システム行列は、システムの特性の少なくとも一部を表す。式（８）のシステム行列は、システムへの入力を示すｕ（ｔ）に依存する。よって、式（８）及び（９）で表されるシステムは、パラメータ可変システムであるともいえる。パラメータ可変システムは、ＰＶ（Parameter Varying）システムともいう。言い換えれば、図７のバッテリモデルで表されるバッテリ４のモデルは、ＰＶシステムによって表されうる。 A (u (t)) in the equation (8) is a matrix of the order (n + 2) × (n + 2) in real space, and is represented by the following equation (10). diag is a function that outputs a diagonal matrix.

A (u (t)) is also called a system matrix. The system matrix represents at least some of the characteristics of the system. The system matrix of equation (8) depends on u (t) indicating the input to the system. Therefore, it can be said that the system represented by the equations (8) and (9) is a parameter variable system. The parameter variable system is also called a PV (Parameter Varying) system. In other words, the model of battery 4 represented by the battery model of FIG. 7 can be represented by the PV system.

The b in the equation (8) and the c in the equation (9) represent the (n + 2) -order column vectors in real space, respectively, and are represented by the following equations (11) and (12). T represents the transposed matrix.

X (t) of the equations (8) and (9) is a state variable and is represented by the following equation (13).

[Estimating the internal state of the system]
The charge rate estimation device 1 according to the present embodiment can estimate the internal state of the battery 4 by estimating the state variable in the PV system representing the model of the battery 4. The control unit 10 inputs the charge / discharge current acquired from the current sensor 2 to the 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 sequentially estimates the SOC of the battery 4.

In this embodiment, it is assumed that the PV system representing the model of battery 4 is a linear parameter variable system. The linear parameter variable system is also referred to as an LPV (Linear Parameter Varying) system. The following description of the LPV system is not limited to the system representing the model of battery 4.

The LPV system can be represented as a state space represented by the following equations (14) to (18). As shown in equations (16) to (18), A as a system matrix can be expressed in polytope form. The polytope form is a form in which a function is represented by a linear combination. The linear combination is also called a linear combination.

Equation (14) is an equation of state that expresses the relationship between the input to the system and the state variables that represent the internal state of the system. Equation (15) is an output equation that expresses the relationship between the state variable and the output from the system. x (t) is a column vector of degree n in real space and represents a state variable. u (t) is an n _u The following column vector of real space, representing an input to the system. y (t) is n _y The following column vector of the real space, representing the output from the system. n, n _u and n _y are set according to the state, the size of the input and output signals, respectively. The size of the matrix represented as A (θ (t)), B and C is set according to the size of each signal.

The u (t) input to the system represented by the equations (14) and (15) is a vector and is shown in bold. The u (t) input to the system represented by the equations (8) and (9) is a scalar and is expressed in fine print. Hereinafter, in order to distinguish in the text of the detailed description of the invention, u (t) representing a vector is hereinafter referred to as u → (t). Similarly, for x (t) and y (t), x (t) and y (t) representing vectors are hereinafter referred to as x → (t) and y → (t), respectively.

式（１９）で、Ｉは単位行列を表す。 In the LPV system represented by equations (14) to (18), it is assumed that a positive-definite matrix X exists for the positive numbers a and ρ, and the linear matrix inequality represented by the following equation (19) holds. To do. The linear matrix inequality is also called LMI (Linear Matrix Inequality). A positive-definite matrix is also called a positive-definite matrix.

In equation (19), I represents the identity matrix.

||・||で示される記号は、ノルムを表す。信号のノルムは、信号の大きさを表す。例えば||ｘ（ｔ）||は、ｘ（ｔ）の大きさを表す。||・||_２で示される記号は、Ｌ_２ノルムを表す。Ｌ_２ノルムは、信号に含まれる成分を二乗平均した値の平方根として算出される。Ｌ_２ノルムは、ノルムの一種である。式（２１）でＬ_２と表される記号は、Ｌ_２空間を示す。式（２１）で、ｕ→は、Ｌ_２空間の元である。 When the LMI represented by the formula (19) holds, the free response and the input / output response in the LPV system represented by the formulas (14) to (18) satisfy the following formulas (20) and (21).

The symbols indicated by || and || represent norms. The norm of a signal represents the magnitude of the signal. For example, || x (t) || represents the magnitude of x (t). Symbol represented by || · || ₂ represents the _{L 2} norm. L ₂ norm is calculated components contained in the signal as the square root of the mean square value. L ₂ norm, is a kind of the norm. The symbol represented by _{L 2 in the} equation (21) _{indicates the L 2} space. In the formula (21), u → is the original _{L 2} space.

It is given as a theorem that equations (20) and (21) are satisfied when equation (19) holds. The theorems represented by equations (19) to (21) are also referred to as the first theorem.

The charge rate estimation device 1 according to the present embodiment estimates the state variables of the system and the output from the system. There can be an error between the estimated value and the true value. The error that occurs between the estimated value and the true value is also called the estimated error. Disturbances can be added to the system inputs. Disturbances applied to the input can increase the estimation error of state variables and outputs.

When a disturbance is applied to the input of the system, it is assumed that the system is represented by the following equations (22) to (24).

x → (t), u → (t) and y → (t) represent system state variables, inputs to the system and outputs from the system, respectively, as in equations (14) and (15). z (t) is an _nz-th order column vector in real space and represents the evaluation output of the system. The evaluation output of the system includes the output from the system to be evaluated with particular attention. The evaluation may be performed on disturbance suppression performance, responsiveness, and the like. Z (t) representing a vector is hereinafter expressed as z → (t). w (t) is an n _w The following column vector of real space, representing the disturbance applied to the input to the system. W (t) representing a vector is hereinafter expressed as w → (t). n _z and n _w are set according to the size of the evaluation output and the disturbance signal, respectively. A (θ (t)) is given by the equations (16) to (18). The size of the coefficient matrix represented as B ₁ , B ₂ , C ₁ , C ₂ and D is set according to the size of the state variables, inputs, outputs, evaluation outputs and disturbance signals.

Equation (22) is an equation of state that expresses the relationship between the input to the system to which the disturbance is applied and the state variable that represents the internal state of the system. Equation (23) is an output equation that expresses the relationship between the state variables and the input to the system and the output from the system. Equation (24) is an evaluation output equation expressing the relationship between the state variable and the evaluation output of the system.

以下、ｘ→（ｔ）、ｙ→（ｔ）及びｚ→（ｔ）の上に記号＾を付した項は、ｘ→＾（ｔ）、ｙ→＾（ｔ）及びｚ→＾（ｔ）とも表す。 In equations (22) to (24), equations (25) to (27) are derived by replacing the state variables, outputs, and evaluation outputs with estimated values, respectively. Estimates of state variables, outputs, and evaluation outputs are represented by the symbols ^ above x, y, and z, respectively.

Hereinafter, the terms with the symbol ^ on x → (t), y → (t) and z → (t) are x → ^ (t), y → ^ (t) and z → ^ (t). Also expressed as.

以下、ｘ→（ｔ）の上に記号~を付した項は、ｘ→~（ｔ）とも表す。 The estimation error of the state variable is expressed by the following equation (28). The estimation error of the state variable is represented by adding the symbol ~ on x → (t).

Hereinafter, the term in which the symbol ~ is added above x → (t) is also referred to as x → ~ (t).

By applying the equations (22) and (25) to the equation obtained by differentiating both sides of the equation (28) at the time (t), the following equation (29) is derived.

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, depending on whether the system matrix is stable, it can be determined whether the estimation error converges.

As an equation containing estimates of state variables, outputs and evaluation outputs, the following equation (30) can be assumed instead of equation (25).

The third term on the right side of equation (30) indicates that the estimation error of the output is fed back to the equation of state. By applying the equations (23) and (26) to the third term on the right side of the equation (30), the following equation (31) is derived.

By applying the equations (22), (30) and (31) to the equation obtained by differentiating both sides of the equation (28) at the time (t), the following equation (32) is derived.

In equation (32), L can be set so that A (θ (t)) -LC is stable. In other words, L can be set such that the estimation error converges regardless of whether the system matrix is stable or not.

The formula composed of the formulas (30), (26) and (27) is also referred to as an observer for the system. The observer is also called a state estimator. An observer is a mechanism that estimates a state variable that cannot be directly observed based on inputs and outputs when at least a part of the state variable cannot be observed directly. An observer for a system that represents a model is also called a model-based observer. L in the formula (30) is also referred to as an observer gain. Setting or determining L is also referred to as observer gain design.

Based on equations (22) to (24) and equations (30), (26) and (27), the estimation errors of state variables, outputs and evaluation outputs are the following equations (33) to (35), respectively. It is represented by. The estimation error of the output and the evaluation output is represented by adding a symbol ~ above y and z, respectively. Hereinafter, the terms in which the symbol ~ is added above y and z are also referred to as y ~ and z ~.

The relationship between the estimation error of the state variable, the output, and the evaluation output shown in the equations (33) to (35) is also referred to as a deviation system. The observer gain may be designed to have an attenuation performance that indicates the rate of attenuation of the estimation error of the state variables that exist in the initial state of the system, or a performance that reduces the influence of disturbance on the estimation error of the evaluation output.

Observer gains can be designed in a variety of ways. For example, it is assumed that a positive-definite matrix X and a matrix Y exist for the positive numbers a and ρ, and the LMI represented by the following equation (36) holds.

It is assumed that the observer gain is designed based on the following equation (37).

システムの初期状態は、時刻（ｔ）が０である場合のシステムの状態である。ｘ→~（０）は、システムの初期状態で存在する状態変数の推定誤差を表す。システムの初期状態で存在する状態変数の推定誤差は、状態推定値の初期値誤差ともいう。ａは、状態推定値の初期値誤差が減衰する速度を表し、減衰度ともいう。ｂは、適宜定められうる係数である。式（３８）は、状態変数の推定誤差の大きさが所定の速度以下で減衰しうることを示す。 When the LMI represented by the formula (36) holds and the observer gain is designed based on the formula (37), the free response to the deviation system represented by the formulas (33) to (35) is the following formula. (38) is satisfied.

The initial state of the system is the state of the system when the time (t) is 0. x → ~ (0) represents the estimation error of the state variable 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 called the initial value error of the state estimation value. a represents the speed at which the initial value error of the state estimated value is attenuated, and is also referred to as the degree of attenuation. b is a coefficient that can be appropriately determined. Equation (38) indicates that the magnitude of the estimation error of the state variable can be attenuated below a predetermined velocity.

ρは、適宜定められうる係数であり、評価出力が外乱から受ける影響の度合いを示す。式（３９）は、評価出力が外乱に対して所定の比率未満に低減されうることを示す。 When the LMI represented by the equation (36) holds and the observer gain is designed based on the equation (37), the input / output response to the deviation system represented by the equations (33) to (35) is as follows. Equation (39) is satisfied.

ρ is a coefficient that can be appropriately determined, and indicates the degree of influence of the evaluation output on the disturbance. Equation (39) indicates that the evaluation output can be reduced to less than a predetermined ratio to the disturbance.

The fact that equations (38) and (39) are satisfied when equation (36) holds and the observer gain is designed based on equation (37) is given as a theorem derived based on the first theorem. Be done. The theorems represented by equations (36) to (39) are also referred to as the second theorem.

[Observer design for battery model]
The charge rate estimation device 1 according to the present embodiment can attenuate the estimation error of the state variable of the system at a predetermined speed or higher by appropriately designing an observer for the system. The charge rate estimation device 1 according to the present embodiment can reduce the influence of disturbance on the estimation error of the evaluation output by appropriately designing the observer for the system.

The system corresponding to the model of battery 4 can be represented by equations (8)-(13). If the model of the battery 4 includes a hysteresis model, disturbances due to the uncertainty of the parameters of the hysteresis model can be added to the input to the system. For example, m and γ included as parameters of the hysteresis model in the equation (2) may have a modeling error with respect to the true value. It may be assumed that the nominal values of m and γ are parameters of the hysteresis model. The nominal values of m and γ are the values assumed as m and γ, respectively. When the nominal value is assumed as a parameter of the hysteresis model, the following equations (40) and (41) are derived by modifying the equations (8) and (9) representing the system. Equation (41) is the same as equation (9).

ｓｇｎ（・）は、符号関数を表す。符号関数は、入力値が正の値である場合に１を出力し、入力値が負の値である場合に−１を出力し、入力値が０である場合に０を出力する関数である。Δｍは、ｍの真値とノミナル値との差を表す。Δγは、γの真値とノミナル値との差を表す。 W (t) in equation (40) represents the disturbance caused by the uncertainty of the parameters of the hysteresis model. w (t) is represented by the following equation (42).

sgn (・) represents a sign function. The sign function is a function that outputs 1 when the input value is a positive value, outputs -1 when the input value is a negative value, and outputs 0 when the input value is 0. .. Δm represents the difference between the true value and the nominal value of m. Δγ represents the difference between the true value and the nominal value of γ.

U (t), y (t) and w (t) contained in the formulas (40) and (41) represent scalars, respectively, as u → (t), y → (t) and w → (t). Distinguished.

ｆが式（４３）で表される場合、式（１３）及び（４０）によれば、外乱を表すｗ（ｔ）の成分は、ｘ（ｔ）に含まれる成分のうちｈ（ｔ）にのみ加わる。 F in the formula (40) is represented by the following formula (43).

When f is represented by the formula (43), according to the formulas (13) and (40), the component of w (t) representing the disturbance is changed to h (t) among the components contained in x (t). Only join.

ｘ→＾（ｔ）及びｙ＾（ｔ）はそれぞれ、ｘ→（ｔ）及びｙ（ｔ）の推定値を表す。ＳＯＣの推定値は、ＳＯＣの上に記号＾を付して表される。ＳＯＣの上に記号＾を付した項は、ＳＯＣ＾とも表す。Ｌは、実数空間の（ｎ＋２）次の列ベクトルであり、オブザーバゲインを表す。 Equations (40) and (41) represent the system of battery 4 taking into account the error of the parameters of the hysteresis model. For the system represented by the formulas (40) and (41), the observer represented by the following formulas (44) and (45) can be configured.

x → ^ (t) and y ^ (t) represent estimates of x → (t) and y (t), respectively. The estimated value of SOC is represented by adding a symbol ^ on top of SOC. A term with the symbol ^ above the SOC is also referred to as SOC ^. L is a (n + 2) -order column vector in real space and represents an observer gain.

αは、適宜定められうる定数である。 Assuming that the SOC estimation error is sufficiently small, the following equation (46) is derived by linearizing _{f OCV (.).}

α is a constant that can be appropriately determined.

It is assumed that the estimation error of the state variable is expressed by the following equation (47).

ｃ_ｌは、以下の式（４９）で表される。

Based on the equations (40) to (47), the following equation (48) is derived.

c _l is expressed by the following equation (49).

ｃ_ｚは、以下の式（５１）で表される。

ｃ_ｚは、状態変数の推定誤差を評価出力に反映させる際に、状態変数の推定誤差に含まれる成分に重み付けを与える。 The following equation (50) is introduced as an evaluation output equation that determines the evaluation output of the system.

_cz is represented by the following equation (51).

c _z, when reflecting the estimation error of the state variable to the evaluation output, giving a weighting to components included in the estimated error of the state variable.

According to the equations (50) and (51), only the SOC component of the state variables is reflected in the evaluation output. In other words, the evaluation output is calculated as an estimation error of SOC. Therefore, z (t) is represented by the following equation (52).

Equations (48) and (50) represent a system in which the input is w (t) and the output is z (t). Hereinafter, the system represented by the formulas (48) and (50) is represented by G (L). G (L) is an LPV system in which the system matrix depends on u (t).

When G (L) is BIBO (Bounded Input Bounded Output) stable and the input / output gain of G (L) is sufficiently small, the SOC estimation error can be reduced regardless of the input of w (t). .. BIBO stability means that if the input to the system is finite, then the output from the system is finite.

The stability of BIBO and the sufficiently small input / output gain of G (L) can be regarded as the constraints represented by the following equations (53) and (54).

Equation (53) is an equation showing the attenuation constraint that the free response of G (L) should satisfy with respect to the estimation error of the state variable in the initial state of the system. a is a positive number indicating the degree of attenuation of the free response of G (L). b is a coefficient that can be appropriately determined. Equation (53) is an equation corresponding to equation (38).

Equation (54) is an equation showing the _{L 2 gain constraint that the L 2} gain of G (L) should satisfy. _{L 2} gain G (L) is defined as the upper bound of the ratio of the _{L 2} norm of the input signal G evaluation output signal of the (L) of _{L 2} norm and G (L). ρ is a positive number that specifies the upper bound range _{of the L 2} gain of G (L). _{The L 2} gain of G (L) means the ratio of the magnitude of the evaluation output to the error of the parameters included in the model represented by the system.

In this embodiment, the observer gain can be designed so that the two constraints represented by the equations (53) and (54) are satisfied at the same time. In other words, the observer gain can be set to satisfy certain constraints. Predetermined constraint involves the attenuation of constraints and L ₂ gain-constrained.

For example, a in equation (53) may be set so that the estimation error of the SOC of the battery 4 converges within a predetermined time. If a is set so that the SOC estimation error converges within a predetermined time, then ρ may be minimized so that equation (54) is further satisfied.

ｕ_ｍｉｎは、｜ｕ（ｔ）｜の最小値である。ｕ_ｍａｘは、｜ｕ（ｔ）｜の最大値である。θ_１（ｕ（ｔ））及びθ_２（ｕ（ｔ））は、ポリトープ形式のパラメータである。 The magnitude of the charge / discharge current of the battery 4 is represented by | u (t) |. When the maximum and minimum values of | u (t) | are known, the system matrix of the system representing the model of the battery 4 can be expressed in the polytope form represented by the following equations (55) to (58).

u _min is the minimum value of | u (t) |. u _max is the maximum value of | u (t) |. θ ₁ (u (t)) and θ ₂ (u (t)) are polytope-type parameters.

The system matrix constitutes at least a part of the parameters of the observer represented by the equations (44) and (45). By representing the system matrix in polytope format, at least some of the observer's parameters are represented in polytope format.

式（５９）及び式（６０）において、以下の式（６１）が成り立つ。

A (u (t)) is expressed in the polytope form, and there are positive-definite matrix X and matrix Y for the positive numbers a and ρ, which are represented by the following equations (59) and (60). It is assumed that LMI holds.

In the formula (59) and the formula (60), the following formula (61) holds.

According to the second theorem, an observer gain such that G (L) satisfies equations (53) and (54) at the same time is designed by the following equation (62).

The positive-definite matrix X and the matrix Y can be calculated so that the LMI represented by the equations (59) and (60) holds and ρ is minimized. Based on the positive-definite matrix X and the matrix Y calculated in this way, _{an observer gain having a smaller L 2} gain can be designed. In the battery model of the battery 4, the L ₂ gain of G (L) is the ratio of the magnitude of the estimation error of the charge rate of the battery 4 to the error of the parameters included in the battery model. By designing an observer gain with a smaller L ₂ gain, the error in estimating the charge rate of the battery 4 depending on the error of the parameters included in the battery model can be reduced. Observer observer gain is designed to have a smaller L ₂ gain, also referred to as robust observer.

The charge rate estimation device 1 according to the present embodiment estimates the SOC of the battery 4 by using an observer based on the model of the battery 4 including the hysteresis characteristic. By using the observer, the SOC estimation accuracy of the battery 4 can be improved even if there is an error in the parameters of the model of the battery 4 due to the influence of the hysteresis characteristic or the like. Further, the calculation load of the charge rate estimation device 1 can be reduced as compared with the case where the parameter error is reduced by the sequential estimation of the parameters of the battery model.

By setting the observer gain to reduce the SOC estimation error according to the error of the parameters included in the battery 4 model, the SOC estimation accuracy of the battery 4 can be improved.

By setting the observer gain so as to satisfy a predetermined constraint condition, the SOC estimation accuracy of the battery 4 can be improved.

Since the system matrix, which is a part of the parameters included in the observer, is expressed in the polytope format as in equations (55)-(58), the observer gain can be easily calculated. Further, even if the observer gain satisfies a predetermined LMI, the calculation of the observer gain can be facilitated.

By including the degree of attenuation a as a parameter in the predetermined LMI satisfied by the observer gain, the influence of the error of the parameter on the estimated value of SOC can be further reduced.

[Charge rate estimation method]
The charge rate estimation device 1 according to the present embodiment may estimate the SOC of the battery 4 by the charge rate estimation method shown in FIG.

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

The control unit 10 acquires an observer for the system represented by the battery model of the battery 4 (step S2). The control unit 10 may design the observer based on the parameters of the battery model, the equation (62), and the like. The control unit 10 may acquire a pre-designed observer from the storage unit 20 or an external device.

The control unit 10 estimates the SOC of the battery 4 (step S3). The control unit 10 can estimate the SOC of the battery 4 based on the acquired observer. By doing so, the estimation accuracy of the SOC of the battery 4 can be improved.

[Example of charge rate estimation result]
The SOC of the battery 4 can be estimated by an observer including an observer gain designed based on the equation (62) and the like. Hereinafter, FIGS. 9, 10 and 11 will be referred to in the description of an example of the SOC estimation result.

To estimate the SOC, a time-varying current was input to the system represented by the battery model of battery 4 as shown in FIG. FIG. 9 shows, as an example of the time variation of the current, the time variation of the current when the battery 4 is mounted on the electric vehicle and the running experiment is performed.

The observer used in the SOC estimation of this example was designed so that G (L) satisfies equations (53) and (54) at the same time. In other words, the observer used in SOC estimation of this example was designed and attenuation constraints and L ₂ gain-constrained together in consideration. On the other hand, as an SOC estimation according to a comparative example, an SOC estimation using an observer designed so that G (L) satisfies the equation (53) was performed. Observer used in SOC estimation according to the comparative example, without considering the L ₂ gain-constrained, which is designed in consideration of only the attenuation restrictions.

As shown in FIG. 10, the SOC of the battery 4 was estimated using the observers designed in each of the examples and the comparative examples. In FIG. 10, the horizontal axis and the vertical axis indicate the time and SOC, respectively. The true value of SOC is indicated by a broken line. The true value of SOC is a value calculated by a method such as integrating the input current to the battery 4. The SOC estimates for the examples are shown by solid lines. The estimated value of SOC according to the comparative example is indicated by the alternate long and short dash line. The estimated value of SOC according to the examples is closer to the true value of SOC as compared with the estimated value of SOC according to the comparative example.

As shown in FIG. 11, the SOC estimation error using the observer of the example is smaller than the SOC estimation error using the observer of the comparative example. The SOC estimation error is the difference between the SOC estimated value and the SOC true value. In FIG. 11, the horizontal axis and the vertical axis indicate the time and SOC estimation errors, respectively.

As a result of calculating the RMSE (Root Mean Square Error) of the SOC estimation error exemplified in FIG. 11, the RMSE of the SOC estimation error using the observer according to the comparative example was 4.5%. On the other hand, the RMSE of the SOC estimation error using the observer according to the example was 1.9%. As compared with the case where the observer is designed in consideration of only the attenuation constrained by the observer is designed in consideration of the predetermined constraints including attenuation constraints and L ₂ gain-constrained, the estimation accuracy of the SOC Can be improved.

Although the embodiments according to 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 modifications or modifications based on the present disclosure. It should be noted, therefore, that these modifications or modifications are within the scope of this disclosure. For example, the functions included in each component and each step can be rearranged so as not to be logically inconsistent, and a plurality of components and steps can be combined or divided into one. Is.

1 Charge rate estimation device 2 Current sensor 3 Voltage sensor 4 Battery 5 Power supply device 10 Control unit 20 Storage unit 201 Voltage source 500 SOC-OCV characteristics 501 Charge SOC-OCV characteristics 502 Discharge SOC-OCV characteristics

Claims (2)

A method of setting an observer gain, which is an observer parameter set for an input / output system representing a model of a battery having a hysteresis characteristic and used for estimating the charge rate of the battery.
The observer specifies the relationship between the observer gain and the state variable including the charge rate of the battery as an element, and the function representing the open circuit voltage of the battery and the state variable with the charge rate of the battery as an argument. And the step of configuring to reflect the above in the output of the observer,
The step of setting the observer gain so as to satisfy the constraint condition for the estimation error of the charge rate according to the disturbance caused by the uncertainty of the parameter related to the hysteresis characteristic included in the model.
Including
The constraint condition is represented by the attenuation constraint satisfied by the free response of the system represented by the disturbance and the estimation error of the charge rate with respect to the estimation error of the state variable in the initial state of the system, and the input / output system. How to set the observer gain, including a gain constraint that constrains the ratio of the magnitude of the evaluation output to the error of the parameters contained in the model. In the method of setting the observer gain according to claim 1 , at least a part of the parameters included in the observer is expressed in a polytope format.
Before SL constraint condition is represented by the predetermined linear matrix inequality, setting the observer gain.

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