JP5847685B2 - Parameter identification apparatus and identification method for continuous time system - Google Patents

Description

  The present invention relates to a parameter identification apparatus and identification method for a continuous time system.

As a conventional parameter identification method for a continuous time system, the one described in Patent Document 1 is known.
In this conventional continuous-time system parameter identification method, a continuous-time input signal is applied to a continuous-time system that can be expressed by a differential equation, and the continuous-time output signal of the system is detected. A state space realized stability that can have a state variable that matches the sample value of the state variable of a stable analog filter realized in the state space, using the sample values to identify parameters on the differential equation of this system Each sampled value signal of the input signal and output signal is input to a group of digital filters, and identification signals corresponding to system parameters are generated from the state variables of each digital filter. System parameters are identified.

JP-A-9-81204

However, the conventional continuous time system identification apparatus and identification method have the following problems.
That is, the relationship between the continuous-time input signal u (t), the continuous-time output signal, and y (t) is described by the following nth-order differential equation, and the parameters (ai, bi) are defined as a single-input single-output system with unknown parameters. ing.
(S _n + a _n-1 s ^n-1 + ... + a ₀ ) y (t) = (b _n sn + b _n-1 s ^n-1 + ... b ₀ ) u (t)
Note that i = 0 to n and s is a Laplace operator.
When this is rewritten, the following equation is obtained.
y (t) = [N (p, θ) / D (p, θ)] × u (t)
Here, θ is an unknown parameter vector and is represented by (ai, bi). P is a differential operator.

  In the parameter identification method of the conventional continuous time system described above, N and D are assumed to be linear with respect to the parameter θ, and the parameters are identified using the differential equation. For a nonlinear model such as an equivalent circuit model of a secondary battery, there is a problem that the parameter cannot be estimated by applying the above-described conventional projection type continuous time system identification method.

  The present invention has been made paying attention to the above problem, and the object of the present invention is to be able to estimate parameters by applying the projection type continuous-time system identification method even to a nonlinear model. It is an object of the present invention to provide a parameter identification apparatus and identification method for a continuous time system.

For this purpose, the parameter identification device of a continuous time system according to the invention as claimed in claim 1 comprises:
An equivalent model representing the target system with multiple parameters,
An input detection unit for detecting an input value to the target system;
An output detector that detects an output value of the target system when an input value is input in a predetermined time range; and
An output prediction unit that calculates a predicted value of an output value based on a parameter and an equivalent model in a predetermined time range;
An error calculator that calculates an error between the output value detected by the output detector and the predicted value calculated by the output predictor;
Based on the sensitivity function for the parameters of the equivalent model (defined by the partial derivative of ∂y ^ (t, θ) / ∂θj, y ^ is the estimated output, t is the time, and θ is the parameter vector) A parameter update unit that updates parameters so that the error calculated by the calculation unit is reduced;
With
Each calculation calculation in the output prediction unit, error calculation unit, and parameter update unit is repeated until the error is minimized, and the parameter is identified by the parameter when the error is minimum.
It is characterized by that.

Moreover, the parameter identification device of the continuous time system of the invention according to claim 2 is:
The parameter identification device of the continuous time system of claim 1,
The target system is a secondary battery,
The equivalent model is a battery model,
The input detection unit is a current sensor that detects the charge / discharge current of the secondary battery,
The output detector is a voltage sensor that detects the terminal voltage of the secondary battery,
The parameters are the charging rate of the secondary battery, the soundness, the offset current of the current sensor, the diffusion resistance in the battery model, the resistance of the electrolyte in the battery model, the time constant of the diffusion process in the battery model. Including at least one of them,
It is characterized by that.

Moreover, the parameter identification method of the continuous time system of the invention described in claim 3 is:
Detect the input value to the target system,
Detecting an output value of the target system when the input value is input in a predetermined time range;
Calculate the predicted value of the output value based on the parameters and equivalent model used in the equivalent model of the target system in the predetermined time range,
Calculate the error between the detected output value and the calculated predicted value,
Based on the sensitivity function for the parameters of the equivalent model (defined by the partial derivative of ∂y ^ (t, θ) / ∂θj, y ^ is the estimated output, t is the time, and θ is the parameter vector) Update the parameters so that
The calculation of the predicted value of the output value, the calculation of the error, and the update of the parameter were repeated until the error was minimized, and the parameter was identified by the parameter when this error was the minimum.
It is characterized by that.

Moreover, the parameter identification method of the continuous-time system of the invention described in claim 4 is:
The method for identifying parameters of a continuous time system according to claim 3,
The target system is a secondary battery,
The equivalent model is a battery model,
The input value detection unit is a current sensor that detects the charge / discharge current of the secondary battery,
The output value detector is a voltage sensor that detects the terminal voltage of the secondary battery,
The parameters are the charging rate of the secondary battery, the soundness, the offset current of the current sensor, the diffusion resistance in the battery model, the resistance of the electrolyte in the battery model, the time constant of the diffusion process in the battery model. Including at least one of them,
It is characterized by that.

  In the continuous time system identification device according to the first aspect of the present invention, the parameter can be estimated by applying the projection type continuous time system identification method to a nonlinear model such as a battery.

  Further, in the continuous time system identification device according to the present invention, the charging rate of the battery, the soundness, the offset current of the current sensor, the diffusion resistance in the battery model, the electrolysis in the battery model At least one of the resistance of the liquid and the time constant of the diffusion process in the battery model can be estimated.

  In the continuous-time system identification method according to the third aspect of the present invention, the parameter can be estimated by applying the projection-type continuous-time system identification method to a nonlinear model such as a battery. it can.

  According to the continuous time system identification method of the present invention described in claim 4, the charging rate of the battery, soundness, offset current of the current sensor, diffusion resistance in the equivalent model, electrolyte solution in the equivalent model At least one of the resistance and the time constant of the diffusion process of the equivalent model can be estimated.

It is a block diagram which shows the structure of the continuous-time system identification apparatus of Example 1 of this invention. It is a signal diagram for demonstrating the stability analysis of the algorithm of the identification method performed with the continuous-time system identification apparatus of Example 1 by closed loop expression. It is a characteristic view which shows the relationship between SOC and OCV of the secondary battery as a target system of the continuous time system identification apparatus of Example 1. It is a figure which shows the equivalent circuit of the secondary battery as an object system. It is a figure which shows the flowchart for the parameter identification performed with the continuous-time system identification apparatus of Example 1. FIG. It is a figure which shows the input used for the simulation of the continuous-time system identification apparatus of Example 1, and its output. It is a figure which shows the table | surface which put together the estimated value of the parameter in the said simulation. It is the figure which showed the comparison result of the measured value and estimated value of the output in the said simulation. It is the figure which showed the comparison result of SOC by the Coulomb count method in the said simulation, and SOC by Example 1. FIG. It is the figure which showed the mode at the time of the repeated update of the parameter estimated value in Example 1 0 times. It is the figure which showed the mode at the time of the repeated update of the parameter estimated value in Example 1 3 times. It is the figure which showed the mode at the time of the repetitive update of the parameter estimated value in Example 1 6 times. It is the figure which showed the mode at the time of nine repetitive updates of the parameter estimated value in Example 1. FIG. It is the figure which showed the mode at the time of the repeated update of the parameter estimated value in Example 1 15 times.

  Hereinafter, embodiments of the present invention will be described in detail based on examples shown in the drawings.

First, the overall configuration of the identification device of the continuous time system according to the first embodiment will be described.
As shown in FIG. 1, the continuous-time system identification apparatus and identification method according to the first embodiment are connected to a secondary battery 1 that is a target system, for example, and a current sensor 2 that detects this charge / discharge current, A voltage sensor 3 for detecting a terminal voltage of the battery 1 when input and a microcomputer 4 are provided.
The current sensor 2 corresponds to the input detection unit of the present invention, and the voltage sensor 3 corresponds to the output detection unit of the present invention.

The microcomputer 4 includes an equivalent model (battery model) 5 of the battery 1 expressed using a plurality of parameters, an output prediction unit 6 that calculates a predicted output value based on the parameters in a predetermined time range, and a voltage sensor The error calculation unit 7 calculates the error between the output value detected in 3 and the output prediction value calculated by the output prediction unit 6, and the error calculation unit 7 And a parameter updating unit 8 that updates the parameters so that the calculated error is reduced.
The sensitivity function will be described later.
Each calculation calculation in the output prediction unit 6, the error calculation unit 7, and the parameter update unit 8 is repeated until the error is minimized, and the parameter is estimated by identifying the sensitivity function when the error is minimum. .

ただし、θは、ｍ次元数ベクトルの集合R^ｍの要素である未知パラメータ・ベクトルであり、N（p, θ）、D(p, θ)はパラメータに関して線形であること、すなわち

と書き表せることを仮定する。なお、Tは転置行列を意味する。 Next, an algorithm of the projection type continuous time system identification method implemented by the continuous time system identification apparatus will be described below.
Now, consider a linear time-invariant system such as

Where θ is an unknown parameter vector that is an element of a set R ^m of m-dimensional number vectors, and N (p, θ) and D (p, θ) are linear with respect to the parameters, that is,

Assuming that T means a transposed matrix.

であると定義する。なお、文字の上の「^」は、推定値であることを意味する。
真のパラメータθ₀が存在するとき、

となる。 Estimated error signal e (t)

Is defined as Note that “^” above the character means an estimated value.
When the true parameter θ ₀ exists,

It becomes.

が導かれる。 Here, if the relationship of the above formulas (2) and (3) is used,

Is guided.

の張る部分空間へe(t)を射影したベクトル表現εは、

を満たす。 Therefore, the basis (vector V)

The vector representation ε that projects e (t) to the subspace spanned by

Meet.

となる。そこで、

にしたがってθ^^ｋを反復更新して、推定値を決定する。 However, since the base V includes the true target system G (p, θ ₀ ), it is necessary to replace this with the estimated value G (p, θ ^).
Note that “^” representing an estimated value is described in the specification differently from a mathematical expression. That is, “^” is shifted after the character (here, “θ”) to which “^” is to be placed because of the notation restriction.
The vector expression ε of the projection obtained at this time uses the term Δ due to the error of G,

It becomes. there,

According to the above, θ ^ ^k is iteratively updated to determine an estimated value.

となり、これを変形して

と書くことができる。 At this time,

And transform this

Can be written.

Therefore, the equilibrium point of this system is θ ^ ^k = θ ₀ , and its stability can be considered as a nominally stable system with an uncertainty of uncertainty Δ.
Equation (14) is equivalent to the closed loop of FIG.
Α is a step width parameter that determines the stability of the algorithm, and is determined between 0 <α <1. The closer α is to 1, the faster the convergence speed, but the lower the stability. Therefore, it is necessary to appropriately determine α.
In other words, when 0 <α <1, the system [? Α / {z? (1? Α)}] × I is stable and its ∞ norm is 1. Therefore, from the small gain theorem, the maximum singular value of Δ is 1 or less regardless of time is a sufficient condition for the algorithm to be stable.

のように構成し、

とすればよい。 Next, in the projection implementation, when input / output data at time t _k (k = 0, 1, 2,..., N) is obtained, the base V _D and the estimated error signal e _D are

Configured as

And it is sufficient.

Here, a secondary battery is taken as an example of the target system. When using a secondary battery, knowing the state of charge (SOC) and the state of health (SOC) from time to time can control the driving conditions of an electric vehicle or issue an alarm. It becomes possible.
However, since these values cannot be detected directly, the projective continuous time system identification method is used.

In an equivalent circuit model of a general battery for estimating a charging rate, two elements of an open circuit voltage (OCV) and an overpotential are considered.
The open circuit voltage is the potential difference between the electrodes in an electrochemical equilibrium state, and the overvoltage is the voltage drop due to the dynamics of the reaction inside the battery when current flows through the battery.

で求められる。
ただし、i(t)は充放電時の電流であり、充電時を正、放電時を負とする。
また、FCC₀は新品時のバッテリの満充電容量(Full Charge Capacity)、SOHはバッテリの劣化の度合いを表す健全度である。さらに、dは電流センサのオフセット誤差である。 There is a one-to-one correspondence between OCV and SOC determined by the material of the electrode, and it is known that this relationship hardly depends on temperature or battery deterioration.
An example of the relationship between OCV and SOC is shown in FIG.
SOC

Is required.
However, i (t) is a current at the time of charging / discharging, and is positive during charging and negative during discharging.
FCC ₀ is a full charge capacity of the battery when it is new, and SOH is a soundness level indicating the degree of deterioration of the battery. D is an offset error of the current sensor.

The overvoltage can be divided into three elements: resistance of an electrolyte solution, charge transfer process at the interface between the electrode and the electrolyte, and ion diffusion process inside the battery.
The charge transfer process is a fast response with a time constant of several milliseconds, and the diffusion process is a slow response with a time constant of several hundred seconds.

と表現する。
ここで、sはラプラス演算子である。R₀は電解液などの抵抗を表しており、Z_ω(s)はワールブルグ・インピーダンスと呼ばれている拡散過程のインピーダンスである。 Here, it is assumed that the charge transfer process is negligible due to the data sampling cycle, etc., and the impedance of the overvoltage part is

It expresses.
Here, s is a Laplace operator. R ₀ represents the resistance of the electrolyte or the like, and Z _ω (s) is the impedance of the diffusion process called Warburg impedance.

と表される。ここで、R_dは直流電流に対する拡散抵抗である。また、τ_dは拡散過程の時定数を表す量であり、ｌを拡散層の厚み、Dを拡散定数とすると、τ_d＝ｌ²/Dを満たす。
このワールブルグ・インピーダンスは、45度の位相遅れを持つことが大きな特徴である。 This Warburg impedance is

It is expressed. Here, R _d is a diffusion resistance with respect to a direct current. Also, τ _d is a quantity representing the time constant of the diffusion process, and satisfies τ _d = l ² / D where l is the thickness of the diffusion layer and D is the diffusion constant.
The main characteristic of the Warburg impedance is that it has a phase delay of 45 degrees.

のように双曲線関数の展開であるtanh（・）の連分数展開に対応する図４に示すようなキャパシタCと抵抗Rとからなるカウエル型の等価回路を扱う。ただし、

である。 The impedance in equation (21) is difficult to handle as it is, but can be approximated using an equivalent circuit.

A cowell type equivalent circuit composed of a capacitor C and a resistor R as shown in FIG. 4 corresponding to the continuous fraction expansion of tanh (•), which is a hyperbolic function expansion, is handled. However,

It is.

Since a dimensionless model cannot be handled in practical use, it is terminated at an appropriate order n.
The model of Eq. (22) is a conventional method in which the resistance and capacitor of the equivalent circuit are determined by only two physical parameters R _d and τ _d , and R _{1 to} R _n and C _{1 to} C _n are all unknowns. This is different from the equivalent circuit model.

とすると、バッテリの端子電圧v(t)は

と表すことができる。ただし、pは微分演算子である。
この式(26)を、電流i(t)が入力、電圧v(t)が出力であるバッテリのモデルとする。 The function of SOC-OCV characteristics as shown in Fig. 2 is expressed as f _OCV (·).

Then, the battery terminal voltage v (t) is

It can be expressed as. Where p is a differential operator.
This equation (26) is a battery model in which the current i (t) is an input and the voltage v (t) is an output.

となる。 Of the battery models, the function f _OCV is obtained by prior experiments. FCC ₀ is a known amount.
Therefore, the unknown parameter θ of the battery model is

It becomes.

が成り立つ。 Since the battery model is not in the form of equations (1) to (5), the projective continuous-time system identification method cannot be directly applied to parameter estimation of the battery model.
Therefore, the algorithm is changed so that the projective continuous-time system identification method can be applied to the parameter estimation of the battery model.
When both sides of equation (1) are partially differentiated by θ _j ,

Holds.

であると解釈しなおすことで、バッテリのモデルのパラメータを推定することができる。式(29)を基底の「感度関数」と定義する。なお、感度関数の定義は式(29)の右辺の?をとったもので定義するようにしてもよい。感度関数は、勾配や傾きの一種と考えることができる。 Therefore, the basis for projective continuous-time system identification is

The battery model parameters can be estimated by reinterpreting as follows. Equation (29) is defined as the basis “sensitivity function”. The sensitivity function may be defined by taking the right side of Equation (29). The sensitivity function can be considered as a kind of gradient or slope.

となる。 When we actually calculate the basis, that is, the sensitivity function,

It becomes.

The v ₁ (t), v ₂ (t), and v ₃ (t) are sensitivity functions for estimating the parameters of the battery model, and are sensitivity functions related to the SOC, SOH, and current sensor offset, respectively.
Where u _s (t) is a unit step signal as follows.

を状態空間によって表現し直すと、

となる。 Next, R _d and τ _d . Consider the differentiation by.

Can be expressed in terms of state space,

It becomes.

となる。 Here, if both sides of the state equation (Equation (38)) and the observation equation (Equation (39)) are partially differentiated by θj,

It becomes.

の応答を計算すれば、基底

が得られる。最後に、

である。これらの基底を用いて、式(16)を構成することでパラメータを推定することができる。 Therefore,

If we calculate the response of

Is obtained. Finally,

It is. Using these bases, the parameter can be estimated by constructing Equation (16).

The above procedure will be described based on the flowchart shown in FIG. 5 for parameter estimation processing executed by the microcomputer of FIG.
In step S0, an experiment is performed in advance to sample current and voltage waveforms from the battery.
Next, the process proceeds to step S1.

In step S1, initialization is performed. That is, the initial estimated value θ ^ ⁰ of the parameter is appropriately determined. The Gauss-Newton method is a kind of gradient method and may fall into a local optimal solution depending on how to select the initial value θ ⁰ of the iteration.
For this reason, it is important to select an appropriate θ ⁰ . In the continuous-time system identification method, it is often easy to give physical meaning to the unknown parameter vector θ, so the initial value of the iteration should be determined using prior information about the target system. is important.
Next, the process proceeds to step S2.

である。ここで、基底ベクトルを

のように、感度関数へと定義し直す。 In step S2, a basis V _D and an estimation error signal e _D are constructed using the parameter estimated values θ ^ ^k obtained in step S2.
The base is

It is. Where the basis vector is

Redefine it as a sensitivity function.

であり、推定電圧y^と観測した電圧yを用いると、

である。
次いで、ステップS3へ進む。 The estimated error signal is

Using the estimated voltage y ^ and the observed voltage y,

It is.
Next, the process proceeds to step S3.

In step S3, it is determined whether or not the base V _D and the estimated error signal e _D have been successfully constructed. If the determination result is YES, the process proceeds to step S4, and if NO, the process returns to step S1 and starts again from the initialization.

を用いて射影を計算する。次に、

によってパラメータ推定値を反復更新する。
このとき、基底の一次独立性が弱まって失敗することがある。その場合には、ステップS1に戻り、別のパラメータ初期推定値θ^⁰を用いて同様の処理を行う。
成功したら、ステップS５へ進む。 In step S4, the parameter estimated value is updated. That is,

Calculate the projection using. next,

Update the parameter estimates repeatedly.
At this time, the primary independence of the basis may be weakened and fail. In that case, the process returns to step S1, and the same processing is performed using another parameter initial estimated value θ ^ ⁰ .
If successful, the process proceeds to step S5.

  In step S5, it is determined whether or not the parameter estimation value has been successfully updated. If the determination result is YES, the process proceeds to step S6, and if NO, the process returns to step S1 and starts again from the initialization.

ここで、εはユーザの設定する十分に小さな数である。
一方、判定結果がNOでパラメータ推定値が収束していなければ、ステップS2に戻り、基底V_Dと推定誤差信号e_Dの構築からやり直す。
以上で、パラメータ推定処理を終える。 In step S6, the final criterion, that is, the convergence determination is performed. If the determination result is YES, that is, if the parameter estimation value has converged, the update is terminated.
However, as the convergence condition, for example, the following expression can be used.

Here, ε is a sufficiently small number set by the user.
On the other hand, if the determination result is NO and the parameter estimation value has not converged, the process returns to step S2 and starts again from the construction of the base V _D and the estimation error signal e _D.
This completes the parameter estimation process.

Here, simulation is performed using input / output data (Fig. 6 (a) is an input current as an input and Fig. 6 (b) is an output voltage as an output) obtained by an electric vehicle running experiment. The parameters were estimated.
The data sampling period was 0.1 second, and the order of Z _W (s) of the battery model was 4. The parameter estimation results at this time are shown in a table in FIG. From this table, the values of these parameters are physically reasonable.

Moreover, the comparison result between the observed output and the model output of Example 1 is shown in FIG. 8 (measurement results are indicated by a solid line and estimation results are indicated by a broken line), and the SOC obtained by the Coulomb count method and the example The comparison result with the SOC estimated in 1 is shown in FIG. 9 (the result by the Coulomb count method is indicated by a solid line, and the estimation result is indicated by a broken line).
From these results, it can be seen that there is an error in the first half of the saddle shape, although it is captured. This may be due to the possibility that the characteristics of the battery have changed during the experiment. If this is taken into account, the estimation accuracy can be further increased.

Here, the state of the number of times the parameter estimation value is repeatedly updated is shown for the output voltage ((a) in each figure below) and SOC ((b) in each figure below) with the measurement result as a solid line and the estimation result as a broken line. It shows in each.
FIG. 10 shows the results for 0 iterations, FIG. 11 for 3 iterations, FIG. 12 for 6 iterations, FIG. 13 for 9 iterations, and FIG. 14 for 15 iterations.
As can be seen from these figures, the estimation accuracy gradually increases by repeatedly performing the estimation update. Therefore, it can be seen that iterative updating of the estimation in Example 1 is effective in improving the estimation accuracy.

  As described above, the parameter identification apparatus and its estimation method of the continuous-time system according to the first embodiment estimate parameters by applying the projection-type continuous-time system identification method to a nonlinear model such as a battery. can do.

Also, when applied to battery 1, the charging rate of battery 1, soundness, offset current of the current sensor, diffusion resistance in battery model 5, electrolyte resistance R ₀ in battery model 5, It is possible to simultaneously estimate at least one of the time constants of the diffusion processes at once.

  As described above, the present invention has been described based on the above-described embodiments. However, the present invention is not limited to the above-described embodiments, and even when there is a design change or the like without departing from the gist of the present invention, it is included in the present invention.

  For example, the continuous-time system parameter identification apparatus and estimation method thereof according to the present invention can be applied to nonlinear models other than batteries.

1 Battery (target system)
2 Current sensor (input detector)
3 Voltage sensor (output detector)
4 Microcomputer
5 Battery model (equivalent model)
6 Output prediction unit
7 Error calculator
8 Parameter update section

Claims (4)

An equivalent model representing the target system with multiple parameters,
An input detection unit for detecting an input value to the target system;
An output detection unit for detecting an output value of the target system when the input value is input in a predetermined time range;
An output prediction unit that calculates a predicted value of the output value based on the parameter and the equivalent model in the predetermined time range;
An error calculating unit that calculates an error between the output value detected by the output detecting unit and the predicted value calculated by the output predicting unit; and a sensitivity function (∂y ^ (t, θ) / ∂ parameter that updates the parameter so that the error calculated by the error calculation unit is reduced based on the partial differential of θj, y ^ is the estimated output, t is the time, and θ is the parameter vector) Update section,
With
Each calculation calculation in the output prediction unit, the error calculation unit, and the parameter update unit is repeated until the error is minimized, and the parameter is identified by a parameter when the error is minimum.
A parameter identification apparatus for a continuous-time system. The parameter identification device for a continuous time system according to claim 1,
The target system is a secondary battery,
The equivalent model is a battery model;
The input detection unit is a current sensor that detects a charge / discharge current of the secondary battery,
The output detection unit is a voltage sensor that detects a terminal voltage of the secondary battery,
The parameters include the charging rate of the secondary battery, the soundness level, the offset current of the current sensor, the diffusion resistance in the battery model, the resistance of the electrolyte in the battery model, and the diffusion process in the battery model. Including at least one of the time constants of
A parameter identification apparatus for a continuous-time system. Detect the input value to the target system,
Detecting an output value of the target system when the input value is input in a predetermined time range;
Calculate the predicted value of the output value based on the parameters used in the equivalent model of the target system and the equivalent model in the predetermined time range
Calculating an error between the detected output value and the calculated predicted value;
Based on the sensitivity function of the parameter of the equivalent model (defined by the partial differentiation of ∂y ^ (t, θ) / ∂θj, where y ^ is the estimated output, t is the time, and θ is the parameter vector) Update the parameters to reduce the error,
The calculation of the predicted value of the output value, the calculation of the error, and the update of the parameter are repeated until the error is minimized, and the parameter is identified by the parameter when the error is minimum.
A continuous-time parameter system identification method characterized by the above. The continuous time parameter system identification method according to claim 3,
The target system is a secondary battery ,
Before Symbol equivalent model is a battery model,
The input value detection unit is a current sensor that detects a charge / discharge current of the secondary battery,
The output value detector is a voltage sensor that detects a terminal voltage of the secondary battery,
The parameters include the charging rate of the secondary battery, the soundness level, the offset current of the current sensor, the diffusion resistance in the battery model, the resistance of the electrolyte in the battery model, and the diffusion process in the battery model. Including at least one of the time constants of
A continuous-time parameter system identification method characterized by the above.

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