Method for Parameter Identification and SOH Estimation of First-Order RC Equivalent Circuit Model for Automotive Lithium Batteries

Abstract

This invention addresses the shortcomings of existing technologies by providing a method for parameter identification and SOH estimation of a first-order RC equivalent circuit model for automotive lithium batteries. The method includes the following steps: 1) Analysis of the principle of unknown parameter identification in chaotic systems; 2) Connecting electronic components such as load-controlled memristors as loads to the output of the first-order RC equivalent circuit model to establish a fourth-order chaotic system; 3) Analyzing the dynamic characteristics of the fourth-order chaotic system, including its phase trajectory diagram and time-domain waveform diagram; 4) Constructing an adaptive control law for the unknown parameters of the fourth-order chaotic system to achieve parameter identification and SOH estimation of the first-order RC equivalent circuit model. This invention's method exhibits high accuracy, stability, higher convergence speed, and stronger nonlinear prediction capabilities.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion power battery parameter estimation technology, and in particular relates to a method for parameter identification and SOH estimation of a first-order RC equivalent circuit model for automotive lithium batteries. Background Technology

[0002] In recent years, environmental and petroleum resource shortages have drawn significant attention from governments worldwide, leading to a surge in interest in new energy electric vehicles across various industries and a growing number of scholars joining related research teams. Lithium-ion batteries, due to their superior energy density, long lifespan, stability, and self-discharge rate compared to other batteries, have become a research hotspot and a focus of widespread application within the industry.

[0003] Since automotive lithium-ion battery systems are essentially rigid systems with highly complex nonlinear dynamic characteristics, and the parameters that the relevant management systems can directly measure online are only the port voltage and current, the various state variables inside the lithium battery, such as SOC, SOH, SOP and SOE, need to be estimated. Therefore, automotive lithium-ion battery systems urgently need to be able to quickly and accurately identify the lithium battery parameters and their various state variables.

[0004] Currently, SOH estimation algorithms can be broadly categorized into four types: internal resistance method, mathematical model method, electrochemical impedance spectroscopy method, and data-driven method. The internal resistance method is not accurate enough for measuring milliohm-level internal resistance; the mathematical model method is affected by the nonlinear characteristics of the battery system; and the electrochemical impedance spectroscopy method requires the battery to be left to stand for several hours to eliminate the effects of battery polarization, making it unsuitable for real-world applications in electric vehicles and primarily used in laboratory analysis. The data-driven method has become a popular research approach, but it requires a large amount of battery data, resulting in a heavy computational burden. In practical applications, the accuracy of this method is often affected by the limitations and uncertainties of data acquisition. Therefore, this invention proposes a parameter identification and SOH estimation method for the first-order RC equivalent circuit model of automotive lithium batteries to address the shortcomings of the aforementioned parameter identification and SOH estimation methods. Summary of the Invention:

[0005] To address the shortcomings of existing technologies, this invention provides a method for parameter identification and SOH estimation of a first-order RC equivalent circuit model for automotive lithium batteries, comprising the following steps:

[0006] 1) Analysis of the principle of identifying unknown parameters in chaotic systems;

[0007] 2) Based on the characteristic that a chaotic system composed of a charge-controlled memristor can generate rich chaotic dynamic behaviors, the charge-controlled memristor electronic components are connected as loads to the output terminal of a first-order RC equivalent circuit model to establish a fourth-order chaotic system.

[0008] 3) Analyze the phase trajectory diagram and time domain waveform diagram of the fourth-order chaotic system to determine its dynamic characteristics;

[0009] 4) Construct an adaptive control law for the unknown parameters of a fourth-order chaotic system to achieve parameter identification and SOH estimation of the first-order RC equivalent circuit model;

[0010] The principle analysis for identifying unknown parameters in chaotic systems described in step 1) is as follows:

[0011] Assume a four-dimensional hyperchaotic system is as follows:

[0012] (1)

[0013] in, For state variables; For unknown parameters of the system,

[0014] If system parameters space is ,but become:

[0015] (2)

[0016] for Other parts that do not contain parameters

[0017] Equation (2) above satisfies the Lipschitz condition, that is, for any , and initial value There exists a constant for each. satisfy:

[0018] (3)

[0019] To effectively identify all parameters of a chaotic system based on a first-order RC equivalent circuit using a memristor, at least two time series are required if there are two Lyapunov exponents greater than zero. Therefore, constructing a linear response system according to equation (1) yields the following dynamic equation:

[0020] (4)

[0021] In the formula, , and ensure the relationship It also holds true.

[0022] Assume the difference between the variables in system (2) and (4) is And the following relationship exists:

[0023] (5)

[0024] Decoupling coefficients and unknown system parameters The adaptive control law over time is as follows:

[0025] (6)

[0026] In the formula, , , It is a constant.

[0027] The nonnegative Lyapunov function for constructing a chaotic system is:

[0028] (7)

[0029] In the formula, It is a constant.

[0030] but The derivative with respect to time is:

[0031] (8)

[0032] When taking When, in equation (8) Established,

[0033] Therefore, as long as the driving quantity is appropriately selected so that equation (5) satisfies the Lipschitz condition, the adaptive control law (6) can be used to make the driving system (1) and the response system (4) achieve adaptive synchronization.

[0034] When the two hyperchaotic systems, the driver and the response, achieve complete synchronization, it is possible to Therefore, the unknown parameters in equation (1) of the driving system Complete identification is possible;

[0035] Step 2) describes the method for establishing a fourth-order chaotic system as follows:

[0036] A first-order RC equivalent circuit model is used to describe the kinetic characteristics of lithium-ion batteries during operation.

[0037] , These are the open-circuit voltage and terminal voltage of the first-order RC equivalent circuit model, respectively. These are the polarization resistance and ohmic internal resistance of the first-order RC equivalent circuit model, respectively. The polarization capacitor is the one used in the first-order RC equivalent circuit model.

[0038] A chaotic system is established using a charge-controlled memristor and a first-order RC equivalent circuit. The mathematical function of the memristor's gain M(q) is:

[0039] (9)

[0040] In the formula: , All are constants, and , ,

[0041] Based on the chaotic system model diagram of the RC equivalent circuit based on memristors These are two inductor coils of different sizes; For resistance; For charge-controlled memristors; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; For flow The current; For flow The current; For flow The current,

[0042] Based on the KCL and KVL laws, assume The direction shown is the reference direction of the current, so the differential equation of the circuit model can be obtained as follows:

[0043] (10)

[0044] The memristor value of memristor M(q) is... , ,Will Substitute into equation (10) and let ,Pick Let there be 4 state variables, and let Then we can obtain:

[0045] (11)

[0046] Equation (11) above is the mathematical model of the dynamics of a fourth-order chaotic system constructed by a charge-controlled memristor and a first-order RC equivalent circuit.

[0047] Step 3) analyzes the phase trajectory diagram and time-domain waveform diagram of the fourth-order chaotic system's dynamic characteristics. The method is as follows:

[0048] When the parameters in the fourth-order chaotic system dynamic mathematical model are respectively taken as: , In At the same time, From equation (11), we can obtain:

[0049] (12)

[0050] In the formula: , , ,

[0051] From equation (12) above, it can be seen that the unknown parameters of the constructed first-order RC equivalent circuit chaotic system based on memristors are: ,in With ohmic resistance A linear relationship exists. It is the reciprocal of the polarization capacitance. The product of polarization resistance and polarization capacitance is given by the state variable: , , , ,

[0052] when When the initial value of the system is set to (0.0, 0.01, 0.0, 0.0), a simulation experiment is conducted using MATLAB software with a step size of 0.01 using the fourth-order Runge-Kutta method. The simulation results show that the system constructed by equation (12) generates a double-vortex chaotic attractor. For equation (12), the chaotic system is obtained by MATLAB simulation. When the initial value of the system is set to (0.0, 0.04, 0.0, 0.0), the Lyapunov exponents of the fourth-order chaotic system are LE1>0, LE2>0, LE3<0, and LE4<0, in the form of (+, +, -, -). This indicates that the fourth-order chaotic system generates a double vortex attractor and belongs to the fourth-order hyperchaotic system.

[0053] Step 4) involves parameter identification and SOH estimation of the first-order RC equivalent circuit model, and the method is as follows:

[0054] Construct a linear drive system based on equation (4), and select... As a driving variable, then Let the adaptive control law of the parameters of the coupled system with time be...

[0055] (13)

[0056] Assume the initial points of the driving system and the response system are selected as follows: , ,parameter for The estimated values, the relationship between A and R0 is A = 1.1 * R0, and the relationship between B and C1 is... The relationship between C and R1, C1 is as follows: Unknown parameters in the response system The initial values ​​were set to (0.25, 14.19, 0.36). Simulation verification showed that the driving system was in a hyperchaotic state at this time. The parameters in the driving system were then... The current value is set to (0.19, 14, 4.4). Using the adaptive control law (13), the fourth-order Runge-Kutta method with a step size of 0.01 is used to simulate the adaptive control law through MATLAB software. The simulation results show that the unknown variable After 2 seconds, it quickly stabilized at values ​​of 0.1912, 14.012, and 4.432, consistent with the drive system parameters. The relative errors of the current set values ​​(0.19, 14, 4.4) are 0.63%, 0.86%, and 0.73%, respectively. The parameters can be calculated according to the following formula (14). Identification value Therefore, it can be seen that under the action of the controller and the adaptive control law, the adaptive control law can quickly and accurately identify the parameters of the first-order RC equivalent circuit model online.

[0057] (14)

[0058] Using the SOH definition method based on internal resistance, the SOH expression is shown below.

[0059] (15)

[0060] In the formula, , , These are the ohmic internal resistances of the automotive lithium battery when it reaches its end-of-life (EOL), the current actual ohmic internal resistance, and the ohmic internal resistance of the new battery, respectively. Therefore, the identification value of the ohmic internal resistance is determined using a first-order RC equivalent circuit model. According to formula (15), the estimated SOH value of lithium-ion battery can be obtained.

[0061] The method for parameter identification and SOH estimation of the first-order RC equivalent circuit model of automotive lithium batteries disclosed in this invention has the following beneficial effects when using the above algorithm:

[0062] This invention establishes a fourth-order chaotic system using a load-controlled memristor and a first-order RC equivalent circuit. It analyzes the dynamic characteristics of this fourth-order chaotic system, including its phase trajectory and time-domain waveform, and constructs an adaptive control law for the unknown parameters of the fourth-order chaotic system based on the memristor's first-order RC equivalent circuit model. This enables online identification of parameters and SOH estimation for the first-order RC equivalent circuit model of lithium-ion batteries. The method of this invention improves the average relative error by 1.34 percentage points and the root mean square error by 2.824 percentage points compared to the FFRLS identification algorithm. The convergence time is also nearly 13 seconds faster than the FFRLS algorithm, demonstrating higher accuracy, stability, faster convergence speed, and stronger nonlinear prediction capabilities. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the first-order RC equivalent circuit model of the present invention;

[0064] Figure 2 This is a diagram of the chaotic system model of the RC equivalent circuit based on memristors according to the present invention;

[0065] Figure 3 This is a system phase diagram of a specific embodiment of the present invention;

[0066] Figure 4 This is a time-domain waveform diagram of a specific embodiment of the present invention;

[0067] Figure 5 This is a Lyapunov index spectrum of a specific embodiment of the present invention;

[0068] Figure 6 Unknown parameters under the action of the controller in a specific embodiment of the present invention Diagram of the identification process;

[0069] Figure 7 The diagram shows the (a) current and (b) voltage of a single battery cell at 25°C according to a specific embodiment of the present invention.

[0070] Figure 8 This is a comparison chart of the adaptive control law and the SOH identification results of the FFRLS algorithm under HPPC operating conditions at 25℃ in a specific embodiment of the present invention.

[0071] Figure 9 This is a graph showing the parameterization verification results of the adaptive control law under the DST condition at 25℃ in a specific embodiment of the present invention;

[0072] Figure 10 The figure shows the parameterization verification results of the FFRLS algorithm under the DST condition at 25℃ in a specific embodiment of the present invention. Detailed Implementation

[0073] The present invention will be further described in detail below with reference to embodiments. The method for parameter identification and SOH estimation of the first-order RC equivalent circuit model of automotive lithium batteries disclosed in this invention comprises the following steps:

[0074] Analysis of the principle of identifying unknown parameters in chaotic systems;

[0075] Assume a four-dimensional hyperchaotic system is as follows:

[0076] (1)

[0077] in, For state variables; For unknown parameters of the system,

[0078] If system parameters space is ,but It can become:

[0079] (2)

[0080] for Other parts that do not contain parameters.

[0081] Equation (2) above satisfies the Lipschitz condition, that is, for any , and initial value There exists a constant for each. satisfy:

[0082] (3)

[0083] To effectively identify all parameters of a chaotic system based on a first-order RC equivalent circuit using a memristor, at least two time series are required if there are two Lyapunov exponents greater than zero. Therefore, constructing a linear response system according to equation (1) yields the following dynamic equation: (4)

[0084] In the formula, , and ensure the relationship It also holds true.

[0085] Assume the difference between the variables in system (2) and (4) is And the following relationship exists:

[0086] (5)

[0087] Decoupling coefficients and unknown system parameters The adaptive control law over time is as follows:

[0088] (6)

[0089] In the formula, , , It is a constant.

[0090] The nonnegative Lyapunov function for constructing a chaotic system is:

[0091] (7)

[0092] In the formula, It is a constant.

[0093] but The derivative with respect to time is:

[0094] (8)

[0095] When taking When, in equation (8) Established.

[0096] Therefore, as long as the driving quantity is appropriately selected so that equation (5) satisfies the Lipschitz condition, the adaptive control law (6) is adopted so that the driving system (1) and the response system (4) achieve adaptive synchronization.

[0097] When the two hyperchaotic systems, the driver and the response, achieve complete synchronization, it is possible to Therefore, the unknown parameters in equation (1) of the driving system It can be fully identified.

[0098] 2) Based on the characteristic that a chaotic system composed of a charge-controlled memristor can generate rich chaotic dynamic behaviors, electronic components such as charge-controlled memristors are connected as loads to the output terminal of a first-order RC equivalent circuit model to establish a fourth-order chaotic system.

[0099] The kinetic characteristics of a lithium-ion battery during operation are described using a first-order RC equivalent circuit model, as shown in the schematic diagram. Figure 1 As shown.

[0100] Figure 1 middle , These are the open-circuit voltage and terminal voltage of the first-order RC equivalent circuit model, respectively. These are the polarization resistance and ohmic internal resistance of the first-order RC equivalent circuit model, respectively. The polarization capacitor is represented by a first-order RC equivalent circuit model. A chaotic system is established using a charge-controlled memristor and a first-order RC equivalent circuit; the schematic diagram is shown below. Figure 2 As shown, the mathematical function of the gain memristor M(q) of the charge-controlled memristor is:

[0101] (9)

[0102] In the formula: , All are constants, and , .

[0103] Figure 2 middle These are two inductor coils of different sizes; For resistance; For charge-controlled memristors; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; For flow The current; For flow The current; For flow The current.

[0104] Based on the KCL and KVL laws, assume Figure 2 middle The direction shown is the reference direction for the current, therefore we can obtain... Figure 2 The differential equation of the circuit model shown is:

[0105] (10)

[0106] The memristor value of memristor M(q) is... , .

[0107] Will Substitute into equation (10) and let (Pick (For 4 state variables), let Then we can obtain:

[0108] (11)

[0109] Equation (11) above is the mathematical model of the dynamics of a fourth-order chaotic system constructed by a charge-controlled memristor and a first-order RC equivalent circuit.

[0110] 3) Analyze the dynamic characteristics of the fourth-order chaotic system, including its phase trajectory diagram and time-domain waveform diagram;

[0111] When the parameters in the fourth-order chaotic system dynamic mathematical model are respectively taken as: , In At the same time, From equation (11), we can obtain:

[0112] (12)

[0113] In the formula: , , .

[0114] From equation (12) above, it can be seen that the unknown parameters of the constructed first-order RC equivalent circuit chaotic system based on memristors are: ,in With ohmic resistance A linear relationship exists. It is the reciprocal of the polarization capacitance. The product of polarization resistance and polarization capacitance is given by the state variable: , , , .

[0115] when When the initial values ​​of the system are set to (0.0, 0.01, 0.0, 0.0), a simulation experiment is conducted using MATLAB software with a fourth-order Runge-Kutta method with a step size of 0.01. The phase trajectory diagram of the system is as follows. Figure 3 As shown, the time-domain waveform is as follows Figure 4 As shown in the figure. The simulation results show that the system constructed by equation (12) generates a double-vortex chaotic attractor.

[0116] For equation (12), the chaotic system was obtained by MATLAB simulation. When the initial values ​​of the system are set to (0.0, 0.04, 0.0, 0.0), the Lyapunov exponent spectrum is as follows: Figure 5 As shown.

[0117] pass Figure 5It can be seen that the Lyapunov exponents of the fourth-order chaotic system established in this paper are LE1>0, LE2>0, LE3<0, and LE4<0, in the form of (+, +, -, -). This indicates that the fourth-order chaotic system generates a double vortex attractor and belongs to the fourth-order hyperchaotic system.

[0118] 4) Construct adaptive control laws for unknown parameters of a fourth-order chaotic system to achieve parameter identification and SOH estimation of the first-order RC equivalent circuit model.

[0119] Construct a linear drive system based on equation (4), and select... As a driving variable, then Let the adaptive control law of the parameters of the coupled system with time be...

[0120] (13)

[0121] Assume the initial points of the driving system and the response system are selected as follows: , ,parameter for The estimated value of the unknown parameter in the response system The initial values ​​were set to (0.25, 14.19, 0.36). Simulation verification showed that the driving system was in a hyperchaotic state at this time. The parameters in the driving system were then... The current value is set to (0.19, 14, 4.4). Using the adaptive control law (13) designed in this paper, the adaptive control law is simulated using MATLAB software with a fourth-order Runge-Kutta method with a step size of 0.01. The simulation results show that the unknown variables... After 2 seconds, it quickly stabilized at values ​​of 0.1912, 14.012, and 4.432, consistent with the drive system parameters. The relative errors of the current setpoints (0.19, 14, 4.4) are 0.63%, 0.86%, and 0.73%, respectively. Unknown parameters under the control of the controller... The identification process is as follows Figure 6 As shown.

[0122] The parameters can be calculated according to the following formula (14). Identification value Therefore, it can be seen that under the action of the controller and the adaptive control law of parameters, the adaptive control law can quickly and accurately identify the parameters of the first-order RC equivalent circuit model online.

[0123] (14)

[0124] Since the 21700 model power-type ternary lithium-ion battery is used as the research object, the SOH definition method based on internal resistance is adopted, and the SOH expression is shown in the following formula.

[0125] (15)

[0126] In the formula, , , These represent the ohmic internal resistance of the automotive lithium battery when it reaches its end-of-life (EOL), the current actual ohmic internal resistance, and the ohmic internal resistance of a new battery, respectively. Therefore, the identification value of the ohmic internal resistance is obtained using a first-order RC equivalent circuit model. According to formula (15), the estimated SOH value of the 21700 model power type ternary lithium-ion battery can be obtained.

[0127] The experimental equipment mainly included an Arbin BT2000 system, an HLT402P constant temperature test chamber, and a PC. The data acquisition frequency was 50Hz, and the experimental ambient temperature was set to 25℃. The HPPC test results of the battery cells at 25℃ are as follows: Figure 7 As shown, the specific steps of the HPPC operating condition test are as follows:

[0128] Step 1: Charge at a constant current of 0.2C to 4.2V, then charge at a constant voltage of 4.2V. Stop charging when the current is ≤0.02C and let it stand for 2 hours. Then discharge at a constant current of 1C. Stop discharging when the discharge capacity reaches 10% of the nominal capacity. At this time, SOC=0.9.

[0129] Step 2: Discharge at a constant current rate of 1C for 20 seconds, then let it rest for 1 hour; then charge at a constant current rate of 1C for 20 seconds, then let it rest for 1 hour; discharge at a constant current rate of 2C for 20 seconds, then let it rest for 1 hour; then charge at a constant current rate of 2C for 20 seconds, then let it rest for 1 hour; then charge at a constant current rate of 2.5C for 20 seconds, then let it rest for 1 hour; then discharge at a constant current rate of 2.5C for 20 seconds, then let it rest for 1 hour; then charge at a constant current rate of 3C for 20 seconds, then let it rest for 1 hour; then discharge at a constant current rate of 3C for 20 seconds, then let it rest for 1 hour. Accumulate the capacity of all pulse charge / discharge cycles during this process (this may be negative) to determine the battery's SOC value at this point.

[0130] Step 3: Discharge at a constant current of 1C. When the discharge capacity reaches 20% of the nominal capacity, stop discharging. At this time, SOC=0.8. Let it stand for 2 hours.

[0131] Step 4: Repeat step 2, adjusting the SOC from 0.7 to 0.1 at 10% SOC intervals, and test the battery charging and discharging current and voltage sequentially.

[0132] During the battery SOC testing process from 0.9 to 0.1, both the adaptive control law algorithm and the FFRLS algorithm were used to identify the parameters of the equivalent circuit model, and the identified parameter values ​​were recorded. The estimated SOH value was then calculated using equation (17). The ambient temperature was set to 25℃. The comparison of the SOH identification results of the adaptive control law and FFRLS algorithms under HPPC conditions is shown in the figure below. Figure 8 As shown.

[0133] By employing both adaptive control and FFRLS algorithms, the parameters of the first-order RC equivalent circuit model were identified in real-time online, yielding parameter identification values ​​for the first-order RC equivalent circuit model of a 1700-type power ternary lithium-ion battery at different SOC points. To further verify the effectiveness of the parameter identification algorithm proposed in this invention, the parameter identification values ​​obtained from the adaptive control and FFRLS algorithms of the first-order RC equivalent circuit model of the lithium-ion battery were substituted into the first-order RC equivalent circuit model, respectively. Model parameter verification was conducted under DST conditions, with the experimental ambient temperature set at 25℃. The predicted battery terminal voltage values ​​were compared and analyzed with the experimentally measured values. The parameterization verification results of the adaptive control law under DST conditions at 25℃ are shown below. Figure 9 As shown, the parameterization verification results of the FFRLS algorithm under the DST condition at 25℃ are as follows: Figure 10 As shown.

[0134] To effectively evaluate the performance of the adaptive control law identification algorithm for the first-order RC equivalent circuit model of automotive lithium-ion batteries, three error models—mean absolute error (MAE), root mean square error (RMS), and mean relative error (MSE)—were used to evaluate the two parameter identification algorithms.

[0135] (25)

[0136] (26)

[0137] (27)

[0138] In the formula: , These are the measured value and the predicted value, respectively. The number of data points.

[0139] Comparative analysis of the adaptive control law identification algorithm and the FFRLS algorithm in Table 1 shows that the adaptive control law identification algorithm for the first-order RC equivalent circuit model parameters improves the average relative error by 1.34 percentage points and the root mean square error by 2.824 percentage points compared to the FFRLS algorithm. The convergence time of the adaptive control law identification algorithm is also nearly 13 seconds faster than that of the FFRLS algorithm. Comparative analysis of the SOH identification errors of the adaptive control law algorithm and the FFRLS algorithm in Table 2 shows that the adaptive control law algorithm is superior to the FFRLS algorithm. This further demonstrates that the adaptive control law identification algorithm proposed in this paper has higher accuracy, stability, faster convergence speed, and stronger nonlinear prediction capability.

[0140] Table 1. Comparison of Parameter Identification Errors between Adaptive Control Law Algorithm and FFRLS Algorithm

[0141]

[0142] Table 2. Comparison of SOH identification errors between the adaptive control law algorithm and the FFRLS algorithm

[0143]

[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for parameter identification and state of health (SOH) estimation of a first-order RC equivalent circuit model of a lithium battery for vehicle, characterized in that, Includes the following steps: 1) Analysis of the principle of identifying unknown parameters in chaotic systems; 2) Based on the characteristic that a chaotic system composed of a charge-controlled memristor can generate rich chaotic dynamic behaviors, the charge-controlled memristor electronic components are connected as loads to the output terminal of a first-order RC equivalent circuit model to establish a fourth-order chaotic system. 3) Analyze the phase trajectory diagram and time domain waveform diagram of the fourth-order chaotic system to determine its dynamic characteristics; 4) Construct an adaptive control law for the unknown parameters of a fourth-order chaotic system to achieve parameter identification and SOH estimation of the first-order RC equivalent circuit model; The principle analysis for identifying unknown parameters in chaotic systems described in step 1) is as follows: Assume a four-dimensional hyperchaotic system is as follows: （1）; in, For state variables; For unknown parameters of the system, If system parameters space is ,but become: （2）; for Other parts that do not contain parameters Equation (2) above satisfies the Lipschitz condition, that is, for any , and initial value There exists a constant for each. satisfy: （3）; To effectively identify all parameters of a chaotic system based on a first-order RC equivalent circuit using a memristor, at least two time series are required if there are two Lyapunov exponents greater than zero. Therefore, constructing a linear response system according to equation (1) yields the following dynamic equation: （4）; In the formula, , and ensure the relationship It also holds true. Assume the difference between the variables in system (2) and (4) is And the following relationship exists: （5）; Decoupling coefficients and unknown system parameters The adaptive control law over time is as follows: （6）; In the formula, , , It is a constant. The nonnegative Lyapunov function for constructing a chaotic system is: （7）; In the formula, It is a constant. but The derivative with respect to time is: （8）; When taking When, in equation (8) Established, Therefore, as long as the driving quantity is appropriately selected so that equation (5) satisfies the Lipschitz condition, the adaptive control law (6) can be used to make the driving system (1) and the response system (4) achieve adaptive synchronization. When the two hyperchaotic systems, the driver and the response, achieve complete synchronization, it is possible to Therefore, the unknown parameters in equation (1) of the driving system Complete identification is possible; Step 2) describes the method for establishing a fourth-order chaotic system as follows: A first-order RC equivalent circuit model is used to describe the kinetic characteristics of lithium-ion batteries during operation. , These are the open-circuit voltage and terminal voltage of the first-order RC equivalent circuit model, respectively. These are the polarization resistance and ohmic internal resistance of the first-order RC equivalent circuit model, respectively. The polarization capacitor is the one used in the first-order RC equivalent circuit model. A chaotic system is established using a charge-controlled memristor and a first-order RC equivalent circuit. The mathematical function of the memristor's gain M(q) is: （9）; In the formula: , All are constants, and , , Based on the chaotic system model diagram of the RC equivalent circuit based on memristors These are two inductor coils of different sizes; For resistance; For charge-controlled memristors; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; for The voltage across the two ends; For flow The current; For flow The current; For flow The current, Based on the KCL and KVL laws, assume The direction shown is the reference direction of the current, so the differential equation of the circuit model can be obtained as follows: （10）; The memristor value of memristor M(q) is... , , Will Substitute into equation (10) and let ,Pick Let there be 4 state variables, and let Then we can obtain: （11）; Equation (11) above is the mathematical model of the dynamics of a fourth-order chaotic system constructed by a charge-controlled memristor and a first-order RC equivalent circuit. Step 3) analyzes the phase trajectory diagram and time-domain waveform diagram of the fourth-order chaotic system's dynamic characteristics. The method is as follows: When the parameters in the fourth-order chaotic system dynamic mathematical model are respectively taken as: , In At the same time, From equation (11), we can obtain: （12）; In the formula: , , , From equation (12) above, it can be seen that the unknown parameters of the constructed first-order RC equivalent circuit chaotic system based on memristors are: ,in With ohmic resistance A linear relationship exists. It is the reciprocal of the polarization capacitance. The product of polarization resistance and polarization capacitance is given by the state variable: , , , , when When the initial value of the system is set to (0.0, 0.01, 0.0, 0.0), a simulation experiment is conducted using MATLAB software with a step size of 0.01 using the fourth-order Runge-Kutta method. The simulation results show that the system constructed by equation (12) generates a double-vortex chaotic attractor. For equation (12), the chaotic system was obtained by MATLAB simulation. hour, Furthermore, when the initial values ​​of the system are set to (0.0, 0.04, 0.0, 0.0), the Lyapunov exponents of the fourth-order chaotic system are LE1>0, LE2>0, LE3<0, and LE4<0, in the form of (+, +, -, -). This indicates that the fourth-order chaotic system generates a double vortex attractor and belongs to the fourth-order hyperchaotic system. Step 4) involves parameter identification and SOH estimation of the first-order RC equivalent circuit model, and the method is as follows: Construct a linear drive system based on equation (4), and select... As a driving variable, then Let the adaptive control law of the parameters of the coupled system with time be... （13）; Assume the initial points of the driving system and the response system are selected as follows: , ,parameter for The estimated values, the relationship between A and R0 is A = 1.1 * R0, and the relationship between B and C1 is... The relationship between C and R1, C1 is as follows: Unknown parameters in the response system The initial values ​​were set to (0.25, 14.19, 0.36). Simulation verification showed that the driving system was in a hyperchaotic state at this time. The parameters in the driving system were then... The current value is set to (0.19, 14, 4.4). Using the adaptive control law (13), the fourth-order Runge-Kutta method with a step size of 0.01 is used to simulate the adaptive control law through MATLAB software. The simulation results show that the unknown variable After 2 seconds, it quickly stabilized at values ​​of 0.1912, 14.012, and 4.432, consistent with the drive system parameters. The relative errors of the current set values ​​(0.19, 14, 4.4) are 0.63%, 0.86%, and 0.73%, respectively. The parameters can be calculated according to the following formula (14). Identification value Therefore, it can be seen that under the action of the controller and the adaptive control law, the adaptive control law can quickly and accurately identify the parameters of the first-order RC equivalent circuit model online. （14）; Using the SOH definition method based on internal resistance, the SOH expression is shown below. （15）; In the formula, , , These are the ohmic internal resistances of the automotive lithium battery when it reaches its end-of-life (EOL), the current actual ohmic internal resistance, and the ohmic internal resistance of the new battery, respectively. Therefore, the identification value of the ohmic internal resistance is determined using a first-order RC equivalent circuit model. According to formula (15), the estimated SOH value of lithium-ion battery can be obtained.

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