JP6737490B2 - System identification method and system identification device - Google Patents

Description

The present disclosure relates to a system identification method and a system identification device.

An apparatus for identifying a system parameter representing a battery model is known (for example, refer to Patent Document 1).

JP, 2017-198542, A

When installed in a vehicle, the battery discharges to provide the current the vehicle needs to operate. When the discharge current increases, the overvoltage of the battery increases and the terminal voltage of the battery decreases. If the terminal voltage of the battery drops, the battery may not be able to supply the current required by the vehicle. In order to determine whether the battery can supply the current required by the vehicle, it is necessary to estimate the overvoltage at the start of discharging the battery with high accuracy.

An object of the present disclosure made in view of such circumstances is to provide a system identification method and a system identification device that can accurately estimate an overvoltage at the start of discharge of a battery.

In order to solve the above problems, the system identification method according to the first aspect is executed by a system identification device that estimates a response of a system that receives a current flowing in a battery as an input and outputs an overvoltage of the battery as an output. The system identification method applies a model of the battery including an FIR model and an ARX model to the system based on time series data of a current flowing through the battery and an overvoltage of the battery within a predetermined period. A first step of identifying the system by. In the system identification method, when no current is input to the system identified in the first step before the input start time and a current is input after the input start time, the system identification method is performed after the input start time. A second step of estimating an overvoltage of the battery output by the system at a later estimation target time based on the model of the battery applied to identify the system in the first step. Of the time series data, the number of data applied to the FIR model is equal to or more than a number obtained by adding 1 to the number obtained by dividing the time from the input start time to the estimation target time by the sampling period.

In order to solve the above problems, a system identification device according to a second aspect includes a response estimation unit that estimates a response of a system in which a current flowing in a battery is input and an overvoltage of the battery is output. The response estimation unit applies a model of the battery including an FIR model and an ARX model to the system based on time series data of a current flowing in the battery and an overvoltage of the battery within a predetermined period. Thereby identifying the system. In the case where no current is input to the identified system before the input start time and a current is input after the input start time, the response estimation unit sets the estimated target time after the input start time. An overvoltage of the battery output by the system is estimated based on a model of the battery applied to identify the system. Of the time series data, the number of data applied to the FIR model is equal to or more than a number obtained by adding 1 to the number obtained by dividing the time from the input start time to the estimation target time by the sampling period.

According to the system identification method of the first aspect, the overvoltage at the start of discharging the battery can be estimated with high accuracy.

According to the system identification device of the second aspect, the overvoltage at the start of discharging the battery can be estimated with high accuracy.

It is a block diagram showing an example of composition of a system identification device concerning one embodiment. It is a figure which shows an example of a battery equivalent circuit. It is a figure which shows a 4th order Foster type RC ladder circuit. It is a figure which shows an example of a SOC-OCV characteristic. It is a block diagram showing an example of composition of a vehicle carrying a system identification device. It is a figure explaining the concept of a μ-Markov model. It is a flowchart which shows an example of a system identification method. 9 is a graph showing an example of the result of estimating the overvoltage for 1 second when μ representing the number of terms of the FIR model included in the μ-Markov model is set to 10. 9 is a graph showing an example of the result of estimating the overvoltage until 10 seconds after, when μ representing the number of terms of the FIR model included in the μ-Markov model is set to 100.

As shown in FIG. 1, the system identification device 1 according to the embodiment includes an observer 10, a response estimation unit 20, and a calculator 25.

The system identification device 1 may be composed of, for example, a processor or a microcomputer. The function of each component provided in the system identification device 1 may be realized by executing a program by a processor or the like, or may be realized by a dedicated processor specialized for specific processing. The system identification device 1 may include a storage unit. The storage unit may be composed of, for example, a semiconductor memory or a magnetic storage device. The system identification device 1 may store data, information, or the like handled in the processing in the storage unit.

The system identification device 1 is connected to a battery 4 via a current sensor 2 and a voltage sensor 3. The system identification device 1 may include a current sensor 2 or a voltage sensor 3.

The battery 4 may be a secondary battery, for example. 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 current sensor 2 measures the charging/discharging current flowing in the battery 4. In the present embodiment, the time is represented by t. The charge/discharge current is represented by u(t) as a function of time. The current sensor 2 outputs the measured value of the charge/discharge current to the system identification device 1.

The voltage sensor 3 measures the terminal voltage of the battery 4. In this embodiment, the terminal voltage is represented by y(t) as a function of time. The voltage sensor 3 outputs the measured value of the terminal voltage to the system identification device 1.

The terminal voltage of the battery 4 is represented as the sum of the open circuit voltage (OCV: Open Circuit Voltage) of the battery 4 and the overvoltage generated inside the battery 4. OCV is the potential difference between the electrodes of the battery 4 in the electrochemical equilibrium state. OCV corresponds to the terminal voltage of the battery 4 when the charging/discharging current does not flow in the battery 4. Overvoltage corresponds to the magnitude of the voltage drop that occurs at the internal impedance. The internal impedance is determined according to the reaction rate of the electrochemical reaction inside the battery 4.

The terminal voltage of the battery 4 changes as a charging/discharging current flows through the battery 4. When the battery 4 is represented as a system, the charge/discharge current flowing in the battery 4 corresponds to the input to the system. The terminal voltage of the battery 4 corresponds to the output of the system. The system identification device 1 identifies a system parameter representing the battery 4.

The state of the battery 4 can be represented by a model including the OCV of the battery 4 and an overvoltage generated inside the battery 4 as parameters. It is assumed that the model representing the state of the battery 4 is approximated by the battery equivalent circuit 4a illustrated in FIG. The model approximated by the battery equivalent circuit 4a is also called a battery model. The input of the battery equivalent circuit 4a corresponds to the charging/discharging current u(t) flowing in the battery 4. It is assumed that the battery 4 is charged when the charge/discharge current u(t) flows in the direction of the arrow. That is, the direction of the arrow represents the direction of the current that charges the battery 4. When the current for charging the battery 4 flows, u(t) has a positive value. When the discharge current flows from the battery 4, u(t) has a negative value. The output of the battery equivalent circuit 4a corresponds to the terminal voltage y(t) of the battery 4. It is assumed that the sign of y(t) is specified by the direction of the arrow. In FIG. 2, y(t) is assumed to be a positive value when the potential of the terminal 41a located on the tip side of the arrow is higher than the potential of the terminal 41b located on the end side of the arrow. The terminals 41a and 41b correspond to the positive electrode terminal and the negative electrode terminal of the battery 4, respectively.

The OCV of the battery 4 is represented as the voltage output by the voltage source 42 in the battery equivalent circuit 4a. The voltage output by the voltage source 42 is represented by OCV(t) as a function of time. The sign of OCV(t) is specified by the direction of the arrow. In FIG. 2, OCV(t) has a positive value when the potential on the tip side of the arrow is higher than the potential on the tip side of the arrow. OCV(t) corresponds to the terminal voltage of the battery 4 when the charging/discharging current does not flow in the battery 4. When the charging/discharging current does not flow in the battery 4, it can be said that u(t)=0. When u(t)=0, y(t)=OCV(t) holds.

The overvoltage of the battery 4 is represented as a voltage across the internal impedance 44 in the battery equivalent circuit 4a. The overvoltage of the battery 4 is represented by η(t) as a function of time. The sign of η(t) is specified by the direction of the arrow. In FIG. 2, η(t) is a positive value when the potential on the tip side of the arrow is higher than the potential on the tip side of the arrow. If u(t) is a positive value, then η(t) is a positive value.

The terminal voltage of the battery 4 is represented by the sum of the OCV of the battery 4 and the overvoltage. That is, y(t)=OCV(t)+η(t) holds. When a current for charging the battery 4 flows, that is, when u(t) has a positive value, η(t) has a positive value. In this case, y(t)>OCV(t) holds. When the discharge current flows from the battery 4, that is, when u(t) has a negative value, η(t) has a negative value. In this case, y(t)<OCV(t) holds.

The internal impedance 44 may be represented by, for example, as shown in FIG. 3, a circuit in which a Warburg impedance including resistors R1 to R4 and capacitors C1 to C4 and a resistor R0 are connected in series. The resistance R0 represents resistance caused by a migration process or the like of the battery 4 in the electrolytic solution. The Warburg impedance represents the impedance caused by the diffusion process of ions in the battery 4. The overvoltage of the battery 4 is represented as a voltage drop generated in the internal impedance 44 of the battery 4 due to the current flowing in the battery equivalent circuit 4a. In FIG. 3, the potential difference between the terminals 41c and 41d corresponds to the overvoltage.

The Warburg impedance is represented as a fourth-order Foster-type circuit. The quartic Foster-type circuit includes four parallel circuits in which a resistor and a capacitor are connected in parallel. Each parallel circuit is connected in series. The four resistors and the four capacitors included in the fourth-order Foster-type circuit are represented as R1 to R4 and C1 to C4, respectively. The order of the Foster-type circuit that represents the internal impedance 44 is not limited to the fourth order, and may be the third order or lower or the fifth order or higher. The internal impedance 44 is not limited to the Foster type circuit, and may be represented by a Cowell type circuit or another linear transfer function model.

The voltage drop in each parallel circuit is represented by v ₁ (t) to v ₄ (t) as a function of time. The voltage drop across the resistor R0 is represented as R0×u(t). In this case, η(t)=R0×u(t)+v ₁ (t)+v ₂ (t)+v ₃ (t)+v ₄ (t).

The parameters of the battery equivalent circuit 4a approximating the battery 4 include the resistance values of the resistors R1 to R4 forming the Warburg impedance, the capacitance values of the capacitors C1 to C4, and the resistance value of the resistor R0. In the present embodiment, it is assumed that the parameters of the battery equivalent circuit 4a are preset. The parameters of the battery equivalent circuit 4a may be sequentially estimated by a Kalman filter or the like.

The OCV of the battery 4 is represented as a function of the state of charge (SOC) of the battery 4. That is, the state of the battery 4 is represented by the SOC of the battery 4 and the overvoltage. The SOC is represented as the ratio of the charge amount to the charge capacity of the battery 4. The relationship between SOC and OCV is called the SOC-OCV characteristic. The SOC-OCV characteristic can be represented by the graph shown in FIG. 4, for example. The horizontal axis and the vertical axis in FIG. 4 represent SOC and OCV, respectively. The SOC-OCV characteristic can be obtained in advance by experiments or the like. The observer 10 can estimate the OCV of the battery 4 based on the SOC estimated value of the battery 4 and the SOC-OCV characteristic of the battery 4. The OCV estimation result by the observer 10 is referred to as an OCV estimated value.

The observer 10 estimates the state of the battery 4 by estimating the SOC and overvoltage of the battery 4. The estimation results of the SOC and the overvoltage by the observer 10 are referred to as the SOC estimation value and the overvoltage estimation value, respectively. Let SOC be represented by SOC(t) as a function of time. When the model of the battery 4 is approximated by the battery equivalent circuit 4a, the system state variables include v ₁ (t) to v ₄ (t). That is, the observer 10 estimates the _{SOC (t), v 1 (} t) ~v 4 and (t).

The SOC and overvoltage of the battery 4 are included in the state variables of the system that represent the model of the battery 4. That is, the observer 10 estimates the state of the battery 4 by estimating the state variable of the system. The observer 10 is also called a state estimator. When the observer 10 cannot directly observe at least a part of the state variables, the observer 10 estimates the state variables that cannot be directly observed based on the input and the output.

The observer 10 can calculate the OCV estimated value of the battery 4 based on the SOC estimated value included in the state variable of the battery 4. The observer 10 can estimate the terminal voltage of the battery 4 based on the OCV estimated value of the battery 4 and the overvoltage estimated value of the battery 4. The observer 10 acquires the measured value of the terminal voltage of the battery 4 and calculates the difference between the measured value of the terminal voltage and the estimated value of the terminal voltage as an estimation error. The observer 10 calculates a parameter to be fed back to the estimated value of the state variable of the system representing the battery 4 based on the estimation error. The parameter fed back to the estimated value of the state variable is also called the state variable correction value. The observer 10 calculates the product of the estimation error and a predetermined coefficient matrix as the state variable correction value. The predetermined coefficient matrix is also called an observer gain. Each element of the observer gain may be a function of the charging/discharging current flowing in the battery, or may be a constant. The observer gain is preset based on the parameters of the equivalent circuit representing the battery 4.

The observer 10 includes a state variable estimation unit 11, an OCV calculation unit 12, and a feedback unit 13. The feedback unit 13 includes a terminal voltage calculation unit 14, a comparator 15, and a state variable correction value calculation unit 16.

The state variable estimation unit 11 estimates the SOC and overvoltage of the battery 4 as the state variables of the system representing the battery 4, based on the measured value u(t) of the charging/discharging current flowing in the battery 4 acquired from the current sensor 2. .. The state variable estimation unit 11 outputs the SOC estimated value to the OCV calculation unit 12 and the overvoltage estimated value to the terminal voltage calculation unit 14. The SOC estimated value is represented as a term with a symbol ^ added to SOC(t). A term with a symbol ^ added to SOC(t) is represented as SOC^(t). The estimated overvoltage value is represented by adding a symbol ^ on η(t) representing the overvoltage. A term with a symbol ^ added to η(t) is represented as η^(t).

The OCV calculation unit 12 calculates the OCV estimated value based on the SOC estimated value acquired from the state variable estimation unit 11 and the SOC-OCV characteristic. The OCV estimated value is expressed as a term with a symbol ^ added to the OCV(t). A term with a symbol ^ added to OCV(t) is represented as OCV^(t). The OCV calculator 12 outputs the OCV estimated value to the terminal voltage calculator 14.

The terminal voltage calculation unit 14 calculates the terminal voltage estimated value based on the OCV estimated value and the overvoltage estimated value. The estimated terminal voltage value is represented as a term with y added to y(t). A term with a symbol ^ added to y(t) is represented as y^(t). The terminal voltage calculator 14 outputs the estimated terminal voltage value to the comparator 15.

The comparator 15 calculates an estimation error based on the measured value y(t) of the terminal voltage of the battery 4 acquired from the voltage sensor 3 and the estimated terminal voltage value y^(t) acquired from the terminal voltage calculation unit 14. calculate. The estimation error is represented as a term with y added to the symbol y(t). A term with a symbol ~ added to y(t) is represented as y~(t). In this case, y~(t)=y(t)-y^(t) holds. The comparator 15 outputs the estimation error to the state variable correction value calculation unit 16.

The state variable correction value calculation unit 16 calculates the state variable correction value based on the estimation error and the observer gain and outputs it to the state variable estimation unit 11. The state variable estimation unit 11 estimates the state variable further based on the state variable correction value, thereby feeding back the estimation error to the estimated value of the state variable and bringing the estimated value of the state variable close to the true value of the state variable. it can.

The observer 10 can bring the estimated value OCV^(t) of the OCV of the battery 4 closer to the true value by feeding back the estimation error. The observer 10 outputs OCV^(t) to the calculator 25. The calculator 25 calculates the difference between the measured value y(t) of the terminal voltage of the battery 4 and OCV^(t) as the overvoltage of the battery 4. The overvoltage calculated by the calculator 25 is referred to as an overvoltage calculated value. The calculated overvoltage value is represented by ηc(t). The calculator 25 outputs the calculated overvoltage ηc(t) to the response estimation unit 20. The response estimation unit 20 acquires the measured value u(t) of the charge/discharge current of the battery 4 and the calculated overvoltage ηc(t) of the battery 4 as time series data. The time series data may include data sampled at a predetermined cycle. The predetermined cycle may be set appropriately. The response estimation unit 20 identifies the system parameter representing the battery 4 based on the time series data of u(t) and ηc(t). The response estimation unit 20 estimates the terminal voltage output by the battery 4 as a response of the system when a predetermined current is input to the battery 4 based on the identified parameter.

As shown in FIG. 5, it is assumed that the system identification device 1 according to the embodiment is mounted on the vehicle 100. Vehicle 100 may include a vehicle that is driven by an engine that is driven by using gasoline, diesel, or the like, or may be a vehicle that is driven by an electric motor.

The vehicle 100 is further equipped with the battery 4. The battery 4 supplies a discharge current to a starter motor that starts the engine or a motor such as a drive motor that becomes the power of the vehicle 100. The battery 4 may charge the electric power regenerated by the electric motor when the vehicle 100 is braked, the electric power generated by the alternator attached to the engine, the electric power supplied by the ground charging facility, or the like.

The vehicle 100 may include a controller 110 such as an ECU (Engine Control Unit). The controller 110 controls the engine or the motor according to the traveling state of the vehicle 100. The controller 110 may be configured separately from the system identification device 1. In this case, the controller 110 may acquire various information such as the identification result of the system representing the model of the battery 4 from the system identification device 1. The controller 110 may implement the function of the system identification device 1 as part of its function. In the present embodiment, it is assumed that the controller 110 realizes the function of the system identification device 1.

The vehicle 100 may further include the display unit 70. The controller 110 may cause the display unit 70 to display various information regarding the vehicle 100. The display unit 70 may display information regarding the state of the battery 4, for example. By doing so, vehicle 100 can notify the driver of various information.

The controller 110 discharges the battery 4 or charges the battery 4 according to an operation such as starting or stopping of the vehicle 100. That is, the charging/discharging current of the battery 4 changes according to the operation of the vehicle 100. When the charging/discharging current of the battery 4 changes, the overvoltage which represents the voltage drop in the internal impedance 44 of the battery 4 changes. The internal impedance 44 of the battery 4 is included in the system parameters representing the model of the battery 4. That is, the overvoltage of the battery 4 is determined based on the system parameters representing the model of the battery 4 and the charge/discharge current of the battery 4.

The battery 4 supplies, for example, the electric current necessary for driving the starter motor so that the starter motor can start the engine of the automobile. In this case, the current discharged by the battery 4 rapidly increases and the overvoltage of the battery 4 increases. When the battery 4 is discharged, the terminal voltage of the battery 4 is represented as a voltage obtained by subtracting the overvoltage from the open circuit voltage. That is, the terminal voltage of the battery 4 decreases as the discharge current increases. Due to the decrease in the terminal voltage of the battery 4, the battery 4 may not be able to supply the current required to drive the starter motor.

The controller 110 may stop the engine from idling when the vehicle 100 is stopped. The controller 110 may determine whether the engine can be restarted after the idling stop, and may stop the engine when it determines that the engine can be restarted. The controller 110 may determine whether the engine can be restarted based on the state of the battery 4. That is, the controller 110 may determine whether to stop the engine idling based on the state of the battery 4.

If the internal resistance of battery 4 is high when battery 4 begins to discharge, battery 4 may not be able to supply the current required to restart the engine. The controller 110 may estimate the output of the overvoltage according to the input of the predetermined current. The controller 110 inputs the current supplied by the battery 4 to restart the engine as a predetermined current into the system, estimates the overvoltage as a response of the system, and determines whether the predetermined current can be supplied based on the estimation result. Good.

The controller 110 may determine whether the engine can be restarted by estimating the internal resistance of the battery 4 when the battery 4 begins to discharge. The controller 110 may determine whether the engine can be restarted based on the internal resistance of the battery 4 at a time t seconds after the battery 4 starts to discharge. The internal resistance of the battery 4 at the time t seconds after the time when the battery 4 starts discharging is referred to as a t-second value resistance. The controller 110 may determine that the engine can be restarted when the t-second value resistance is less than the determination reference value. The determination reference value may be set based on the magnitude of the current that the battery 4 can supply. The determination reference value is not limited to this example and may be set as appropriate.

For example, the battery 4 needs to discharge at least the current for driving the motor for the time for cranking when the engine restarts from the idling stop. The time for the engine to perform cranking is also called the cranking time. The cranking time is set to 0.1 second, for example. In this case, the controller 110 may determine that the engine can be restarted from idling when the t-second value resistance when the cranking time is set as t seconds is less than the determination reference value.

For example, a vehicle equipped with an engine and a motor may drive the motor as needed while the engine is running to assist the engine. Such a vehicle is also called a parallel hybrid vehicle. In a parallel hybrid vehicle, when the engine load is large during acceleration traveling or uphill traveling, the battery 4 needs to discharge the current for driving the motor for the time the motor assists the engine. The time during which the motor assists the engine is also called the assist time. The assist time is set to 10 seconds, for example. In this case, the controller 110 may determine that the motor can assist the engine when the t-second value resistance when the assist time is set as t seconds is less than the determination reference value. The controller 110 may calculate the time during which the motor can assist the engine by calculating the value of t so that the condition that the t-second value resistance is less than the determination reference value is satisfied. The controller 110 can continuously estimate the time during which the motor assist is possible by sequentially updating the t-second value resistance corresponding to the assist time.

For example, in a vehicle equipped with an engine and a motor, the engine may generate electric power to supply electric power to the motor and charge the battery 4 while traveling by the motor. Such a vehicle is also called a series hybrid vehicle. The series-type hybrid vehicle has, as traveling modes, an EV mode in which the motor is driven only by the electric power of the battery 4 to travel, and a hybrid mode in which the electric power of the battery 4 and the electric power generated by the engine and the motor is driven to travel. .. In a series hybrid vehicle, the running mode may be preferentially set to the EV mode in order to reduce the electric power generated by the engine as much as possible. The battery 4 needs to discharge the current for driving the motor for the time the vehicle travels in the EV mode. The time that the vehicle travels in the EV mode is also referred to as the EV travel time. The EV running time is set to, for example, 10 seconds. In this case, the controller 110 may determine that the vehicle can travel in the EV mode if the t-second value resistance when the EV travel time is set as t seconds is less than the determination reference value. The controller 110 may calculate the time during which the vehicle can travel in the EV mode by calculating the value of t such that the condition that the t-second value resistance is less than the determination reference value is satisfied. The controller 110 can continuously estimate the time during which the vehicle can travel in the EV mode by sequentially updating the t-second value resistance corresponding to the EV travel time.

The controller 110 may acquire the terminal voltage of the battery 4 output by the system when a predetermined current is input to the system representing the model of the battery 4. The controller 110 may calculate, as a t-second value resistance, a ratio of the terminal voltage of the battery 4 and the predetermined current at a time t seconds after the time when the predetermined current is started to be input to the system.

The controller 110 can highly accurately determine whether or not the engine can be restarted by calculating the t-second value resistance of the battery 4 with high accuracy. As a result, the controller 110 can highly accurately determine whether to stop the engine at idling. The controller 110 may cause the display unit 70 to display the determination result as to whether or not to stop the engine idling.

In the present embodiment, the controller 110 estimates the overvoltage output when a step current is input to the battery 4. The step current is expressed as a current that does not flow before the predetermined time and flows at a constant value after the predetermined time. The overvoltage output as a response to the input of the step current is called the step response. If the constant value is 1 amp, the step response after t seconds represents t seconds value resistance.

In order to estimate the t-second value resistance of the battery 4 with high accuracy, it is required to estimate with accuracy the overvoltage of the battery 4 output by the system when a current is input to the system representing the battery model. The system identification device 1 applies an input/output model that specifies a relationship between an input and an output of the system to the system, and identifies parameters of the input/output model to be applied, thereby highly accurately determining the output of the system with respect to a predetermined input. Can be estimated by

In the present embodiment, the system representing the battery model is considered to be a discrete time system. The sampling period in a discrete time system is represented by Ts. The inputs and outputs in the continuous time system are denoted u(t) and y(t), respectively, using time t. It is assumed that the input and the output in the discrete-time system are represented by u[k] and y[k], respectively. In this case, k represents the number of sampling steps. Further, it is assumed that t=kTs holds. It is assumed that the current starts to be input to the system at time (t=0) corresponding to k=0. t=0 is also referred to as an input start time. When the output y[k] of the kth step is estimated, the time (t=kTs) corresponding to the kth step is referred to as the estimation target time. The estimation target time is a time after the input start time.

In this embodiment, the input/output model is assumed to be approximated by a predetermined model. It is assumed that the predetermined model is represented by a linear transfer function. The system identification device 1 can estimate the response after t seconds by specifying the parameters of the transfer function representing a predetermined model.

<ARX model>
It is assumed that an ARX (Auto Regressive eXogenous) model is applied as a predetermined model that approximates the input/output model. The ARX model can represent a system with a finite number of parameters.

式（１）において、ａ₁〜ａ_na、及び、ｂ₀〜ｂ_nbは、ＡＲＸモデルのパラメータである。ｎ_a及びｎ_bは、ＡＲＸモデルの次数を表している。ｗ［ｋ］は、その平均値が０となる白色雑音である。 The ARX model is described by the difference equation represented by the following equation (1).

In Expression (1), a _{1 to} a _na and b _{0 to} b _nb are parameters of the ARX model. n _a and n _b represent the orders of the ARX model. w[k] is white noise whose average value is 0.

Ｔは、転置行列を表している。 The parameter vector θ and the data vector ψ of the ARX model are represented by the following equations (2) and (3), respectively.

T represents a transposed matrix.

By applying the expressions (2) and (3) to the expression (1), the expression (1) is transformed into the following expression (4).

The model represented by equation (4) is called a linear regression model. The system identification device 1 can estimate the parameter vector θ of the linear regression model by analyzing the input data and the output data of the system by a method such as the least square method. The system identification device 1 can calculate the t-second value resistance as the response of the system based on the ARX model to which the estimated parameters are applied. The parameter estimation in the ARX model corresponds to the parameter estimation of the transfer function.

In the ARX model, the number of parameters represents the order of the ARX model. If the order of the ARX model is different from the order of the true system, the parameter estimation error will be large. As a result, the estimation error of the t-second value resistance calculated as the response of the system becomes large.

<FIR model>
It is assumed that a FIR (Finite Impulse Response) model is applied as a predetermined model that approximates the input/output model. The FIR model can represent the response after t seconds as the sum of the impulse responses at the sampling time between the start time and the time after t seconds. The t-second value resistance is expressed as the sum of impulse responses to the input at each time during the time from the time when the resistance value is estimated to the time t seconds before. The system identification device 1 can easily calculate the t-second value resistance by applying the FIR model.

式（１）において、ｂ₀〜ｂ_nfは、ＦＩＲモデルのパラメータである。ｎ_fは、ＦＩＲモデルの項数を表している。つまり、式（５）で表されるＦＩＲモデルは、（ｎ_f＋１）個のインパルス応答で打ち切られている。ｗ［ｋ］は、ｕ［ｋ］と独立であり、且つ、その平均値が０となる白色雑音である。 The FIR model is described by the difference equation represented by the following equation (5).

In Expression (1), b _{0 to} b _nf are parameters of the FIR model. n _f represents the number of terms in the FIR model. That is, the FIR model represented by the equation (5) is censored with (n _f +1) impulse responses. w[k] is white noise that is independent of u[k] and has an average value of 0.

The FIR model is represented by a linear regression model like the ARX model. The system identification device 1 can estimate the parameters of the linear regression model by analyzing the input data and the output data of the system by a method such as the least square method. The system identification device 1 sets t _f value resistance based on the impulse response calculated as a parameter of the FIR model by setting n _f representing the number of terms of the FIR model so that t≦Ts·n _f holds. Can be calculated. The impulse response estimation in the FIR model corresponds to the estimation of the transfer function parameters.

If no noise is present, the impulse response g[k] of the FIR model is expressed by the following equation (6).

That is, the parameter b _{i of the} FIR model is equal to g[i] representing the value of the impulse response g[k] of the system after i steps. By applying the equation (6) to the equation (5), the equation (5) is transformed into the following equation (7). Expression (7) represents the value calculated as the output of the system when the FIR model is applied.

The system identification device 1 can estimate the output of the system by estimating the impulse response as a parameter of the FIR model regardless of the order of the system.

On the other hand, the true output of the system is represented by the convolution of the system's impulse response g[k] and the input u[k] as shown in equation (8) below.

According to equation (8), the true output of the system is described as the sum of an infinite number of impulse responses. On the other hand, according to equation (7), the output of the system represented by the FIR model is truncated with a finite number of (n _f +1) impulse responses. That is, the output of the system represented by the FIR model contains at least the error due to the truncated terms with respect to the true output of the system. The system identification device 1 can reduce the error by increasing the number of n _f . However, the larger the number of n _f, the larger the number of parameters that the system identification device 1 should identify. The increase in the number of parameters causes an increase in the load on the system identification device 1.

<μ-Markov model>
In the present embodiment, the μ-Markov model is applied as a predetermined model that approximates the input/output model. The μ-Markov model is represented as a model that combines the ARX model and the FIR model.

ｕ［ｋ］及びｙ［ｋ］はそれぞれ、システムの入力及び出力を表している。 The μ-Markov model in the discrete-time system is described in the form shown in the following Expression (9).

u[k] and y[k] represent the input and output of the system, respectively.

The first term on the right side of Expression (9) represents the FIR model. h _i (iε{0,..., μ}) represents the impulse response of the system. In this case, the number of terms described in the impulse response is (μ+1). If the model of the battery 4 has no direct term, h ₀ =0 holds. The second and third terms on the right side of Expression (9) represent the ARX model. a′ _i and b′ _i (iε{(μ+1),..., μ+p}) are parameters of the ARX model. p represents the order of the ARX model. w[k] is white noise that is independent of u[k] and has an average value of 0.

The μ-Markov model is represented by a linear regression model like the ARX model or FIR model. The system identification device 1 can estimate the parameters of the linear regression model by analyzing the input data and the output data of the system by a method such as the least square method.

The μ-Markov model is composed of (μ+1) inputs and (k-μ-1) to (k-μ-p) steps included in a period starting from the k-th step to the (k-μ)-th step. The output y[k] of the k-th step is determined based on the p inputs and outputs included in the period up to. That is, the system parameter representing the battery 4 is identified based on the time series data of the input and the output within the predetermined period. The input and the output correspond to the current flowing in the battery 4 and the overvoltage of the battery 4, respectively. The predetermined period corresponds to the period from the k-th step to the (k-μ-p) step.

The (μ+1) inputs in the period from the k-th step to the (k-μ)-th step are reflected in the output y[k] based on the terms of the FIR model included in the μ-Markov model. The period from the k-th step to the (k-μ)-th step is referred to as the first period. That is, the system identification device 1 estimates the overvoltage at the estimation target time, based on the value estimated by applying the input in the first period that goes back to the past from the estimation target time to the FIR model.

The p inputs and outputs in the period from the (k−μ−1)th step to the (k−μ−p)th step are output y[k] based on the terms of the ARX model included in the μ-Markov model. Reflected in. The period from the (k-μ-1)th step to the (k-μ-p)th step is referred to as a second period. That is, the system identification device 1 estimates the overvoltage at the estimation target time, based on the value estimated by applying the input in the second period that goes back to the past from the first period to the ARX model. In the μ-Markov model, the output estimation error caused by the application of the FIR model to the system is corrected by the application of the ARX model.

Here, the concept of the μ-Markov model will be described with reference to FIG. The graph shown in FIG. 6 represents the concept of calculating the estimated value of the output of the system at the estimation target time by integrating the components of the impulse response to the input at each past time. The horizontal axis of the graph represents steps in a discrete time system. A larger number of steps corresponds to a step that is traced back a long time in the past from the estimation target time. The vertical axis of the graph represents the signal strength of the impulse response. The estimated value of the output is calculated by calculating the product of the signal strength of the impulse response and the sampling period Ts in each step and integrating the values calculated in each step.

The estimated value of the output is approximated to the true value by integrating up to the component of the impulse response to the input at steps that were traced infinitely in the past. In the graph of FIG. 6, the area of the hatched portion with the diagonal line rising to the right represents the true value of the output at the estimation target time. However, the FIR model breaks the integration step into a finite number. The component integrated by the FIR model is represented by the dashed rectangle. In the FIR model, the impulse response that is four steps back from the estimation target time is integrated. The signal strength of the impulse response to the input at each step is represented by b ₁ ~b _4. It can be said that the component integrated by the FIR model contributes to the estimation based on the FIR model.

When a finite number of integrating steps are cut off, the components of the impulse response to the input at the steps going back to the past before the cut-off step are not integrated by the FIR model and are not reflected in the estimated value of the output. In FIG. 6, the components that are not reflected in the estimated output value in the FIR model are represented by the two-dot chain rectangle. The component represented by the two-dot chain line rectangle is reflected in the estimated value of the output when the number of steps integrated in the FIR model is increased. That is, as the number of steps integrated in the FIR model is increased, the output of the system is calculated as a value closer to the true value. As described above, when the parameters of the μ-Markov model are estimated based on the input data and the output data of the system, the parameters of the FIR model are estimated only by estimating the parameters of the FIR model. There is an error. That is, the estimation error of the parameters of the FIR model is due to the FIR model being cut off with a finite number of terms.

Here, the estimation error of the parameters of the FIR model is reduced by considering the term representing the ARX model. That is, the estimated values of the parameters of the FIR model are brought close to the true values. In FIG. 6, components represented by a two-dot chain line rectangle that are not reflected in the output estimated value in the FIR model are reflected in the output estimated value as terms representing the ARX model. In other words, the estimation based on the ARX model can complement the components that are not reflected in the estimated value of the output by the FIR model. By doing so, the system identification device 1 can bring the estimated values of the parameters of the FIR model close to the true value based on the ARX model configured by a finite number of terms. As a result, the output of the system based on the impulse response estimated by applying the μ-Markov model is closer to the true value than the output of the system based on the impulse response estimated by applying only the FIR model. In other words, the censored term that was supposed to continue infinitely in the FIR model is replaced by a finite number of terms that compose the ARX model. This allows the parameter estimation result to approach the true value without infinitely increasing the number of terms in the FIR model. In other words, the system identification device 1 can identify the system with high accuracy by applying the FIR model and the ARX model to identify the system.

By applying the μ-Markov model to the system, the system identification device 1 can accurately estimate the finite-time impulse response regardless of the true order of the system. The t-second value resistance is calculated based on the sum of finite time impulse responses. Therefore, the system identification device 1 can estimate the t-second value resistance of the battery 4 as the response of the system with high accuracy by applying the μ-Markov model to the system representing the model of the battery 4. The system identification device 1 can calculate the t-second value resistance as a ratio between the estimated overvoltage value at the estimation target time and the predetermined current input at the estimation target time.

<Example of battery estimation>
In the present embodiment, the system identification device 1 identifies the system parameters by applying the μ-Markov model to the system representing the battery model shown in FIGS. 2 and 3.

Equation (9) represents the impulse response and (mu + 1) number of parameters (h ₀ ~hμ), 2p number of parameters included in the ARX model (aμ ₊₁ ~aμ _{+ p,} and, bμ ₊₁ ~bμ _{+ p} ) and. The system identification device 1 can identify a system by estimating (μ+2p+1) parameters.

The system identification device 1 can estimate the system parameters based on an equation derived from a data set in which u(t) and ηc(t) are associated with each other. When there are Q unknown parameters, each parameter can be analytically calculated based on a simultaneous equation including at least Q equations. The μ-Markov model has (μ+2p+1) unknown parameters. Therefore, in order to analytically calculate each parameter of the μ-Markov model, at least (μ+2p+1) equations are required. One equation is derived based on one data set in which u(t) and ηc(t) are associated with each other. Therefore, at least (μ+2p+1) data sets are required.

The system identification device 1 may obtain, for example, (μ+2p+1) or more data sets in which the input and the output of the system are associated with each other. When the system identification device 1 acquires (μ+2p+1) or more data sets, it can set an equation including at least (μ+2p+1) parameters as unknowns. The system identification device 1 can analytically calculate (μ+2p+1) parameters by solving the equation. The system identification device 1 can calculate the system parameters with high accuracy by acquiring (μ+2p+1) or more data.

The system identification device 1 acquires the measured value u(t) of the current input to the system for T seconds and the overvoltage calculated value ηc(t) corresponding to the input current by sampling at a predetermined timing. You can If the system identification device 1 acquires u(t) and ηc(t) at the sampling cycle Ts, T representing the period of acquiring data is Ts and the number of data required for system identification. Is set to a value larger than the product of (μ+2p+1).

The more the u(t) and the ηc(t) are acquired, the system identification device 1 can bring the estimated values of the μ parameters representing the impulse response closer to the true value. That is, the parameters of the FIR model can be asymptotically estimated with respect to the true value. On the other hand, the estimated values of the 2p parameters included in the ARX model may not approach the true values regardless of the number of u(t) and ηc(t) data. That is, the parameters of the ARX model may have an error of a predetermined value or more with respect to the true value.

The system identification device 1 calculates an overvoltage output as a response from a system to which a predetermined current is input, based on the identified parameter of the μ-Markov model. In the present embodiment, it is assumed that the current is not input before the input start time and the predetermined current is input after the input start time. That is, it is assumed that no current is input to the system before the first step and a predetermined current is input to the system after the first step. In this case, the system identification device 1 can calculate the overvoltage as the response of the system. The system identification device 1 can calculate the overvoltage with high accuracy by calculating the overvoltage based on the parameter of the μ-Markov model. As a result, the overvoltage at the start of discharging the battery 4 is estimated with high accuracy.

When a predetermined current is input to the system for t seconds from the input start time to the estimation target time, the system identification device 1 is based on the overvoltage at the estimation target time and the predetermined current input to the battery 4 at the estimation target time. Thus, the t-second value resistance can be calculated. The system identification device 1 may calculate the ratio of the overvoltage and the predetermined current as the t-second value resistance. The system identification device 1 can calculate the t-second value resistance with high accuracy by calculating the overvoltage with high accuracy. When the system identification device 1 is installed in the vehicle 100, the system identification device 1 calculates the t-second value resistance with high accuracy, so that the controller 110 can determine with high accuracy whether or not to stop the engine idling. ..

If the predetermined current input after the input start time is a constant current, the system identification device 1 can calculate the overvoltage as the step response of the system. The system identification device 1 can calculate an overvoltage when a constant current is input to the system for t seconds as a t second value resistance. That is, when the overvoltage is calculated as the step response after t seconds, the calculated overvoltage is regarded as the t-second value resistance. By doing so, the system identification device 1 can easily calculate the t-second value resistance.

When μ≧t/Ts is satisfied for the number of terms (μ+1) described in the impulse response, the system identification device 1 can calculate the t-second value resistance based on only the impulse response parameter. In other words, the number of data applied to the FIR model in the time series data is the number obtained by dividing the time from the input start time to the estimation target time by the sampling period (corresponding to t/Ts) plus 1 ( If the number is equal to or larger than (corresponding to t/Ts+1), the system identification device 1 can calculate the t-second value resistance based on only the impulse response parameter. Furthermore, in other words, when the length of the first period is set to be equal to or longer than the length of the period from the input start time to the estimation target time, the system identification device 1 determines the time t seconds based on only the impulse response parameter. Value resistance can be calculated. Specifically, the system identification device 1 calculates the t-second value resistance as a value obtained by adding the coefficient hi of the first term on the right side representing the FIR model in the above equation (9) in the range of i=0 to μ. You can In other words, the system identification device 1 uses the coefficient of each term included in the period from the input start time to the estimation target time of the FIR model applied for identifying the system as the internal resistance of the battery 4 at the estimation target time. May be calculated. The coefficient of each term of the FIR model corresponds to the parameter of the impulse response. In other words, the system identification device 1 starts the input from the term corresponding to the input at the estimation target time in the model of the battery 4 applied to identify the system as the internal resistance of the battery 4 at the estimation target time. You may calculate the sum of the coefficient of each term to the term corresponding to the input in time.

The system identification device 1 calculates the t-second value resistance based only on the impulse response parameter, so that the t-second value does not depend on the parameter of the ARX model that may have an error of a predetermined value or more with respect to the true value. Value resistance can be calculated. As a result, the system identification device 1 can estimate the t-second value resistance with high accuracy regardless of the estimation accuracy of the parameters of the ARX model.

The number of data applied to the FIR model in the time series data corresponds to the number (μ+1) obtained by dividing the time from the input start time to the estimation target time by the sampling period (corresponding to μ) (μ+1). ) May be the same number. In other words, the system identification device 1 may set the length of the first period so that the length of the first period matches the length of the period from the input start time to the estimation target time. By doing so, the number of parameters of the FIR model is reduced within the range in which the t-second value resistance is calculated based only on the parameters of the impulse response. Reducing the number of parameters reduces the load of parameter estimation.

The system identification device 1, and the observer 10 and the response estimation unit 20 included in the system identification device 1 may execute the system identification method including the procedure of the flowchart shown in FIG. 7, for example.

The observer 10 acquires the measured value u(t) of the current flowing in the battery 4 and the measured value y(t) of the terminal voltage of the battery 4 (step S1). The observer 10 acquires u(t) from the current sensor 2. The current flowing through the battery 4 includes at least one of a current output by the battery 4 by discharging and a current input for charging the battery 4. The observer 10 acquires y(t) from the voltage sensor 3.

The observer 10 estimates the state variable of the system representing the battery model based on u(t) and y(t) (step S2). In the observer 10, the state variable estimation unit 11 calculates the SOC estimated value SOC^(t), and the OCV calculation unit 12 calculates the OCV estimated value OCV^(t). In the system identification device 1, the calculator 25 calculates the difference between OCV^(t) and y(t) as the overvoltage calculation value ηc(t). The system identification device 1 holds data that combines u(t) and ηc(t). The system identification device 1 may store the data in the storage unit.

The system identification device 1 determines whether data for a period of T seconds has been acquired (step S3). Let T be a value larger than the product of the sampling period Ts and the number of data required for system identification.

When the system identification device 1 has not acquired the data for the period of T seconds (step S3: NO), the system identification device 1 returns to the procedure of step S1.

When the system identification device 1 acquires the data for the period of T seconds (step S3: YES), the response estimation unit 20 identifies the system parameter representing the battery model (step S4). The response estimation unit 20 identifies the system based on the acquired data for T seconds. The response estimation unit 20 identifies the parameter of the μ-Markov model representing the system based on the acquired data for T seconds.

The response estimation unit 20 estimates the response when a predetermined current is input to the identified system (step S5). The response estimation unit 20 may calculate the overvoltage of the battery 4 as the response of the system. The response estimator 20 can calculate a value obtained by integrating the product of the impulse response at each sampling time and the instantaneous value of the predetermined current from the current input start time to the time t seconds later as the overvoltage. When the predetermined current input to the system has a constant value, the response estimation unit 20 can calculate the sum of impulse responses at each sampling time as the t-second value resistance.

The system identification device 1 can estimate the t-second value resistance of the battery 4 by using the model of the battery 4 illustrated in FIGS. 2 and 3 as a target system. The order of the model illustrated in FIGS. 2 and 3 is fourth order. Therefore, the order of the target system is the fourth order. The system identification device 1 can calculate the one-second value resistance by setting t to 1, for example.

As an example, it is assumed that the parameters of the internal impedance 44 of the battery 4 shown in FIG. 3 are set to the values shown below.
R0=3.6mΩ
R1=2.19mΩ
R2=0.243 mΩ
R3=8.75×10 ^-2 mΩ
R4=4.47×10 ^-2 mΩ
C1 to C4=6.72 kF
The sampling period Ts is set to 0.1 second. In this case, by setting μ to 10 or more, the one-second resistance is calculated based on only the impulse response parameter.

When the target system was discretized assuming a zero-order hold for the input signal to the target system, the following equation (10) was derived as a discrete-time transfer function.

By applying the μ-Markov model, ARX model, and FIR model to the target system assumed as described above, the estimation result of the one-second resistance in each model can be calculated. The true value of the one-second value resistor is 3.9699 mΩ.

As Case 1, it is assumed that the order p of the ARX model and the order p of the ARX model included in the μ-Markov model are set to the fourth order which is the order of the true system. It is assumed that n _f , which represents the number of impulse response terms in the FIR model, and μ, which represents the number of impulse response terms included in the μ-Markov model, are set to 10. The data used to identify the parameters of the target system is the normality of the measured value of the terminal voltage of the battery 4 representing the output of the target system, with the average value 0 as the observation noise and the variance of 1.0×10 ⁻⁷ . Suppose white noise is added.

The parameters of each model were identified under the condition that 1000 different noises were added. In each model, the one second resistance was estimated based on the identified parameters. The estimation result of the 1 second resistance for 1000 times was as follows. The unit is mΩ.
μ-Markov model: mean 3.9686, standard deviation ±3.6892×10 ^-3
ARX model: average value 4.0131, standard deviation ±5.7713×10 ^-3
FIR model: average value 3.9609, standard deviation ±2.9357×10 ^-3

Further, as Case 2, it is assumed that the order p of the ARX model and the order p of the ARX model included in the μ-Markov model are set to a quadratic order different from the quartic order of the true system. In Case 2, the estimation result of 1000 second 1 second value resistance was as follows. The unit is mΩ.
μ-Markov model: average value 3.9691, standard deviation ±3.6603×10 ^-3
ARX model: average value 3.9887, standard deviation ±6.4469×10 ⁻³
FIR model: average value 3.9609, standard deviation ±2.9357×10 ^-3

According to the above results, the estimated value of the 1-second value resistance when the μ-Markov model is applied is closer to the true value than the estimated value of the 1-second value resistance when the ARX model and the FIR model are applied. .. That is, the estimation accuracy of the one-second resistance when the μ-Markov model is applied is higher than the estimation accuracy of the one-second resistance when the ARX model and the FIR model are applied.

In this example, since μ representing the number of terms of the impulse response of the μ-Markov model is set to 10, the one-second resistance based on the μ-Markov model is the sum of the impulse responses from 0 step to 10 steps. Is calculated as That is, the one second resistance is calculated without being based on the parameters of the ARX model. As a result, whether the 1-second value resistance estimation accuracy based on the μ-Markov model is the case when the order of the ARX model matches the order of the true system (Case 1) or does not match (Case 2). Determined regardless. As a result, the estimation accuracy of the 1-second value resistance based on the μ-Markov model is higher than the estimation accuracy of the 1-second value resistance based on the ARX model.

In Case 2 described above, when normal white noise with an average value of 0 and a variance of 5.0×10 ⁻⁸ is added as the observation noise (Case 3), the step response of the overvoltage is as illustrated in the graph of FIG. It was calculated. The horizontal axis of the graph in FIG. 8 represents time. The unit of time is seconds. The vertical axis of the graph in FIG. 8 represents overvoltage. The unit of overvoltage is mV. The graph of FIG. 8 shows the calculation result of the step response of the overvoltage until 1 second later. Since the sampling period Ts is set to 0.1 second and μ representing the number of terms of the impulse response of the μ-Markov model is set to 10, one second after the one second shown in the graph of FIG. The one second value resistance corresponding to the step response of the overvoltage is calculated based only on the parameters of the impulse response.

In Case 3 described above, when μ representing the number of terms in the impulse response of the μ-Markov model is set to 100 (Case 4), the overvoltage step response is calculated as illustrated in the graph of FIG. 9. The horizontal axis of the graph in FIG. 9 represents time. The unit of time is seconds. The vertical axis of the graph in FIG. 9 represents overvoltage. The unit of overvoltage is mV. The graph of FIG. 9 shows the calculation result of the step response of the overvoltage until after 10 seconds. The sampling period Ts is set to 0.1 second, and μ representing the number of terms of the impulse response of the μ-Markov model is set to 100, so that 10 seconds after 10 seconds shown in the graph of FIG. The 10-second value resistance corresponding to the overvoltage step response is calculated based only on the parameters of the impulse response.

In the graphs of FIGS. 8 and 9, the true value is represented by a solid line. In Case 3 and Case 4, the calculation result of the step response based on the μ-Markov model was within the upper and lower limits represented by the broken line. On the other hand, the calculation results of the step response based on the FIR model in Case 3 and Case 4 were within the upper and lower limits represented by the one-dot chain line. The calculation result of the step response based on the ARX model was within the upper and lower limits represented by the chain double-dashed line. With reference to FIGS. 8 and 9, the calculation result of the step response based on the μ-Markov model is closer to the true value than the calculation result of the step response based on the FIR model and the ARX model. Further, the variation in the calculation result of the step response based on the μ-Markov model is smaller than the variation in the calculation result of the step response based on the FIR model and the ARX model. That is, the system identification device 1 can improve the estimation accuracy of the step response by identifying the system based on the μ-Markov model. Further, as the time elapses from the input start time, the step response estimation error increases. However, it can be said that the estimated value of the step response based on the μ-Markov model is unlikely to deviate from the true value even after 0.5 seconds elapses.

Although the embodiments according to the present disclosure have been described based on the drawings and the examples, it should be noted that those skilled in the art can easily make various variations or modifications based on the present disclosure. Therefore, it should be noted that these variations or modifications are included in the scope of the present disclosure. For example, the functions included in each constituent unit or each step can be rearranged so as not to logically contradict, and a plurality of constituent units and steps can be combined or divided into one. Is.

1 System Identification Device 2 Current Sensor 3 Voltage Sensor 4 Battery 4a Battery Equivalent Circuit 41a to 41d Terminal 42 Voltage Source 44 Internal Impedance 10 Observer 11 State Variable Estimator 12 OCV Calculator 13 Feedback Unit 14 Terminal Voltage Estimator 15 Comparator 16 State Variable correction value calculation unit 20 Response estimation unit 25 Computing unit 70 Display unit 100 Vehicle 110 Controller

Claims (9)

A system identification method executed by a system identification device that estimates the response of a system that receives a current flowing in a battery as an input and outputs the overvoltage of the battery,
The system is identified by applying a model of the battery including an FIR model and an ARX model to the system based on time series data of a current flowing in the battery and an overvoltage of the battery within a predetermined period. The first step to do,
In the system identified in the first step, when the current is not input before the input start time and the current is input after the input start time, at the estimated target time after the input start time. A second step of estimating an overvoltage of the battery output by the system based on a model of the battery applied to identify the system in the first step,
Of the time series data, the number of data applied to the FIR model is a number equal to or larger than the number obtained by dividing the time from the input start time to the estimation target time by the sampling period by one,
System identification method. The system identification method according to claim 1, wherein the time from the input start time to the estimation target time is a cranking time when the vehicle equipped with the system identification device restarts the engine after idling stop. The time from the input start time to the estimation target time is a time during which the motor is driving the vehicle while a vehicle equipped with an engine, a motor, and the system identification device is running. The system identification method described. As an internal resistance of the battery at the estimation target time, a coefficient of a term included in a period from the input start time to the estimation target time of the FIR model applied to identify the system in the first step. The system identification method according to any one of claims 1 to 3, wherein the sum of the above is calculated. The system identification method according to any one of claims 1 to 4, wherein in the second step, an overvoltage of the battery at the estimation target time is estimated when a constant-value current is input to the system. .. Of the time series data, the number of data applied to the term of the FIR model is the same as the number obtained by adding 1 to the number obtained by dividing the time from the input start time to the estimation target time by the sampling period. The system identification method according to any one of claims 1 to 5. 7. The system identification method according to claim 1, wherein in the first step, the parameters of the FIR model are identified based on the FIR model and the ARX model. In the second step, the internal resistance of the battery at the estimation target time is calculated based on the overvoltage of the battery at the estimation target time and the current input to the battery at the estimation target time. The system identification method according to any one of 1 to 7. A response estimation unit that estimates the response of the system that receives the current flowing in the battery as an input and outputs the overvoltage of the battery,
The response estimation unit,
The system is identified by applying a model of the battery including an FIR model and an ARX model to the system based on time series data of a current flowing through the battery and an overvoltage of the battery within a predetermined period. Then
When no current is input to the identified system before the input start time, and when a current is input after the input start time, the system outputs the estimated target time after the input start time. Estimating the overvoltage of the battery based on the parameters of the model of the battery applied to identify the system,
Of the time series data, the number of data applied to the FIR model is a number equal to or larger than the number obtained by dividing the time from the input start time to the estimation target time by the sampling period by one,
System identification device.

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