JP2022028363A - System identification device and system identification method - Google Patents

Abstract

To provide a new system identification device and a method with which it is possible to achieve system identification for nonlinearly acting parameters while taking directly into account errors that accumulate over multiple steps.SOLUTION: A system identification device D pertaining to the present invention does by a computer, system identification of a model of prescribed system that performs a prescribed operation. The system identification device D comprises: a result data acquisition unit 42 which, when a prescribed input value is inputted to the system, acquires a plurality of pieces of result data which is obtained from the system for each of multiple points of time arranged in sequence of time; an estimate data acquisition unit 43 which, when the prescribed input value is inputted to the model, acquires a plurality of pieces of estimate data which is estimated by the model for each of multiple points of time; and a parameter processing unit 44 for minimizing an evaluation function of the model based on difference between the result data and estimate data obtained for each of multiple points of time and thereby finding the parameter.SELECTED DRAWING: Figure 1

Description

The present invention relates to a system identification device and a system identification method for system identification of a model of a predetermined system that performs a predetermined operation.

A model of the system is required for a simulation (numerical experiment) for a predetermined system that performs a predetermined operation, and the model of the system may be used in controlling the system. In this simulation and control, the accuracy depends on the accuracy of the model, so it is desired to accurately identify the parameters that define the model. A method for identifying this parameter is disclosed in, for example, Patent Document 1.

The parameter identification method disclosed in Patent Document 1 identifies unknown parameters including the bulk modulus and flow coefficient of the vertical articulated hydraulic manipulator based on a state-space equation representing a nonlinear model of the vertical articulated hydraulic manipulator. ..

JP-A-2015-77643

The parameter identification method disclosed in Patent Document 1 can identify a non-linear model, but the present invention is a new system that can identify a system that directly considers an error accumulating parameters that act non-linear over a plurality of steps. It is to provide an identification device and a system identification method.

As a result of various studies, the present inventor has found that the above object can be achieved by the following invention. That is, the system identification device according to one aspect of the present invention is a device that system-identifies a model of a predetermined system that performs a predetermined operation by a computer, and when a predetermined input value is input to the system, it is time-series. A performance data acquisition unit that acquires a plurality of performance data obtained from the system at each of a plurality of time points arranged in the line, and when the predetermined input value is input to the model, it is estimated by the model at each of the plurality of time points. The parameter is obtained by minimizing the estimation data acquisition unit that acquires a plurality of estimation data and the evaluation function of the model based on the difference between the actual data and the estimation data obtained at each of the plurality of time points. It is provided with a parameter processing unit for obtaining.

Since such a system identification device uses the evaluation function of the model based on the difference between the actual data and the estimated data obtained at each of a plurality of time points, an error of accumulating parameters acting non-linearly over a plurality of steps. The system can be identified while directly considering.

In another aspect, in the system identification apparatus described above, the parameter processing unit minimizes the evaluation function under a constraint condition that defines a range that the parameters of the model can take. Ask.

Such a system identification device obtains the parameter by minimizing the evaluation function under the constraint condition that defines the range that the parameter can take, so that the parameter can be identified so as to satisfy a predetermined condition. ..

In another aspect, in these system identification devices described above, the parameter processing unit obtains the parameter by iterative calculation using the gradient information of the evaluation function.

Since such a system identification device repeatedly calculates using the gradient information of the evaluation function, the parameters can be optimally converged.

In another aspect, in these system identification devices described above, the predetermined system controls a hydraulic pressure pump, a hydraulic pressure actuator that converts the hydraulic pressure generated by the hydraulic pressure pump into mechanical power, and the hydraulic pressure. It is a hydraulic system including a hydraulic control valve, and the predetermined operation is an operation of moving a predetermined object by the hydraulic actuator.

A hydraulic system usually contains a large number of parameters that act non-linearly, which can provide a system identification device capable of accurately system-identifying a model of a hydraulic system.

The system identification method according to one aspect of the present invention is a method of system-identifying a model of a predetermined system performing a predetermined operation by a computer, and is arranged in time series when a predetermined input value is input to the system. A performance data acquisition process for acquiring a plurality of performance data obtained from the system at each of a plurality of time points, and a plurality of estimations made by the model at each of the plurality of time points when the predetermined input value is input to the model. The parameter is obtained by minimizing the estimation data acquisition process for acquiring the estimated data of the model and the evaluation function of the model based on the difference between the actual data and the estimated data obtained at each of the plurality of time points. It is equipped with a parameter processing process.

Since such a system identification method uses the evaluation function of the model based on the difference between the actual data and the estimated data obtained at each of a plurality of time points, an error of accumulating parameters that act non-linearly over a plurality of steps. The system can be identified while directly considering.

The system identification apparatus and system identification method according to the present invention can identify a system by directly considering an error accumulating over a plurality of steps of parameters acting non-linearly.

It is a block diagram which shows the structure of the system identification apparatus in an embodiment. It is a flowchart which shows the operation of the system identification apparatus. It is a schematic diagram which shows the structure of the hydraulic system of Example 1. FIG. It is a figure for demonstrating each comparison result of the actual value, the estimated value of Example 1, and the estimated value of a comparative example. It is a schematic diagram which shows the structure of the mechanical system of Example 2.

Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. It should be noted that the configurations with the same reference numerals in the respective drawings indicate the same configurations, and the description thereof will be omitted as appropriate. In the present specification, when they are generically referred to, they are indicated by reference numerals without subscripts, and when they refer to individual configurations, they are indicated by reference numerals with subscripts.

(Embodiment)
The system identification device in the embodiment is a device that system-identifies a model of a predetermined system that performs a predetermined operation by a computer. This system identification device includes a performance data acquisition unit that acquires a plurality of performance data obtained from the system at each of a plurality of time points arranged in a time series when a predetermined input value is input to the system, and the predetermined input. When a value is input to the model, an estimation data acquisition unit that acquires a plurality of estimation data estimated by the model at each of the plurality of time points, and the actual data and the estimation data obtained at each of the plurality of time points. It is provided with a parameter processing unit for obtaining the parameters by minimizing the evaluation function of the model based on each difference from the above. Such a system identification device will be described in more detail below.

FIG. 1 is a block diagram showing a configuration of a system identification device according to an embodiment. As shown in FIG. 1, the system identification device D in the embodiment includes, for example, an input unit 1, an output unit 2, an interface unit (IF unit) 3, a control processing unit 4, and a storage unit 5.

The input unit 1 is connected to the control processing unit 4, and is input to, for example, various commands such as a command for instructing the start of system identification, the name of a predetermined system S to be the target of system identification, and the system S. It is a device for inputting various data necessary for operating the system identification device D, such as an input value, into the system identification device D, for example, a keyboard, a mouse, or the like. The output unit 2 is a device connected to the control processing unit 4 and outputs commands and data input from the input unit 1 and model parameters obtained by the system identification device D according to the control of the control processing unit 4. For example, a display device such as a CRT display, a liquid crystal display and an organic EL display, a printing device such as a printer, and the like.

A so-called touch panel may be configured from the input unit 1 and the output unit 2. In the case of configuring this touch panel, the input unit 1 is a position input device that detects and inputs an operation position such as a resistance film method or a capacitance method, and the output unit 2 is a display device. In this touch panel, the position input device is provided on the display surface of the display device, candidates for one or a plurality of input contents that can be input to the display device are displayed, and the user displays the input contents that he / she wants to input. When the position is touched, the position is detected by the position input device, and the display content displayed at the detected position is input to the system identification device D as the operation input content of the user. With such a touch panel, since the user can intuitively understand the input operation, the system identification device D that is easy for the user to handle is provided.

The IF unit 3 is a circuit that is connected to the control processing unit 4 and inputs / outputs data to / from an external device according to the control of the control processing unit 4, for example, RS-232C or RS-, which is a serial communication method. An interface circuit of 485, an interface circuit using the Bluetooth (registered trademark) standard, an interface circuit for infrared communication such as the IrDA (Infrared Data Association) standard, and an interface circuit using the USB (Universal Serial Bus) standard. .. Further, the IF unit 3 is a circuit that communicates with an external device, and may be, for example, a data communication card, a communication interface circuit according to the IEEE802.11 standard, or the like.

The storage unit 5 is a circuit connected to the control processing unit 4 and stores various predetermined programs and various predetermined data according to the control of the control processing unit 4. The various predetermined programs include, for example, a control processing program, and the control processing program includes a control program that controls each part 1 to 3 and 5 of the system identification device D according to the function of each part. , A performance data acquisition program that acquires a plurality of performance data obtained from the system S at each of a plurality of time points arranged in a time series when a predetermined input value is input to the system S, or the system that inputs the predetermined input value. An estimation data acquisition program that acquires a plurality of estimated data estimated by the model at each of the plurality of time points when input to the model of S, and the actual data and the estimated data obtained at each of the plurality of time points. A parameter processing program or the like that obtains the parameters by minimizing the evaluation function of the model based on each difference under the constraint condition that defines the range that the parameters of the model can take is included. The various predetermined data include data necessary for executing each of these programs. Such a storage unit 5 includes, for example, a ROM (Read Only Memory) which is a non-volatile storage element, an EEPROM (Electrically Erasable Programmable Read Only Memory) which is a rewritable non-volatile storage element, and the like. The storage unit 5 includes a RAM (Random Access Memory) or the like that serves as a working memory of the so-called control processing unit 4 that stores data or the like generated during the execution of the predetermined program. The storage unit 5 may be provided with a hard disk device capable of storing a large capacity in order to store learning data having a relatively large capacity.

The control processing unit 4 is a circuit for system-identifying a model of a predetermined system S that controls each unit 1 to 3 and 5 of the system identification device D according to the function of each unit and performs a predetermined operation. The control processing unit 4 includes, for example, a CPU (Central Processing Unit) and its peripheral circuits. The control processing unit 4 is functionally configured with the control unit 41, the actual data acquisition unit 42, the estimation data acquisition unit 43, and the parameter processing unit 44 by executing the control processing program.

The control unit 41 controls each of the units 1 to 3 and 5 of the system identification device D according to the functions of the respective units, and controls the entire system identification device D.

When a predetermined input value is input to the system S, the actual data acquisition unit 42 acquires a plurality of actual data obtained from the system S at each of a plurality of time points arranged in a time series. For example, as shown in FIG. 1, the actual data acquisition unit 42 inputs an input value to the system S and takes in the actual data from the system S via IF3 at a predetermined sampling interval, thereby arranging in a time series. A plurality of actual data obtained from the system S are acquired at each of a plurality of time points. In this case, the parameters are identified online. Alternatively, for example, when a predetermined input value is input to the system S, a plurality of actual data obtained from the system S at each of a plurality of time points arranged in a time series are indicated by a broken line via the input unit 1. It is stored in advance in the actual data storage unit 51 functionally provided in the storage unit 5, and the actual data acquisition unit 42 is arranged in chronological order when a predetermined input value is input to the system S from the actual data storage unit 51. A plurality of actual data obtained from the system S are acquired at each of a plurality of time points. In this case, the parameters are identified offline.

The plurality of actual data stored in advance in the actual data storage unit 51 may be downloaded from, for example, a server device that manages the plurality of actual data via the network and the IF unit 3. Alternatively, for example, the plurality of actual data stored in advance in the actual data storage unit 51 is stored in the plurality of actual data from a memory card such as a USB memory or an SD card (registered trademark) via the IF unit 3. It may be downloaded. Alternatively, for example, a CD drive device or a DVD drive device is further provided in the system identification device D, and the plurality of actual data stored in advance in the actual data storage unit 51 is a CD-R that stores the plurality of actual data. It may be downloaded from a non-transitory recording medium (Non-transistor computer readable medium) that can be read by a computer, such as (Compact Disk Record) or DVD-R (Digital Versaille Disk Record).

The estimation data acquisition unit 43 acquires a plurality of estimation data estimated by the model of the system S at each of the plurality of time points when the predetermined input value is input to the model.

The parameter processing unit 44 defines a range in which the parameters of the model can take an evaluation function of the model based on each difference (each prediction error) between the actual data and the estimated data obtained at each of the plurality of time points. The above parameters are obtained by minimizing under the constraint condition.

Such an estimation data acquisition unit 43 and a parameter processing unit 44 will be described in more detail below.

ｓｕｂｊｅｃｔ ｔｏ

ここで、θ∈Ｒ^ｌは、推定パラメータを含むベクトルである。ｘ_ｋ∈Ｒ^ｎは、状態方程式（４）によって予測された離散時刻ｋにおけるシステムの状態、すなわち、複数の時点ｋごとに求められる推定データである（ｋ＝０～Ｎ）。上付きバーｘ_ｋ∈Ｒ^ｎは、離散時刻ｋにおいて実際に計測されたシステムの状態、すなわち、複数の時点ｋごとに求められる実績データであり、次式（６）によって表される。なお、変数を説明する文章において、記載の都合上、文字Ａの上部に“－”を付けたＡを「上付きバーＡ」と記載する。上付きバーｕ_ｋ∈Ｒ^ｎは、離散時刻ｋにおける制御入力、すなわち、所定の入力値であり、次式（７）によって表される。Ｊは、評価関数である。φ：Ｒ^ｎ→Ｒ は、終端コストである。Ｌ：Ｒ^ｎ×Ｒ→Ｒは、ランニングコストである。ｆ：Ｒ^ｎ×Ｒ^ｍ→Ｒ^ｎは、離散化されたシステムの状態方程式である。θ_ｍｉｎ∈Ｒ^ｌおよびθ_ｍａｘ∈Ｒ^ｌは、パラメータθの上下限、すなわち、拘束条件である。式（５）は、ベクトル要素ごとの不等式である。

The processing of the estimation data acquisition unit 43 and the parameter processing unit 44 is expressed as a constrained optimization problem of the following equations (1) to (5).

subject to

Where θ ∈ R ^l is a vector containing the estimation parameters. x _k ∈ R ⁿ is the state of the system at the discrete time k predicted by the equation of state (4), that is, the estimated data obtained at each of a plurality of time points k (k = 0 to N). The superscript bar x _k ∈ R ⁿ is the state of the system actually measured at the discrete time k, that is, the actual data obtained at each of a plurality of time points k, and is expressed by the following equation (6). In the text explaining the variable, for convenience of description, A with "-" at the top of the letter A is described as "superscript bar A". The superscript bar u _k ∈ R ⁿ is a control input at the discrete time k, that is, a predetermined input value, and is expressed by the following equation (7). J is an evaluation function. φ: R ⁿ → R is the termination cost. L: R ⁿ × R → R is a running cost. f: R ⁿ × R ^m → R ⁿ is the equation of state of the discretized system. θ _min ∈ R ^l and θ _max ∈ R ^l are the upper and lower limits of the parameter θ, that is, the constraints. Equation (5) is an inequality for each vector element.

The constrained conditional optimization problems of Eqs. (1) to (5) are solved by the following method.

ここで、Ｑ_φ∈Ｒ^ｎ×ｎとＱ_L∈Ｒ^ｎ×ｎは、定数重み行列である。 Unlike the conventional least squares method, the termination cost and the running cost in the evaluation function are set as in the following equations (8) and (9) in order to consider the square error over a plurality of steps.

Here, Q _φ ∈ R ^{n × n} and Q _L ∈ R ^{n × n} are constant weight matrices.

ここで、λ_ｋ＋１∈Ｒ^ｎは、等式拘束条件（４）に対するラグランジュ乗数である。Ｈ：Ｒ^ｎ×Ｒ^ｎ×Ｒ^ｌ×Ｒ→Ｒは、次式（１１）で定義されるハミルトニアン関数である。

In order to solve the equations (1) and (2) in consideration of the constraints (3) to (5), the Lagrangian of the following equation (10) is introduced.

Here, λ _{k + 1} ∈ R ⁿ is a Lagrange multiplier for the equation constraint condition (4). H: R ⁿ × R ⁿ × R ^l × R → R is a Hamiltonian function defined by the following equation (11).

ここで、δｘ_ｋ∈Ｒ^ｎは、ｘ_ｋの変分である。δ（上付きバーＪ）＝０であるから、最適性の必要条件は、次式（１３）ないし（１５）のように得られる。

By variational calculation, the variation of Lagrangian is obtained by the following equation (12).

Here, δ x _k ∈ R ⁿ is a variation of x _k . Since δ (superscript bar J) = 0, the requirement for optimality can be obtained as in the following equations (13) to (15).

ここで、「←」は、代入演算子である。η∈Ｒは、更新係数である。この更新計数ηは、評価関数の勾配（∂Ｊ／∂θ）が１回の繰り返し計算でパラメータθに与える影響度を設定する値であり、また、収束の速度を設定する値であり、システムＳ等に応じて予め適宜に設定される。評価関数の勾配（∂Ｊ／∂θ）は、次のように導出される。 Based on these requirements, the optimum parameter θ is numerically obtained by iterative calculation using the gradient information of the evaluation function J. For example, the optimum parameter θ can be obtained by repeatedly applying an update rule such as the following equation (16).

Here, "←" is an assignment operator. η ∈ R is the update factor. This update count η is a value that sets the degree of influence that the gradient of the evaluation function (∂J / ∂θ) has on the parameter θ in one iterative calculation, and is a value that sets the speed of convergence, and is a system. It is appropriately set in advance according to S and the like. The gradient of the evaluation function (∂J / ∂θ) is derived as follows.

First, the predicted values x ₀ , x ₁ , ..., X _N of the state at each time are derived using the equations (3), (4) and the current estimated value θ. Next, λ _N is derived by substituting x _N into equation (13). Then, the Lagrange multipliers λ ₁ , λ ₂ , ..., λ _N at each time are derived by solving Eq. (14) in the opposite direction. Since x ₀ , x ₁ , ..., X and λ ₁ , λ ₂ , ..., λ _N derived by this clearly satisfy the equations (4), (13) and (14). , The Lagrangian calculated using these and its variation satisfy the following equations (17) and (18).

Since the equation (18) has only the term of dθ, it can be rewritten as the following equation (19).

A sufficiently small η and the parameter θ updated with Eq. (16) and Eq. (19) always decrease the merit function J. Therefore, when the parameter θ is updated until the local optimum value of the evaluation function J is reached, that is, until (∂J / ∂θ) becomes sufficiently small (= the necessary condition (15) is satisfied), the parameter θ becomes local. Converges to the optimum value. When updating the parameter θ, the update range is limited so that each parameter satisfies the equation (5).

In this way, the constrained conditional optimization problem of Eqs. (1) to (5) is solved.

The input unit 1, the output unit 2, the IF unit 3, the control processing unit 4, and the storage unit 5 in the system identification device D can be configured by, for example, a computer such as a desktop type or a notebook type.

Next, the operation of this embodiment will be described. FIG. 2 is a flowchart showing the operation of the system identification device.

When the power of the system identification device D having such a configuration is turned on, the necessary initialization of each part is executed and the system identification device D starts its operation. The control processing unit 4 is functionally configured with the control unit 41, the actual data acquisition unit 42, the estimation data acquisition unit 43, and the parameter processing unit 44 by executing the control processing program. It is assumed that the equations (1) to (5) in the system S for obtaining the model are input and stored in advance in the system identification device D.

When the system identification is started, first, the system identification device D initializes the parameter θ to an applicable value by the parameter processing unit 44 of the control processing unit 4 (S1). Since the initial value of the parameter θ is the initial value of the iterative calculation, it may be any value.

Next, the system identification device D acquires the actual data of the equations (6) and (7) in the system S for which the model is obtained by the actual data acquisition unit 42 of the control processing unit 4 (S2).

Next, the system identification device D uses the estimation data acquisition unit 43 of the control processing unit 4 to predict the state of the system S at each time (estimated data of the system S at each time) x ₀ , x ₁ , ... , X _N are obtained using the equations (3), (4) and the current parameter θ (parameter θ estimated in the previous iterative calculation) (S3).

Next, the system identification device D obtains λ _N by substituting x _N into the equation (13) by the parameter processing unit 44 (S4).

Next, the system identification device D obtains and updates the parameter θ by the parameter processing unit 44 using the equations (16) and (19) (S5).

Next, the system identification device D determines whether or not (∂J / ∂θ) is sufficiently small by the parameter processing unit 44 (S6). More specifically, the parameter processing unit 44 determines whether or not (∂J / ∂θ) is equal to or less than a preset small predetermined threshold value. As a result of this determination, if (∂J / ∂θ) is equal to or less than the threshold value and sufficiently small, the system identification device D then executes the process S7, while the result of the determination, (∂J). If / ∂θ) is larger than the threshold value and not sufficiently smaller, the system identification device D returns the process to the process S2. This causes the iterative calculation to be performed.

In this process S7, the system identification device D outputs the obtained parameter θ to the output unit 2 by the control process unit 4, and ends this process. If necessary, the system identification device D may output the obtained parameter θ to the external device via the IF unit 3 by the control processing unit 4.

As described above, the system identification device D and the system identification method implemented therein are the actual data obtained at a plurality of time points k; the difference between the superposition bar x _k and the estimated data; x _k . Since the evaluation function J of the model of the system S based on the above is used, the parameter θ acting in a non-linear manner can be system-identified while directly considering the error accumulated over a plurality of steps. The system identification device D and the system identification method are superior in estimation accuracy as compared with the conventional method of system identification considering only an error of one step.

Since the system identification device D and the system identification method obtain the parameter θ by minimizing the evaluation function J under the constraint conditions θ _min to θ _max that define the range that the parameter θ can take. The parameter θ can be identified so as to satisfy a predetermined condition.

Since the system identification device D and the system identification method are repeatedly calculated using the gradient information (∂J / ∂θ) of the evaluation function J (θ ← θ−η (∂J / ∂θ)), the parameter θ is optimal. Can converge to.

Next, Example 1 and Example 2 in which each model of the hydraulic system and the mechanical system is obtained by the system identification device D will be described.

(Example 1)
FIG. 3 is a schematic view showing the configuration of the hydraulic system of the first embodiment. FIG. 4 is a diagram for explaining each comparison result between the actual value, the estimated value of Example 1, and the estimated value of the comparative example. FIG. 4A shows the time change of the discharge pressure P _p in the hydraulic pump 61, FIG. _4B shows the time change of the input / output pressure Ph of the first port 633 in the hydraulic actuator 63, and FIG. 4C shows the time change of the hydraulic actuator 63. The time change of the input / output pressure _Pr of the second port 634 in the above is shown, and each of these horizontal axes is the elapsed time, and each of these vertical axes is the pressure. FIG. 4D shows the time change of the piston position x _c in the hydraulic actuator 63, the horizontal axis thereof is the elapsed time, and the vertical axis thereof is the position. FIG. 4E shows the time change of the piston speed in the hydraulic actuator 63, the horizontal axis thereof is the elapsed time, and the vertical axis thereof is the speed.

The first embodiment is a case where a predetermined system S for obtaining a model and performing a predetermined operation is a hydraulic system. The hydraulic system 6 in the first embodiment has, for example, as shown in FIG. 3, a hydraulic pump 61 that generates hydraulic pressure, a hydraulic actuator 63 that converts the hydraulic pressure generated by the hydraulic pump 61 into mechanical power, and the hydraulic pressure. It is provided with a hydraulic control valve 62 for controlling the above. In the hydraulic system 6, the predetermined operation is an operation of moving a predetermined object Ob with the hydraulic actuator 63. The hydraulic actuator 63 includes a cylinder 631 and a piston 632, and the cylinder 631 has a first port 633 for inputting / outputting oil at one end thereof and a second port 634 for inputting / outputting oil at the other end. Be prepared. The hydraulic pump 61 is connected to the hydraulic control valve 62, and the hydraulic control valve 62 is connected to the first and second ports 633 and 634, respectively. In such a hydraulic system 6, the hydraulic pressure generated by the hydraulic pump 61 is applied to the hydraulic actuator 63 by the hydraulic control valve 62 inputting oil from the first port 633, and the piston 632 acts from the one end to the other. It moves to the end (from the left side to the right side of the paper), oil is output from the second port 634, and the oil is returned to the hydraulic control valve 62. The movement of the piston 632 causes the object Ob to move from the left side to the right side of the paper. On the other hand, the hydraulic pressure generated by the hydraulic pump 61 is applied to the hydraulic actuator 63 by the hydraulic control valve 62 inputting oil from the second port 634, and the piston 632 moves from the other end to the one end (from the right side of the paper). (To the left), oil is output from the first port 633 and returns to the hydraulic control valve 62. The movement of the piston 632 causes the object Ob to move from the right side to the left side of the paper.

ここで、Ｐ_ｐは、油圧ポンプ６１における吐出圧である。Ｐ_ｈは、油圧アクチュエータ６３にける第１ポート６３３の入出力圧である。Ｐ_ｒは、油圧アクチュエータ６３における第２ポート６３４の入出力圧である。Ｐ_ｔは、タンクにおける圧力である。ｘ_ｃは、ピストン位置である。ｋは、体積弾性係数である。Ｖ_ｐ、Ｖ_ｈ、Ｖ_ｒは、それぞれ、Ｐ_ｐ、Ｐ_ｈ、Ｐ_ｒが生じる場所の容積である。Ａ_ｈ、Ａ_ｒは、それぞれ、ピストンの断面積である。ｌ_ｃは、シリンダ長さである。ｍは、対象物Ｏｂによる負荷質量である。Ｆは、ピストン速度に依存する摩擦力である。ａ_Ｆ、ｂ_Ｆ は、定数である。Ｑは、それぞれの場所における油の流量である。Ｃ_ｉｎ、Ｃ_ｏｕｔは、流量係数である。ｕは、油圧制御弁６２の制御弁位置（本油圧システム６の制御入力）である。Ｖは、油圧制御弁６２における制御弁の開口特性を表す関数である。Ｇは、圧力特性を表す関数である。 The state and the equation of state of such a hydraulic system 6 are expressed by the following equations (20) and (21).

Here, P _p is the discharge pressure in the hydraulic pump 61. _Ph is the input / output pressure of the first port 633 in the hydraulic actuator 63. _Pr is the input / output pressure of the second port 634 in the hydraulic actuator 63. _Pt is the pressure in the tank. x _c is the piston position. k is a bulk modulus. V _p , V _h , and V _r are the volumes of the places where P _p , _Ph , and _Pr occur, respectively. A _h and _Ar are the cross-sectional areas of the piston, respectively. l _c is the cylinder length. m is the load mass due to the object Ob. F is a frictional force that depends on the piston speed. a _F and b _F are constants. Q is the flow rate of oil at each location. C _in and C _out are flow coefficients. u is the control valve position of the hydraulic control valve 62 (control input of the hydraulic system 6). V is a function representing the opening characteristic of the control valve in the hydraulic control valve 62. G is a function representing the pressure characteristic.

In the first embodiment, in order to apply the equation of state as the equation (4), the equation of state in the form of a differential equation is converted into a discrete equation by using the Runge-Kutta method.

In Example 1, the parameter θ of the following equation (22) was system-identified by the system identification device D in the above-described embodiment. Here, the parameters V _p , V _h , V _r , and b _F of the parameters θ act non-linearly. Since these parameters θ are positive in their physical sense, θ _min is set to 0 vector and θ _max is set to the vector in which each element is infinite as a constraint condition.

The simulation result in the model of the hydraulic system 6 obtained by system-identifying the parameter θ of the equation (22) by the system identification device D in the above-described embodiment is shown by a solid line in FIG. In FIG. 4, the actual data is shown by the dotted line, and the simulation result of the comparative example is shown by the alternate long and short dash line. The comparative example is a model in which the hydraulic system 6 is approximated by the method of least squares.

Compared to the comparative example, the system identification device D in the embodiment can estimate the parameters V _p , V _h , V _r , and b _F that act non-linearly, and can estimate including the prediction error for a plurality of steps. From FIG. 4, it can be seen that the actual data is closer to the actual data in the first embodiment than in the comparative example, and the accuracy of the simulation using the system-identified parameter θ is excellent.

(Example 2)
FIG. 5 is a schematic view showing the configuration of the mechanical system of the second embodiment. The second embodiment is a case where a predetermined system S for obtaining a model and performing a predetermined operation is a mechanical system. The mechanical system 7 in the second embodiment is, for example, a damper provided with a spring 71, as shown in FIG. In this mechanical system 7, the predetermined operation is an operation of supporting a predetermined object Ob with the spring 71.

ここで、ｋは、ばね定数である。ｃは、粘性係数である。ｍは、対象物Ｏｂによる負荷質量である。ｆは、力である。ｐは、質点の位置である。 The state and the equation of state of such a mechanical system 7 are expressed by the following equations (23) and (24).

Here, k is a spring constant. c is a viscosity coefficient. m is the load mass due to the object Ob. f is a force. p is the position of the mass point.

In order to apply the equation of state as equation (4), the equation of state is converted into a discrete equation as in the following equation (25) using, for example, the Euler method.

Here, tk is a time corresponding to the discrete time _k . The superscript dot x ( _tk ) is the superscript dot x at time _tk . Δt is the discretization period of time.

Such a mechanical system 7 can also generate a model of the mechanical system 7 by system-identifying with the system identification device D in the above-described embodiment.

In addition, in the above-mentioned embodiment and Example 1 and Example 2, for example, a set of a set shown in the formula (6) and the formula (7), a plurality of achievements obtained from the system at each of a plurality of time points arranged in a time series. Although the data was used, a plurality of sets of the plurality of actual data may be used. As a result, by exchanging the actual data to be used every time the parameter θ is updated, the parameter θ that equally reflects the error with all the actual data can be obtained.

Further, in the above-described embodiment and in the first and second embodiments, the parameter θ is obtained by minimizing the evaluation function J under the constraint conditions θ _min to θ _max , but the constraint condition is taken into consideration. In the case of the system S, which is not necessary, the parameter θ may be obtained by minimizing the evaluation function J without any constraint condition.

Further, in the above-described embodiment and in the first and second embodiments, the termination cost and the running cost in the evaluation function J are not limited to the equations (8) and (9), but are predicted by the model. Any function may be used as long as it is a function whose value increases according to the difference (prediction error) between the behavior of the system and the behavior of the actual system.

Further, in the above-described embodiment and in the first and second embodiments, the update rule of the parameter θ is not limited to the equation (16) which is the update rule of the classical gradient method, and the gradient of the evaluation function J is not limited to the equation (16). Various informed gradient methods may be used. For example, the conjugate gradient method or the gradient method with inertia may be used.

Further, in the above, Examples 1 and 2 show an example in which the system identification device D is applied to the hydraulic system 6 and the mechanical system 7, but the present invention is not limited thereto, and a predetermined operation is performed. It is widely applicable to the given system to be performed.

In order to express the present invention, the present invention has been appropriately and sufficiently described through embodiments with reference to the drawings above, but those skilled in the art can easily modify and / or improve the above embodiments. It should be recognized that it is possible. Therefore, unless the modified or improved form implemented by a person skilled in the art is at a level that deviates from the scope of rights of the claims stated in the claims, the modified form or the improved form is the scope of rights of the claims. It is interpreted to be included in.

D System identification device 1 Input unit 2 Output unit 3 Interface unit (IF unit)
4 Control processing unit 5 Storage unit 41 Control unit 42 Actual data acquisition unit 43 Estimated data acquisition unit 44 Parameter processing unit 51 Actual data storage unit

Claims (5)

A system identification device that uses a computer to identify a model of a predetermined system that performs a predetermined operation.
A performance data acquisition unit that acquires a plurality of performance data obtained from the system at each of a plurality of time points arranged in a time series when a predetermined input value is input to the system.
An estimation data acquisition unit that acquires a plurality of estimation data estimated by the model at each of the plurality of time points when the predetermined input value is input to the model.
It is provided with a parameter processing unit for obtaining the parameters by minimizing the evaluation function of the model based on the difference between the actual data and the estimated data obtained at each of the plurality of time points.
System identification device. The parameter processing unit obtains the parameter by minimizing the evaluation function under a constraint condition that defines a range that the parameter of the model can take.
The system identification apparatus according to claim 1. The parameter processing unit obtains the parameter by iterative calculation using the gradient information of the evaluation function.
The system identification apparatus according to claim 1 or 2. The predetermined system is a hydraulic system including a hydraulic pressure pump that generates hydraulic pressure, a hydraulic actuator that converts the hydraulic pressure generated by the hydraulic pressure pump into mechanical power, and a hydraulic pressure control valve that controls the hydraulic pressure. Is an operation of moving a predetermined object with the hydraulic actuator.
The system identification apparatus according to any one of claims 1 to 3. It is a system identification method that identifies a model of a predetermined system that performs a predetermined operation by a computer.
A performance data acquisition process for acquiring a plurality of performance data obtained from the system at each of a plurality of time points arranged in a time series when a predetermined input value is input to the system.
An estimation data acquisition step of acquiring a plurality of estimation data estimated by the model at each of the plurality of time points when the predetermined input value is input to the model.
A parameter processing step for obtaining the parameters by minimizing the evaluation function of the model based on the difference between the actual data and the estimated data obtained at each of the plurality of time points is provided.
System identification method.

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