WO2024053026A1 - Plant model generation device and computer-readable recording medium - Google Patents

Plant model generation device and computer-readable recording medium Download PDF

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WO2024053026A1
WO2024053026A1 PCT/JP2022/033597 JP2022033597W WO2024053026A1 WO 2024053026 A1 WO2024053026 A1 WO 2024053026A1 JP 2022033597 W JP2022033597 W JP 2022033597W WO 2024053026 A1 WO2024053026 A1 WO 2024053026A1
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plant model
plant
predetermined
stabilization
characteristic parameter
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PCT/JP2022/033597
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French (fr)
Japanese (ja)
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太郎 小木曽
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ファナック株式会社
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Priority to PCT/JP2022/033597 priority Critical patent/WO2024053026A1/en
Priority to JP2023515248A priority patent/JP7343731B1/en
Publication of WO2024053026A1 publication Critical patent/WO2024053026A1/en

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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/4155—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by programme execution, i.e. part programme or machine function execution, e.g. selection of a programme
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring

Definitions

  • the present invention relates to a plant model generation device and a computer-readable recording medium.
  • a simulator is used to simulate the operation of a machine to be controlled (for example, Patent Document 1). Simulations are sometimes performed using data collected when the machine is actually operated. The knowledge obtained through simulation is used in the analysis and design of real-world controlled objects.
  • the simulation is performed by modeling a servo system that follows the rotational speed of the main shaft, the position of the feed axis, etc. to desired values, for example.
  • the main shaft and feed shaft to be controlled in a servo system will be referred to as a plant
  • a model that simulates a plant will be referred to as a plant model.
  • the behavior of industrial machinery can be modeled using ordinary differential equations, for example. Then, the behavior of the industrial machine can be simulated by updating the state quantity through numerical calculation at every predetermined sample time ⁇ t.
  • a simulation in which the behavior of industrial machinery is modeled using ordinary differential equations and the state quantities of a plant are updated through numerical calculations at every predetermined sample time ⁇ t composes ordinary differential equations, even though the operation of the actual machine is stable.
  • the state quantity may become unstable (divergence/oscillation).
  • the sampling time ⁇ t be about 0.5 to 2 times the servo control period.
  • instability can be avoided by reducing the sampling time ⁇ t, but there is a problem in that the amount of calculation increases. Therefore, there is a desire in the field to ensure the stability of simulations while avoiding an increase in the amount of calculations.
  • the plant model generation device solves the above problems by ensuring the stability of a resonant system plant model by changing specific mechanical characteristic parameters for a simulator that simulates plant behavior using ordinary differential equations. do. If stabilization cannot be achieved by adjusting parameters, make the resonant plant model a rigid body.
  • One aspect of the present disclosure is a plant model generation device that generates a plant model that simulates the behavior of a plant to be controlled by numerical calculation of a predetermined formula by calculating coefficients of the numerical calculation, a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of the plant; a stabilization processing unit that adjusts predetermined characteristic parameters so that numerical calculations satisfy stabilization conditions that cause damped vibration; and a plant model based on the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit.
  • This is a plant model generation device comprising: a coefficient calculating unit that calculates coefficients of the present invention.
  • a computer-readable recording medium recording a program, comprising: a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of the plant; and the simulation conditions; a stabilization processing section that adjusts a predetermined characteristic parameter based on the characteristic parameter so that numerical calculations in a predetermined plant model satisfy stabilization conditions that cause damped vibration;
  • This is a computer-readable recording medium that records a program that causes a computer to operate as a coefficient calculation unit that calculates coefficients of a plant model based on characteristic parameters of the plant model.
  • FIG. 1 is a schematic hardware configuration diagram of a diagnostic device according to an embodiment of the present invention.
  • FIG. 1 is a block diagram schematically showing the functions of a diagnostic device according to a first embodiment of the present invention. It is a figure which illustrates the structure of the feed axis
  • FIG. 2 is a diagram showing an example of a plant model of a two-inertial resonance system.
  • FIG. 2 is a diagram showing an example of a block diagram of a two-inertia resonance system.
  • FIG. 3 is a diagram showing an example of a rigid body model. 3 is a flowchart illustrating the flow of processing executed by a stabilization processing unit.
  • FIG. 1 is a schematic hardware configuration diagram showing the main parts of a plant model generation device according to an embodiment of the present invention.
  • the plant model generation device 1 of the present invention can be implemented, for example, as a control device that controls the industrial machine 4 based on a control program. Further, the plant model generation device 1 of the present invention can be used in a personal computer attached to a control device that controls the industrial machine 4 based on a control program, a personal computer connected to the control device via a wired/wireless network, or a cell. It can be implemented on a computer, fog computer 6, cloud server 7. In this embodiment, an example is shown in which the plant model generation device 1 is installed on a personal computer connected to a control device of an industrial machine 4 via a network.
  • the CPU 11 included in the plant model generation device 1 of the present invention is a processor that controls the plant model generation device 1 as a whole.
  • the CPU 11 reads a system program stored in the ROM 12 via the bus 22, and controls the entire plant model generation device 1 according to the system program.
  • the RAM 13 temporarily stores temporary calculation data, display data, various data input from the outside, and the like.
  • the non-volatile memory 14 is composed of, for example, a memory backed up by a battery (not shown), a SSD (Solid State Drive), etc., and the stored state is maintained even when the power of the plant model generation device 1 is turned off.
  • the nonvolatile memory 14 stores data and programs read from the external device 72 via the interface 15, data and programs input via the input device 71, data acquired from the industrial machine 4, and the like.
  • the data and programs stored in the nonvolatile memory 14 may be expanded to the RAM 13 when executed/used. Further, various system programs such as a known analysis program are written in the ROM 12 in advance.
  • the interface 15 is an interface for connecting the CPU 11 of the plant model generation device 1 to an external device 72 such as a USB device. From the external device 72 side, for example, programs related to the functions of the plant model generation device 1, various data related to service provision, etc. can be read. Furthermore, programs and various data edited within the plant model generation device 1 can be stored in external storage means via the external device 72.
  • the display device 70 outputs and displays each data read into the memory, data obtained as a result of executing programs, system programs, etc. via the interface 18. Further, an input device 71 composed of a keyboard, a pointing device, etc. passes commands, data, etc. based on operations by a worker to the CPU 11 via the interface 19.
  • the interface 20 is an interface for connecting the CPU 11 of the plant model generation device 1 and the network 5.
  • the network 5 may be a WAN (Wide Area Network) composed of a leased line or the like, or may be a wide area network such as the Internet.
  • industrial machines 4 such as machine tools and robots installed in factories, fog computers 6, cloud servers 7, and the like. Each of these devices exchanges data with the plant model generation device 1 via the network 5.
  • FIG. 2 is a schematic block diagram showing the functions included in the plant model generation device 1 according to the first embodiment of the present invention.
  • Each function provided in the plant model generation device 1 according to the present embodiment is achieved by the CPU 11 included in the plant model generation device 1 shown in FIG. 1 executing a system program and controlling the operation of each part of the plant model generation device 1. Realized.
  • the plant model generation device 1 of this embodiment includes a simulation condition acquisition section 110, a characteristic parameter acquisition section 120, a stabilization processing section 130, a coefficient calculation section 140, and an output section 150.
  • the RAM 13 to nonvolatile memory 14 of the plant model generation device 1 include a plant model storage section 200, which is an area where a template of a plant model is stored in advance, and a simulation condition acquired by the simulation condition acquisition section 110.
  • a simulation condition storage section 210, which is an area, and a characteristic parameter storage section 220, which is an area for storing characteristic parameters acquired by the characteristic parameter acquisition section 120, are prepared in advance.
  • the simulation condition acquisition unit 110 Based on the plant model template stored in the plant model storage unit 200, the simulation condition acquisition unit 110 identifies conditions required when performing a simulation using the plant model. Then, the specified simulation conditions are acquired and stored in the simulation condition storage section 210.
  • the simulation conditions include at least a sample time ⁇ t in the simulation.
  • the simulation condition acquisition unit 110 may display, for example, on the display device 70 a screen that prompts input of simulation conditions, and acquire the simulation conditions by inputting from the input device 71. Alternatively, the simulation conditions may be read and acquired from the external device 72. Furthermore, the simulation conditions may be acquired from a computer such as the fog computer 6 or the cloud server 7 via the network 5.
  • the characteristic parameter acquisition unit 120 Based on the plant model template stored in the plant model storage unit 200, the characteristic parameter acquisition unit 120 identifies characteristic parameters required when performing simulation using the plant model. Then, the characteristic parameters of the identified plant model are acquired and stored in the characteristic parameter storage section 220.
  • the characteristic parameters of the plant model differ depending on the plant model. For example, consider the configuration of a feed shaft provided in a plant treated as a control target, as illustrated in FIG. In the example shown in FIG. 3, the feed shaft drives the table (work stand) by decelerating the rotation of the motor with a belt pulley and converting it into linear motion with a ball screw.
  • Such a controlled object can be modeled as a two-inertia resonant system in which the rotor inertia of the motor and the inertia of a rigid body called a table are coupled by a single spring element, as illustrated in FIG.
  • a single spring element refers to everything from the belt pulley to the ball screw as one spring element.
  • FIG. 5 is a block diagram illustrating a model of a two-inertia resonance system.
  • u is the torque input to the motor as the manipulated variable of the servo system
  • v M is the speed of the motor
  • v L is the speed of the table
  • J M is the rotor inertia moment
  • J L is the table inertia moment
  • C M is the The viscous friction (damping property) of the motor
  • C T is the damping property when torque is transmitted between the motor and the table
  • K T is the spring constant of a single spring element
  • R is the table inertia moment J L and the rotor inertia moment J This is the inertia ratio with M.
  • 1/(Z-1) represents an integral element.
  • the block diagram illustrated in FIG. 5 assumes that viscous friction proportional to inertia acts on the motor and table.
  • Equation 1 A is a system matrix
  • B is an input matrix
  • 1/(Z-1) is an integral element.
  • Examples of other plant models include, for example, a rigid model.
  • the controlled object is modeled as a rigid system in which the rotor inertia of the motor and the table inertia are integrated.
  • the plant model storage unit 200 stores in advance an equation representing the characteristics of such a controlled object as a plant model.
  • the plant model storage unit 200 may store characteristic parameters that are not included in the expression representing the plant model, or may store relational expressions indicating the relationships between the respective characteristic parameters.
  • the characteristic parameters of a two-inertia resonance system model include the natural frequency f a of the spring-table when the motor shaft is fixed, the reduction ratio r B of the belt pulley, and the ball Examples include the thread pitch l S and the table mass M L .
  • Such characteristic parameters can be used to calculate other characteristic parameters.
  • the table moment of inertia J L can be calculated using the following equation 3 using the belt pulley reduction ratio r B , the ball screw pitch I S , and the table mass M L.
  • the spring constant K T of a single spring element can be calculated using the following equation 4 using the natural frequency fa of the spring-table when the motor shaft is fixed, and the moment of inertia J L of the table.
  • the characteristic parameter acquisition unit 120 specifies necessary characteristic parameters based on the characteristic parameters included in the expression expressing the characteristics of the controlled object and the relational expression of each characteristic parameter. For example, things that can be calculated from other characteristic parameters, such as the table moment of inertia J L or the spring constant K T of a single spring element, may be obtained directly or from the values of other characteristic parameters. It may be calculated indirectly.
  • the characteristic parameter acquisition unit 120 may acquire the characteristic parameters of such a plant model by displaying, for example, a screen on the display device 70 that prompts input of the characteristic parameters, and inputting the characteristic parameters from the input device 71.
  • the characteristic parameters of the plant model may be read and acquired from the external device 72.
  • the characteristic parameters of the plant model may be acquired from a computer such as the fog computer 6 or the cloud server 7 via the network 5.
  • the stabilization processing unit 130 derives stabilization conditions under which damped vibration occurs in the plant model, based on the simulation conditions stored in the simulation condition storage unit 210 and the characteristic parameters stored in the characteristic parameter acquisition unit 120. Then, if a stabilization condition that causes damped oscillation exists, a plant model is generated in which predetermined characteristic parameters are set in a range where damped oscillation occurs. On the other hand, if there are no stabilizing conditions that cause damped vibration, a plant model is generated with characteristic parameters adjusted to become a rigid body model.
  • the plant model generated by the stabilization processing unit 130 uses a plant model that expresses the operation of the controlled object using a predetermined formula. For example, consider a plant model of a two-inertial resonant system as exemplified by Equation 1. In such a case, when the plant model is numerically calculated, the stabilization conditions can be set as conditions that do not cause divergence or oscillation. In the case of the plant model illustrated in Equation 1, the stabilization conditions can be determined using the eigenvalue ⁇ of the system matrix A.
  • Equation 1 the eigenvalue ⁇ of the system matrix A is expressed as Equation 5 below.
  • J A is the composite value of the moments of inertia of the two-inertial resonant system
  • C A is the composite value of the damping properties of the two-inertial resonant system.
  • the stabilization processing unit 130 determines a stabilization condition in which the eigenvalue ⁇ does not exceed 1 based on the given simulation conditions and characteristic parameters. Then, in order to stabilize the numerical calculation of the plant model, simulation conditions or characteristic parameters are adjusted. At this time, characteristic parameters such as the rotor inertia moment J M , the table inertia moment J L , and the spring constant K T of the single spring element represent characteristics that strongly control the behavior of the industrial machine 4 to be controlled. , if these are adjusted, the purpose of the simulation may not be achieved. Furthermore, when the value of the sampling time ⁇ t is decreased, the amount of calculation increases.
  • the stabilization processing unit 130 adjusts at least one of the damping property composite value C A , the viscous friction C M of the motor, and the damping property CT when torque is transmitted between the motor and the table. By doing so, adjustment is made so that the eigenvalue ⁇ does not exceed 1.
  • Equation 5 (1) The eigenvalue of Equation 5 (1) is determined only by the viscous friction C M of the motor, regardless of the damping property C T when torque is transmitted between the motor and the table.
  • the stabilization condition regarding Equation 5 (1) can be expressed by Equation 6 below. Since the viscous friction C M of the motor does not usually fail to satisfy the condition for stabilizing the eigenvalue of Equation 5 (1), there is no need to determine the condition for stabilizing the eigenvalue.
  • the upper limit of the damped oscillation C A can be expressed by the following equation 9.
  • C A exceeds the upper limit expressed by Equation 9
  • the plant becomes overdamped. Even with overdamping, the plant is still stable. Since vibration due to resonance does not occur with overdamping, if a two-inertial resonant system is used as a plant model, it is desirable that C A satisfy Equation 9.
  • the stabilization processing unit 130 first derives stabilization conditions for numerical calculation of the plant model based on the simulation conditions and the characteristic parameters of the plant model (step SA01). Then, it is determined whether there is a composite value C A of damping properties that satisfies the conditions for producing damped oscillations, that is, whether the condition of Equation 7, which is the condition for producing damped oscillations, is satisfied (step SA02). If there is a damping composite value C A that satisfies the conditions for generating damped vibration (Yes in step SA02), then it is determined whether the damping composite value CA satisfies Equation 8 ( Step SA03).
  • Equation 8 is not satisfied (No in step SA03), that is, if C A is less than the lower limit value + tolerance value ⁇ , the attenuation is combined so that the combined value C A of the attenuation becomes K T ⁇ t + ⁇ .
  • the characteristic parameters of at least one of the value C A , the viscous friction C M of the motor, and the damping property C T when torque is transmitted between the motor and the table are adjusted (step SA04).
  • the stabilization processing unit 130 satisfies Equation 9, which indicates the upper limit value of the composite value C A of damping properties that causes damped vibration. It is determined whether or not to do so (step SA05). If Equation 9 is not satisfied (No in step SA05), the composite value C A of the damping property is adjusted so that the composite value C A of the damping property becomes the upper limit value 2 ⁇ (J A K T ). The characteristic parameters of at least one of the viscous friction C M and the damping property C T when torque is transmitted between the motor and the table are adjusted (step SA06).
  • step SA07 the stabilization processing unit 130 changes the plant model to a rigid body model.
  • the conditions for stabilizing the rigid body model are similar to those expressed in Equation 6. Therefore, this stabilization condition is usually satisfied.
  • the coefficient calculation unit 140 calculates each coefficient of the formula representing the plant model based on the plant model determined by the stabilization processing unit 130, the characteristic parameters of the plant model that satisfy the stabilization conditions, and the simulation conditions.
  • the coefficient calculation unit 140 calculates each coefficient in the difference equation illustrated in Equation 1 and Equation 2 based on the characteristic parameters of the plant model determined by the stabilization processing unit 130 and the simulation conditions. Generate the model.
  • the output unit 150 outputs the plant model generated by the coefficient calculation unit 140 calculating the coefficients.
  • the output unit 150 may display and output an expression representing the generated plant model to the display device 70.
  • the data may be stored and output to an external memory device via the external device 72.
  • the output may be transmitted to the industrial machine 4 or to a computer such as the fog computer 6 or the cloud server 7 via the network 5.
  • the output plant model is used to perform simulations with a simulation device, digital twin system, etc.
  • the plant model generation device 1 can be expected to ensure stability of numerical calculations while avoiding an increase in the amount of calculations when constructing a servo system simulator.
  • the characteristic parameters are adjusted in advance by the stabilization processing unit 130 when calculating the coefficients of the plant model, the numerical calculation of the plant model is stabilized, which contributes to improving the reliability of the product.
  • the plant model generation device 1 according to this embodiment differs from the plant model generation device 1 according to the first embodiment in the stabilization processing by the stabilization processing unit 130.
  • the stabilization processing unit 130 determines whether the composite value C A of attenuation characteristics satisfies Equation 8. If Equation 8 is not satisfied, that is, if C A is less than the lower limit value + tolerance, the characteristic parameters are temporarily adjusted so that the composite value C A of the attenuation property becomes K T ⁇ t+ ⁇ .
  • the stabilization processing unit 130 determines whether or not the provisionally adjusted characteristic parameter satisfies the overdamping stabilization condition expressed by Equation 10 below. If the conditions are satisfied, the temporarily adjusted characteristic parameters are output as adjusted characteristic parameters.
  • the plant model is changed to a rigid body model.
  • the method of changing to a rigid body model is the same as that according to the first embodiment.
  • the present invention is not limited to the above-described embodiments, and can be implemented in various forms by making appropriate changes.
  • the present invention can also be applied to other plant models modeled in the form of general ordinary differential equations. techniques are applicable.

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Abstract

A plant model generation device according to the present disclosure is provided with: a simulation condition acquisition unit that acquires a simulation condition including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of a plant; a stabilization processing unit that adjusts, on the basis of the simulation condition and the characteristic parameters, a prescribed characteristic parameter such that a numerical calculation in a prescribed plant model satisfies a condition for stabilization that results in damped oscillation; and a coefficient calculation unit that calculates a coefficient of the plant model on the basis of the adjusted characteristic parameter of the prescribed plant model.

Description

プラントモデル生成装置及びコンピュータ読み取り可能な記録媒体Plant model generation device and computer readable recording medium
　本発明は、プラントモデル生成装置及びコンピュータ読み取り可能な記録媒体に関する。 The present invention relates to a plant model generation device and a computer-readable recording medium.
　制御対象となる機械について、シミュレータを用いて動作のシミュレーションを行うことが行われている（例えば、特許文献１など）。シミュレーションは、実際に機械を動作させた際に収集したデータを用いて行うこともある。シミュレーションを行うことで得られた知見は、現実の制御対象の解析や設計などに用いられる。 A simulator is used to simulate the operation of a machine to be controlled (for example, Patent Document 1). Simulations are sometimes performed using data collected when the machine is actually operated. The knowledge obtained through simulation is used in the analysis and design of real-world controlled objects.
　産業機械の挙動を模擬するシミュレーションをする場合、例えば主軸の回転数や送り軸の位置などを所望の値に追従させるサーボシステムをモデル化してシミュレーションを行う。以下では、サーボシステムにおいて制御対象となる主軸や送り軸をプラントと呼び、プラントを模擬したモデルのことをプラントモデルと呼ぶ。産業機械の挙動は、例えば常微分方程式でモデル化することができる。そして、予め定めた所定のサンプル時間Δｔごとの数値計算で状態量を更新することで、産業機械の挙動をシミュレーションできる。 When performing a simulation that simulates the behavior of an industrial machine, the simulation is performed by modeling a servo system that follows the rotational speed of the main shaft, the position of the feed axis, etc. to desired values, for example. Hereinafter, the main shaft and feed shaft to be controlled in a servo system will be referred to as a plant, and a model that simulates a plant will be referred to as a plant model. The behavior of industrial machinery can be modeled using ordinary differential equations, for example. Then, the behavior of the industrial machine can be simulated by updating the state quantity through numerical calculation at every predetermined sample time Δt.
特開２００４－１８８５４１号公報Japanese Patent Application Publication No. 2004-188541
　産業機械の挙動を常微分方程式でモデル化したプラントの状態量を所定のサンプル時間Δｔごとの数値計算で更新するシミュレーションは、実機の動作が安定であるにも関わらず、常微分方程式を構成するシステム行列Ａ次第で状態量が不安定化（発散・発振）することがある。 A simulation in which the behavior of industrial machinery is modeled using ordinary differential equations and the state quantities of a plant are updated through numerical calculations at every predetermined sample time Δt composes ordinary differential equations, even though the operation of the actual machine is stable. Depending on the system matrix A, the state quantity may become unstable (divergence/oscillation).
　サーボシステムのシミュレータであれば、サンプル時間Δｔはサーボ制御周期の０．５～２倍程度が妥当である。実機の動作が安定であるにも関わらず不安定化したシミュレータにおいては、サンプル時間Δｔを小さくすれば、不安定化を回避できるが、計算量が増大するという課題がある。
　そのため現場では、計算量の増大を避けつつ、シミュレーションの安定性を担保したいという要望がある。 In the case of a servo system simulator, it is appropriate that the sampling time Δt be about 0.5 to 2 times the servo control period. In a simulator that has become unstable even though the operation of the actual machine is stable, instability can be avoided by reducing the sampling time Δt, but there is a problem in that the amount of calculation increases.
Therefore, there is a desire in the field to ensure the stability of simulations while avoiding an increase in the amount of calculations.
　本発明によるプラントモデル生成装置は、プラントの挙動を常微分方程式で模擬するシミュレータについて、特定の機械特性パラメータを変更することで共振系のプラントモデルの安定性を担保することで、上記課題を解決する。パラメータの調整で安定化できない場合は、共振系のプラントモデルを剛体とする。 The plant model generation device according to the present invention solves the above problems by ensuring the stability of a resonant system plant model by changing specific mechanical characteristic parameters for a simulator that simulates plant behavior using ordinary differential equations. do. If stabilization cannot be achieved by adjusting parameters, make the resonant plant model a rigid body.
　そして、本開示の一態様は、制御対象となるプラントの挙動を所定の式の数値計算で模擬するプラントモデルを、前記数値計算の係数を算出することで生成するプラントモデル生成装置であって、少なくともサンプル時間を含むシミュレーション条件を取得するシミュレーション条件取得部と、前記プラントの特性を示す特性パラメータを取得する特性パラメータ取得部と、前記シミュレーション条件と、前記特性パラメータに基づいて、所定のプラントモデルにおける数値計算が減衰振動を生じる安定化の条件を満足するように所定の特性パラメータを調整する安定化処理部と、前記安定化処理部が調整した所定のプラントモデルの特性パラメータに基づいて、プラントモデルの係数を算出する係数算出部と、を備えたプラントモデル生成装置である。 One aspect of the present disclosure is a plant model generation device that generates a plant model that simulates the behavior of a plant to be controlled by numerical calculation of a predetermined formula by calculating coefficients of the numerical calculation, a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of the plant; a stabilization processing unit that adjusts predetermined characteristic parameters so that numerical calculations satisfy stabilization conditions that cause damped vibration; and a plant model based on the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit. This is a plant model generation device comprising: a coefficient calculating unit that calculates coefficients of the present invention.
　本開示の他の態様は、制御対象となるプラントの挙動を所定の式の数値計算で模擬するプラントモデルを、前記数値計算の係数を算出することで生成するプラントモデル生成装置としてコンピュータを動作させるプログラムを記録したコンピュータ読み取り可能な記録媒体であって、少なくともサンプル時間を含むシミュレーション条件を取得するシミュレーション条件取得部、前記プラントの特性を示す特性パラメータを取得する特性パラメータ取得部、前記シミュレーション条件と、前記特性パラメータに基づいて、所定のプラントモデルにおける数値計算が減衰振動を生じる安定化の条件を満足するように所定の特性パラメータを調整する安定化処理部、前記安定化処理部が調整した所定のプラントモデルの特性パラメータに基づいて、プラントモデルの係数を算出する係数算出部、としてコンピュータを動作させるプログラムを記録したコンピュータ読み取り可能な記録媒体である。 Another aspect of the present disclosure operates a computer as a plant model generation device that generates a plant model that simulates the behavior of a plant to be controlled by numerical calculation of a predetermined formula by calculating coefficients of the numerical calculation. A computer-readable recording medium recording a program, comprising: a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of the plant; and the simulation conditions; a stabilization processing section that adjusts a predetermined characteristic parameter based on the characteristic parameter so that numerical calculations in a predetermined plant model satisfy stabilization conditions that cause damped vibration; This is a computer-readable recording medium that records a program that causes a computer to operate as a coefficient calculation unit that calculates coefficients of a plant model based on characteristic parameters of the plant model.
　本開示の一態様により、サーボシステムのシミュレータを構築するにあたり、計算量の増大を避けつつ、数値計算の安定性を担保されることが期待できる。 According to one aspect of the present disclosure, when building a servo system simulator, it is expected that stability of numerical calculations can be ensured while avoiding an increase in the amount of calculations.
本発明の一実施形態による診断装置の概略的なハードウェア構成図である。FIG. 1 is a schematic hardware configuration diagram of a diagnostic device according to an embodiment of the present invention. 本発明の第１実施形態による診断装置の概略的な機能を示すブロック図である。FIG. 1 is a block diagram schematically showing the functions of a diagnostic device according to a first embodiment of the present invention. 制御対象として扱うプラントが備える送り軸の構成を例示する図である。It is a figure which illustrates the structure of the feed axis|shaft with which the plant handled as a control object is equipped. ２慣性共振系のプラントモデルの例を示す図である。FIG. 2 is a diagram showing an example of a plant model of a two-inertial resonance system. ２慣性共振系のブロック線図の例を示す図である。FIG. 2 is a diagram showing an example of a block diagram of a two-inertia resonance system. 剛体モデルの例を示す図である。FIG. 3 is a diagram showing an example of a rigid body model. 安定化処理部が実行する処理の流れを例示するフローチャートである。3 is a flowchart illustrating the flow of processing executed by a stabilization processing unit.
　以下、本発明の実施形態を図面と共に説明する。
　図１は本発明の一実施形態によるプラントモデル生成装置の要部を示す概略的なハードウェア構成図である。本発明のプラントモデル生成装置１は、例えば制御用プログラムに基づいて産業機械４を制御する制御装置として実装することができる。また、本発明のプラントモデル生成装置１は、制御用プログラムに基づいて産業機械４を制御する制御装置に併設されたパソコンや、有線／無線のネットワークを介して制御装置と接続されたパソコン、セルコンピュータ、フォグコンピュータ６、クラウドサーバ７の上に実装することができる。本実施形態では、プラントモデル生成装置１を、ネットワーク介して産業機械４の制御装置と接続されたパソコンの上に実装した例を示す。 Embodiments of the present invention will be described below with reference to the drawings.
FIG. 1 is a schematic hardware configuration diagram showing the main parts of a plant model generation device according to an embodiment of the present invention. The plant model generation device 1 of the present invention can be implemented, for example, as a control device that controls the industrial machine 4 based on a control program. Further, the plant model generation device 1 of the present invention can be used in a personal computer attached to a control device that controls the industrial machine 4 based on a control program, a personal computer connected to the control device via a wired/wireless network, or a cell. It can be implemented on a computer, fog computer 6, cloud server 7. In this embodiment, an example is shown in which the plant model generation device 1 is installed on a personal computer connected to a control device of an industrial machine 4 via a network.
　本発明のプラントモデル生成装置１が備えるＣＰＵ１１は、プラントモデル生成装置１を全体的に制御するプロセッサである。ＣＰＵ１１は、バス２２を介してＲＯＭ１２に格納されたシステム・プログラムを読み出し、該システム・プログラムに従ってプラントモデル生成装置１全体を制御する。ＲＡＭ１３には一時的な計算データや表示データ、及び外部から入力された各種データ等が一時的に格納される。 The CPU 11 included in the plant model generation device 1 of the present invention is a processor that controls the plant model generation device 1 as a whole. The CPU 11 reads a system program stored in the ROM 12 via the bus 22, and controls the entire plant model generation device 1 according to the system program. The RAM 13 temporarily stores temporary calculation data, display data, various data input from the outside, and the like.
　不揮発性メモリ１４は、例えば図示しないバッテリでバックアップされたメモリやＳＳＤ（Ｓｏｌｉｄ　Ｓｔａｔｅ　Ｄｒｉｖｅ）等で構成され、プラントモデル生成装置１の電源がオフされても記憶状態が保持される。不揮発性メモリ１４には、インタフェース１５を介して外部機器７２から読み込まれたデータやプログラム、入力装置７１を介して入力されたデータやプログラム、産業機械４から取得したデータ等が記憶される。不揮発性メモリ１４に記憶されたデータやプログラムは、実行時／利用時にはＲＡＭ１３に展開されても良い。また、ＲＯＭ１２には、公知の解析プログラムなどの各種システム・プログラムが予め書き込まれている。 The non-volatile memory 14 is composed of, for example, a memory backed up by a battery (not shown), a SSD (Solid State Drive), etc., and the stored state is maintained even when the power of the plant model generation device 1 is turned off. The nonvolatile memory 14 stores data and programs read from the external device 72 via the interface 15, data and programs input via the input device 71, data acquired from the industrial machine 4, and the like. The data and programs stored in the nonvolatile memory 14 may be expanded to the RAM 13 when executed/used. Further, various system programs such as a known analysis program are written in the ROM 12 in advance.
　インタフェース１５は、プラントモデル生成装置１のＣＰＵ１１とＵＳＢ装置等の外部機器７２と接続するためのインタフェースである。外部機器７２側からは、例えばプラントモデル生成装置１の機能に係るプログラムや、サービス提供に係る各種データ等を読み込むことができる。また、プラントモデル生成装置１内で編集したプログラムや各種データ等は、外部機器７２を介して外部記憶手段に記憶させることができる。 The interface 15 is an interface for connecting the CPU 11 of the plant model generation device 1 to an external device 72 such as a USB device. From the external device 72 side, for example, programs related to the functions of the plant model generation device 1, various data related to service provision, etc. can be read. Furthermore, programs and various data edited within the plant model generation device 1 can be stored in external storage means via the external device 72.
　表示装置７０には、メモリ上に読み込まれた各データ、プログラムやシステム・プログラム等が実行された結果として得られたデータ等が、インタフェース１８を介して出力されて表示される。また、キーボードやポインティングデバイス等から構成される入力装置７１は、インタフェース１９を介して作業者による操作に基づく指令，データ等をＣＰＵ１１に渡す。 The display device 70 outputs and displays each data read into the memory, data obtained as a result of executing programs, system programs, etc. via the interface 18. Further, an input device 71 composed of a keyboard, a pointing device, etc. passes commands, data, etc. based on operations by a worker to the CPU 11 via the interface 19.
　インタフェース２０は、プラントモデル生成装置１のＣＰＵ１１とネットワーク５とを接続するためのインタフェースである。ネットワーク５は、専用線などで構成されるＷＡＮ（Wide Area Network）であってもよいし、インターネットなどの広域ネットワークであってもよい。ネットワーク５には、工場などに設置された工作機械やロボットなどの産業機械４や、フォグコンピュータ６、クラウドサーバ７等が接続されている。これらの各装置は、ネットワーク５を介してプラントモデル生成装置１との間で相互にデータのやり取りを行っている。 The interface 20 is an interface for connecting the CPU 11 of the plant model generation device 1 and the network 5. The network 5 may be a WAN (Wide Area Network) composed of a leased line or the like, or may be a wide area network such as the Internet. Connected to the network 5 are industrial machines 4 such as machine tools and robots installed in factories, fog computers 6, cloud servers 7, and the like. Each of these devices exchanges data with the plant model generation device 1 via the network 5.
　図２は、本発明の第１実施形態によるプラントモデル生成装置１が備える機能を概略的なブロック図として示したものである。本実施形態によるプラントモデル生成装置１が備える各機能は、図１に示したプラントモデル生成装置１が備えるＣＰＵ１１がシステム・プログラムを実行し、プラントモデル生成装置１の各部の動作を制御することにより実現される。 FIG. 2 is a schematic block diagram showing the functions included in the plant model generation device 1 according to the first embodiment of the present invention. Each function provided in the plant model generation device 1 according to the present embodiment is achieved by the CPU 11 included in the plant model generation device 1 shown in FIG. 1 executing a system program and controlling the operation of each part of the plant model generation device 1. Realized.
　本実施形態のプラントモデル生成装置１は、シミュレーション条件取得部１１０、特性パラメータ取得部１２０、安定化処理部１３０、係数算出部１４０、出力部１５０を備える。また、プラントモデル生成装置１のＲＡＭ１３乃至不揮発性メモリ１４には、予めプラントモデルのひな型が記憶されている領域であるプラントモデル記憶部２００、シミュレーション条件取得部１１０が取得したシミュレーション条件を記憶するための領域であるシミュレーション条件記憶部２１０、及び特性パラメータ取得部１２０が取得した特性パラメータを記憶するための領域である特性パラメータ記憶部２２０が予め用意されている。 The plant model generation device 1 of this embodiment includes a simulation condition acquisition section 110, a characteristic parameter acquisition section 120, a stabilization processing section 130, a coefficient calculation section 140, and an output section 150. In addition, the RAM 13 to nonvolatile memory 14 of the plant model generation device 1 include a plant model storage section 200, which is an area where a template of a plant model is stored in advance, and a simulation condition acquired by the simulation condition acquisition section 110. A simulation condition storage section 210, which is an area, and a characteristic parameter storage section 220, which is an area for storing characteristic parameters acquired by the characteristic parameter acquisition section 120, are prepared in advance.
　シミュレーション条件取得部１１０は、プラントモデル記憶部２００に記憶されているプラントモデルのひな型に基づいて、プラントモデルによるシミュレーションを実行する際に必要となる条件を特定する。そして、特定したシミュレーション条件を取得し、シミュレーション条件記憶部２１０に記憶する。シミュレーション条件は、少なくともシミュレーションにおけるサンプル時間Δｔを含む。シミュレーション条件取得部１１０は、例えばシミュレーション条件の入力を促す画面を表示装置７０へと表示し、入力装置７１からの入力によりシミュレーション条件を取得してもよい。また、外部機器７２からシミュレーション条件を読み出して取得してもよい。更に、フォグコンピュータ６やクラウドサーバ７などのコンピュータからネットワーク５を介してシミュレーション条件を取得するようにしてもよい。 Based on the plant model template stored in the plant model storage unit 200, the simulation condition acquisition unit 110 identifies conditions required when performing a simulation using the plant model. Then, the specified simulation conditions are acquired and stored in the simulation condition storage section 210. The simulation conditions include at least a sample time Δt in the simulation. The simulation condition acquisition unit 110 may display, for example, on the display device 70 a screen that prompts input of simulation conditions, and acquire the simulation conditions by inputting from the input device 71. Alternatively, the simulation conditions may be read and acquired from the external device 72. Furthermore, the simulation conditions may be acquired from a computer such as the fog computer 6 or the cloud server 7 via the network 5.
　特性パラメータ取得部１２０は、プラントモデル記憶部２００に記憶されているプラントモデルのひな型に基づいて、プラントモデルによるシミュレーションを実行する際に必要となる特性パラメータを特定する。そして、特定したプラントモデルの特性パラメータを取得し、特性パラメータ記憶部２２０に記憶する。プラントモデルの特性パラメータは、プラントモデルによって異なる。例えば、図３に例示するような、制御対象として扱うプラントが備える送り軸の構成を考える。図３の例では、送り軸はモータの回転をベルトプーリで減速し、ボールねじで直動運動に変換してテーブル（ワーク台）を駆動している。このような制御対象は、図４に例示するように、モータのロータ慣性とテーブルという剛体の慣性とが単一のばね要素で結合された２慣性共振系としてモデル化することができる。単一のばね要素とは、ベルトプーリからボールねじまでをひとつのばね要素として見立てたものである。 Based on the plant model template stored in the plant model storage unit 200, the characteristic parameter acquisition unit 120 identifies characteristic parameters required when performing simulation using the plant model. Then, the characteristic parameters of the identified plant model are acquired and stored in the characteristic parameter storage section 220. The characteristic parameters of the plant model differ depending on the plant model. For example, consider the configuration of a feed shaft provided in a plant treated as a control target, as illustrated in FIG. In the example shown in FIG. 3, the feed shaft drives the table (work stand) by decelerating the rotation of the motor with a belt pulley and converting it into linear motion with a ball screw. Such a controlled object can be modeled as a two-inertia resonant system in which the rotor inertia of the motor and the inertia of a rigid body called a table are coupled by a single spring element, as illustrated in FIG. A single spring element refers to everything from the belt pulley to the ball screw as one spring element.
　図５は、２慣性共振系のモデルをブロック線図で例示したものである。図５において、ｕはサーボシステムの操作量としてモータに入力されるトルク、ｖMはモータの速度、ｖLはテーブルの速度、ＪMはロータ慣性モーメント、ＪLはテーブル慣性モーメント、ＣMはモータの粘性摩擦（減衰性）、ＣTはモータ－テーブル間でトルクが伝達される時の減衰性、ＫTは単一ばね要素のばね定数、Ｒはテーブル慣性モーメントＪLとロータ慣性モーメントＪMとのイナーシャ比である。また、１／（Ｚ－１）は、積分要素を表している。図５に例示するブロック線図は、モータ、テーブルには慣性に比例した粘性摩擦が働くものと仮定したものである。 FIG. 5 is a block diagram illustrating a model of a two-inertia resonance system. In Fig. 5, u is the torque input to the motor as the manipulated variable of the servo system, v M is the speed of the motor, v L is the speed of the table, J M is the rotor inertia moment, J L is the table inertia moment, and C M is the The viscous friction (damping property) of the motor, C T is the damping property when torque is transmitted between the motor and the table, K T is the spring constant of a single spring element, and R is the table inertia moment J L and the rotor inertia moment J This is the inertia ratio with M. Further, 1/(Z-1) represents an integral element. The block diagram illustrated in FIG. 5 assumes that viscous friction proportional to inertia acts on the motor and table.
　図５のブロック線図で示したモデルについて、時刻ｔ＝ｋΔｔの状態で、時刻（ｔ＋Δｔ）＝（ｋ＋１）Δｔの時点におけるモータ速度ｖM、テーブルの速度ｖL、ばね要素の伸びｘTを計算するための差分方程式は数１式のように示すことができる。なお、数１式において、Ａはシステム行列、Ｂは入力行列、１／（Ｚ－１）は積分要素である。 Regarding the model shown in the block diagram of FIG. 5, in the state of time t=kΔt, the motor speed v M , table speed v L , and spring element extension x T at time (t+Δt)=(k+1)Δt are The difference equation for calculation can be expressed as shown in Equation 1. Note that in Equation 1, A is a system matrix, B is an input matrix, and 1/(Z-1) is an integral element.
Figure JPOXMLDOC01-appb-M000001
Figure JPOXMLDOC01-appb-M000001
　他のプラントモデルの例として、例えば剛性モデルがある。図６は、制御対象をモータのロータ慣性とテーブル慣性とが一体化した剛体系としてモデル化したものである。このように構成した場合、時刻ｔ＝ｋΔｔの状態で、時刻（ｔ＋Δｔ）＝（ｋ＋１）Δｔの時点におけるモータ及びテーブルの速度ｖ（＝ｖM＝ｖL）を計算するための差分方程式は数２式のように示すことができる。 Examples of other plant models include, for example, a rigid model. In FIG. 6, the controlled object is modeled as a rigid system in which the rotor inertia of the motor and the table inertia are integrated. In this case, the difference equation for calculating the speed v (=v M =v L ) of the motor and table at time (t+Δt)=(k+1)Δt in the state of time t=kΔt is as follows. It can be shown as equation 2.
Figure JPOXMLDOC01-appb-M000002
Figure JPOXMLDOC01-appb-M000002
　プラントモデル記憶部２００には、このような制御対象の特性を表す式がプラントモデルとして予め記憶されている。プラントモデル記憶部２００には、プラントモデルを表す式に含まれない特性パラメータが記憶されていてもよく、また、それぞれの特性パラメータの関係を示す関係式が記憶されていてもよい。例えば、２慣性共振系のモデルの特性パラメータは、数１式に含まれるもの以外にも、モータ軸を固定した時のばね－テーブルの固有振動数ｆa、ベルトプーリの減速比ｒB、ボールねじのピッチｌS、テーブル質量ＭLなどが例示される。このような特性パラメータは、他の特性パラメータを算出するために用いることができる。例えば、テーブル慣性モーメントＪLは、ベルトプーリの減速比ｒB、ボールねじのピッチｌS、テーブル質量ＭLを用いた以下の数３式で算出することができる。また、単一ばね要素のばね定数ＫTは、モータ軸を固定した時のばね－テーブルの固有振動数ｆa、テーブル慣性モーメントＪLを用いた以下の数４式で算出することができる。 The plant model storage unit 200 stores in advance an equation representing the characteristics of such a controlled object as a plant model. The plant model storage unit 200 may store characteristic parameters that are not included in the expression representing the plant model, or may store relational expressions indicating the relationships between the respective characteristic parameters. For example, in addition to those included in Equation 1, the characteristic parameters of a two-inertia resonance system model include the natural frequency f a of the spring-table when the motor shaft is fixed, the reduction ratio r B of the belt pulley, and the ball Examples include the thread pitch l S and the table mass M L . Such characteristic parameters can be used to calculate other characteristic parameters. For example, the table moment of inertia J L can be calculated using the following equation 3 using the belt pulley reduction ratio r B , the ball screw pitch I S , and the table mass M L. Further, the spring constant K T of a single spring element can be calculated using the following equation 4 using the natural frequency fa of the spring-table when the motor shaft is fixed, and the moment of inertia J L of the table.
Figure JPOXMLDOC01-appb-M000003
Figure JPOXMLDOC01-appb-M000003
Figure JPOXMLDOC01-appb-M000004
Figure JPOXMLDOC01-appb-M000004
　特性パラメータ取得部１２０は、このような制御対象の特性を表す式に含まれる特性パラメータや、それぞれの特性パラメータの関係式に基づいて、必要な特性パラメータを特定している。例えば、テーブル慣性モーメントＪLや単一ばね要素のばね定数ＫTなどのような他の特性パラメータから算出可能なものについては、直接取得するようにしてもよいし、他の特性パラメータの値から間接的に算出するようにしてもよい。特性パラメータ取得部１２０は、このようなプラントモデルの特性パラメータを、例えば特性パラメータの入力を促す画面を表示装置７０へと表示し、入力装置７１からの入力により特性パラメータを取得してもよい。また、外部機器７２からプラントモデルの特性パラメータを読み出して取得してもよい。更に、フォグコンピュータ６やクラウドサーバ７などのコンピュータからネットワーク５を介してプラントモデルの特性パラメータを取得するようにしてもよい。 The characteristic parameter acquisition unit 120 specifies necessary characteristic parameters based on the characteristic parameters included in the expression expressing the characteristics of the controlled object and the relational expression of each characteristic parameter. For example, things that can be calculated from other characteristic parameters, such as the table moment of inertia J L or the spring constant K T of a single spring element, may be obtained directly or from the values of other characteristic parameters. It may be calculated indirectly. The characteristic parameter acquisition unit 120 may acquire the characteristic parameters of such a plant model by displaying, for example, a screen on the display device 70 that prompts input of the characteristic parameters, and inputting the characteristic parameters from the input device 71. Alternatively, the characteristic parameters of the plant model may be read and acquired from the external device 72. Furthermore, the characteristic parameters of the plant model may be acquired from a computer such as the fog computer 6 or the cloud server 7 via the network 5.
　安定化処理部１３０は、シミュレーション条件記憶部２１０に記憶されたシミュレーション条件、及び特性パラメータ取得部１２０に記憶された特性パラメータに基づいて、プラントモデルに減衰振動が生じる安定化の条件を導出する。そして、減衰振動が生じる安定化の条件が存在する場合、所定の特性パラメータを減衰振動が生じる範囲に設定したプラントモデルを生成する。一方で、減衰振動が生じる安定化の条件が存在しない場合、剛体モデルとなるように特性パラメータを調整したプラントモデルを生成する。 The stabilization processing unit 130 derives stabilization conditions under which damped vibration occurs in the plant model, based on the simulation conditions stored in the simulation condition storage unit 210 and the characteristic parameters stored in the characteristic parameter acquisition unit 120. Then, if a stabilization condition that causes damped oscillation exists, a plant model is generated in which predetermined characteristic parameters are set in a range where damped oscillation occurs. On the other hand, if there are no stabilizing conditions that cause damped vibration, a plant model is generated with characteristic parameters adjusted to become a rigid body model.
　安定化処理部１３０が生成するプラントモデルは、制御対象の動作を所定の式で示したものを用いる。例えば数１式に例示した、２慣性共振系のプラントモデルを考える。このような場合、当該プラントモデルを数値計算した場合に、発散や発振をすることがない条件を安定化の条件とすることができる。数１式に例示したプラントモデルの場合、システム行列Ａの固有値λを用いて安定化の条件を求めることができる。 The plant model generated by the stabilization processing unit 130 uses a plant model that expresses the operation of the controlled object using a predetermined formula. For example, consider a plant model of a two-inertial resonant system as exemplified by Equation 1. In such a case, when the plant model is numerically calculated, the stabilization conditions can be set as conditions that do not cause divergence or oscillation. In the case of the plant model illustrated in Equation 1, the stabilization conditions can be determined using the eigenvalue λ of the system matrix A.
　数１式において、システム行列Ａの固有値λは以下に示す数５式となる。なお、数５式において、ＪAは２慣性共振系の慣性モーメントの合成値、ＣAは２慣性共振系の減衰性の合成値である。全ての固有値λの値が１を超えない場合、プラントモデルにおける数値計算は、状態量が発散や発振をすることなく安定する。 In Equation 1, the eigenvalue λ of the system matrix A is expressed as Equation 5 below. In Equation 5, J A is the composite value of the moments of inertia of the two-inertial resonant system, and C A is the composite value of the damping properties of the two-inertial resonant system. When the values of all the eigenvalues λ do not exceed 1, numerical calculations in the plant model are stable without divergence or oscillation of state quantities.
Figure JPOXMLDOC01-appb-M000005
Figure JPOXMLDOC01-appb-M000005
　安定化処理部１３０は、与えられたシミュレーション条件及び特性パラメータに基づいて、固有値λが１を超えない安定化の条件について判定する。そして、プラントモデルの数値計算を安定化させるために、シミュレーション条件又は特性パラメータを調整する。この時、ロータ慣性モーメントＪM、テーブル慣性モーメントＪL、単一ばね要素のばね定数ＫTなどの特性パラメータは、制御対象となる産業機械４の挙動を強く支配する特性を表すものであるから、これらを調整するとシミュレーションの目的が達成されなくなる恐れがある。また、サンプル時間Δｔの値を小さくすると、計算量が増大する。そこで、安定化処理部１３０は、減衰性の合成値ＣA、モータの粘性摩擦ＣM、及びモータ－テーブル間でトルクが伝達される時の減衰性ＣTの少なくともいずれかの値を調整することで、固有値λが１を超えなくなるように調整をする。 The stabilization processing unit 130 determines a stabilization condition in which the eigenvalue λ does not exceed 1 based on the given simulation conditions and characteristic parameters. Then, in order to stabilize the numerical calculation of the plant model, simulation conditions or characteristic parameters are adjusted. At this time, characteristic parameters such as the rotor inertia moment J M , the table inertia moment J L , and the spring constant K T of the single spring element represent characteristics that strongly control the behavior of the industrial machine 4 to be controlled. , if these are adjusted, the purpose of the simulation may not be achieved. Furthermore, when the value of the sampling time Δt is decreased, the amount of calculation increases. Therefore, the stabilization processing unit 130 adjusts at least one of the damping property composite value C A , the viscous friction C M of the motor, and the damping property CT when torque is transmitted between the motor and the table. By doing so, adjustment is made so that the eigenvalue λ does not exceed 1.
　数５式（１）の固有値については、モータ－テーブル間でトルクが伝達される時の減衰性ＣTとは無関係にモータの粘性摩擦ＣMのみで決まる。数５式（１）に関する安定化の条件は、以下の数６式で表すことができる。モータの粘性摩擦ＣMが、数５式（１）の固有値の安定化の条件を満たさないことは通常は無いので、当該固有値における安定化の条件に付いて判定する必要は無い。 The eigenvalue of Equation 5 (1) is determined only by the viscous friction C M of the motor, regardless of the damping property C T when torque is transmitted between the motor and the table. The stabilization condition regarding Equation 5 (1) can be expressed by Equation 6 below. Since the viscous friction C M of the motor does not usually fail to satisfy the condition for stabilizing the eigenvalue of Equation 5 (1), there is no need to determine the condition for stabilizing the eigenvalue.
Figure JPOXMLDOC01-appb-M000006
Figure JPOXMLDOC01-appb-M000006
　数５式（２），数５式（３）の固有値については、減衰性の合成値ＣAによって、プラントに減衰振動が生じる場合と、過減衰になる場合とがある。減衰振動するＣAが存在するための条件は、以下の数７式で表すことができる。 Regarding the eigenvalues of Equation 5 (2) and Equation 5 (3), there are cases where damped vibration occurs in the plant and cases where overdamping occurs depending on the composite value C A of damping properties. The conditions for the existence of damped oscillating C A can be expressed by the following equation 7.
Figure JPOXMLDOC01-appb-M000007
Figure JPOXMLDOC01-appb-M000007
　また、数７式を満たす場合において安定化の条件を満たすＣAの下限値は、以下の数８式で表すことができる。なお、数８式において、δは予め定めた所定のトレランス値である。 Further, when formula 7 is satisfied, the lower limit value of C A that satisfies the stabilization condition can be expressed by formula 8 below. Note that in Equation 8, δ is a predetermined tolerance value.
Figure JPOXMLDOC01-appb-M000008
Figure JPOXMLDOC01-appb-M000008
　減衰振動するＣAの上限値は、以下の数９式で表すことができる。ＣAが数９式で表す上限値を超えるとプラントは過減衰になる。過減衰であってもプラントはなお安定である。過減衰では共振による振動は生じないため、プラントモデルとして２慣性共振系を用いるのであればＣAは数９式を満たすことが望ましい。 The upper limit of the damped oscillation C A can be expressed by the following equation 9. When C A exceeds the upper limit expressed by Equation 9, the plant becomes overdamped. Even with overdamping, the plant is still stable. Since vibration due to resonance does not occur with overdamping, if a two-inertial resonant system is used as a plant model, it is desirable that C A satisfy Equation 9.
Figure JPOXMLDOC01-appb-M000009
Figure JPOXMLDOC01-appb-M000009
　安定化処理部１３０が実行する安定化処理の流れを図７のフローチャートを用いて説明する。安定化処理部１３０は、初めにシミュレーション条件及びプラントモデルの特性パラメータに基づいて、プラントモデルの数値計算の安定化条件を導出する（ステップＳＡ０１）。そして、減衰振動が生じる条件を満たす減衰性の合成値ＣAが存在するか否か、すなわち減衰振動が生じる条件である数７式の条件を満足するか否かを判定する（ステップＳＡ０２）。そして、減衰振動が生じる条件を満たす減衰性の合成値ＣAが存在する場合（ステップＳＡ０２でＹｅｓ）、次に減衰性の合成値ＣAが数８式を満足するか否かを判定する（ステップＳＡ０３）。そして、数８式を満足しない場合（ステップＳＡ０３でＮｏ）、即ちＣAが下限値＋トレランス値δ未満である場合、減衰性の合成値ＣAがＫTΔｔ＋δになるように減衰性の合成値ＣA、モータの粘性摩擦ＣM、及びモータ－テーブル間でトルクが伝達される時の減衰性ＣTの少なくともいずれかの特性パラメータを調整する（ステップＳＡ０４）。 The flow of the stabilization process executed by the stabilization processing unit 130 will be explained using the flowchart of FIG. 7. The stabilization processing unit 130 first derives stabilization conditions for numerical calculation of the plant model based on the simulation conditions and the characteristic parameters of the plant model (step SA01). Then, it is determined whether there is a composite value C A of damping properties that satisfies the conditions for producing damped oscillations, that is, whether the condition of Equation 7, which is the condition for producing damped oscillations, is satisfied (step SA02). If there is a damping composite value C A that satisfies the conditions for generating damped vibration (Yes in step SA02), then it is determined whether the damping composite value CA satisfies Equation 8 ( Step SA03). If Equation 8 is not satisfied (No in step SA03), that is, if C A is less than the lower limit value + tolerance value δ, the attenuation is combined so that the combined value C A of the attenuation becomes K T Δt + δ. The characteristic parameters of at least one of the value C A , the viscous friction C M of the motor, and the damping property C T when torque is transmitted between the motor and the table are adjusted (step SA04).
　また、安定化処理部１３０は、ＣAが下限値＋トレランス値δ以上である場合（ステップＳＡ０３でＹｅｓ）、減衰振動を生じる減衰性の合成値ＣAの上限値を示す数９式を満足するか否かを判定する（ステップＳＡ０５）。そして、数９式を満足しない場合（ステップＳＡ０５でＮｏ）、減衰性の合成値ＣAが上限値である２√（ＪAＫT）になるように減衰性の合成値ＣA、モータの粘性摩擦ＣM、及びモータ－テーブル間でトルクが伝達される時の減衰性ＣTの少なくともいずれかの特性パラメータを調整する（ステップＳＡ０６）。 In addition, when C A is greater than or equal to the lower limit value + tolerance value δ (Yes in step SA03), the stabilization processing unit 130 satisfies Equation 9, which indicates the upper limit value of the composite value C A of damping properties that causes damped vibration. It is determined whether or not to do so (step SA05). If Equation 9 is not satisfied (No in step SA05), the composite value C A of the damping property is adjusted so that the composite value C A of the damping property becomes the upper limit value 2√(J A K T ). The characteristic parameters of at least one of the viscous friction C M and the damping property C T when torque is transmitted between the motor and the table are adjusted (step SA06).
　そして、安定化処理部１３０は、減衰振動を生じる減衰性の合成値ＣAが存在しない場合（ステップＳＡ０２でＮｏ）、プラントモデルを剛体モデルへと変更する（ステップＳＡ０７）。剛体モデルの安定化の条件は、数６式で表されたものと同様である。そのため、通常はこの安定化の条件は満たされる。 Then, if the composite value C A of damping properties that causes damped vibration does not exist (No in step SA02), the stabilization processing unit 130 changes the plant model to a rigid body model (step SA07). The conditions for stabilizing the rigid body model are similar to those expressed in Equation 6. Therefore, this stabilization condition is usually satisfied.
　なお、過減衰であるならば、プラントモデルを剛体モデルとしても産業機械４の挙動を十分に模擬できるため、安定化処理部１３０はステップＳＡ０５でＮｏの場合に、プラントモデルを剛体モデル（ステップＳＡ０７）としてもよい。 Note that if the plant model is overdamped, the behavior of the industrial machine 4 can be sufficiently simulated even if the plant model is a rigid model. ).
　係数算出部１４０は、安定化処理部１３０が決定したプラントモデルと、安定化の条件を満たすプラントモデルの特性パラメータ、及びシミュレーション条件に基づいて、プラントモデルを表す式の各係数を算出する。係数算出部１４０は、例えば数１式、数２式に例示した差分方程式における各係数を、安定化処理部１３０が決定したプラントモデルの特性パラメータ、及びシミュレーション条件に基づいて計算することで、プラントモデルを生成する。 The coefficient calculation unit 140 calculates each coefficient of the formula representing the plant model based on the plant model determined by the stabilization processing unit 130, the characteristic parameters of the plant model that satisfy the stabilization conditions, and the simulation conditions. The coefficient calculation unit 140 calculates each coefficient in the difference equation illustrated in Equation 1 and Equation 2 based on the characteristic parameters of the plant model determined by the stabilization processing unit 130 and the simulation conditions. Generate the model.
　出力部１５０は、係数算出部１４０が係数を算出することで生成したプラントモデルを出力する。出力部１５０は、例えば生成したプラントモデルを表す式を、表示装置７０に対して表示出力するようにしてもよい。また、外部機器７２を介して外部のメモリ機器に記憶出力するようにしてもよい。更に、ネットワーク５を介して、産業機械４に対して送信出力したり、フォグコンピュータ６、クラウドサーバ７などのコンピュータに対して送信出力したりしてもよい。出力されたプラントモデルは、シミュレーション装置やデジタルツインシステムなどでシミュレーションを行うために用いられる。 The output unit 150 outputs the plant model generated by the coefficient calculation unit 140 calculating the coefficients. For example, the output unit 150 may display and output an expression representing the generated plant model to the display device 70. Further, the data may be stored and output to an external memory device via the external device 72. Furthermore, the output may be transmitted to the industrial machine 4 or to a computer such as the fog computer 6 or the cloud server 7 via the network 5. The output plant model is used to perform simulations with a simulation device, digital twin system, etc.
　上記構成を備えた本実施形態によるプラントモデル生成装置１は、サーボシステムのシミュレータを構築するにあたり、計算量の増大を避けつつ、数値計算の安定性を担保されることが期待できる。シミュレータを外販する場合などに、プラントモデルが不安定で発散・発振すると「シミュレータの欠陥＝ソフトのバグ」と捉えられる恐れがある。しかしながら、プラントモデルの係数を算出するにあたって、安定化処理部１３０により事前に特性パラメータを調整しているため、プラントモデルの数値計算が安定し、商品の信頼性向上に寄与する。 The plant model generation device 1 according to this embodiment with the above configuration can be expected to ensure stability of numerical calculations while avoiding an increase in the amount of calculations when constructing a servo system simulator. When selling a simulator externally, if the plant model is unstable and diverges or oscillates, there is a risk that it will be interpreted as a ``simulator defect = software bug.'' However, since the characteristic parameters are adjusted in advance by the stabilization processing unit 130 when calculating the coefficients of the plant model, the numerical calculation of the plant model is stabilized, which contributes to improving the reliability of the product.
　以下では、本発明の第２実施形態によるプラントモデル生成装置１について説明する。本実施形態によるプラントモデル生成装置１は、安定化処理部１３０による安定化処理が第１実施形態によるプラントモデル生成装置１と異なる。 Hereinafter, a plant model generation device 1 according to a second embodiment of the present invention will be described. The plant model generation device 1 according to this embodiment differs from the plant model generation device 1 according to the first embodiment in the stabilization processing by the stabilization processing unit 130.
　本実施形態による安定化処理部１３０は、減衰性の合成値ＣAが数８式を満足するか否かを判定する。そして、数８式を満足しない場合、即ちＣAが下限値＋トレランス以下である場合、減衰性の合成値ＣAがＫTΔｔ＋δになるような特性パラメータへと仮調整する。 The stabilization processing unit 130 according to the present embodiment determines whether the composite value C A of attenuation characteristics satisfies Equation 8. If Equation 8 is not satisfied, that is, if C A is less than the lower limit value + tolerance, the characteristic parameters are temporarily adjusted so that the composite value C A of the attenuation property becomes K T Δt+δ.
　そして、安定化処理部１３０は、仮調整した特性パラメータについて、以下に示す数１０式の過減衰の安定化の条件を満足するか否かを判定する。そして、条件を満足する場合、仮調整した特性パラメータを調整後の特性パラメータとして出力する。 Then, the stabilization processing unit 130 determines whether or not the provisionally adjusted characteristic parameter satisfies the overdamping stabilization condition expressed by Equation 10 below. If the conditions are satisfied, the temporarily adjusted characteristic parameters are output as adjusted characteristic parameters.
Figure JPOXMLDOC01-appb-M000010
Figure JPOXMLDOC01-appb-M000010
　一方、数１０式の安定化の条件を満足しない場合は、プラントモデルを剛体モデルへと変更する。剛体モデルへの変更方法は、第１実施形態によるものと同様である。 On the other hand, if the stabilization condition of Equation 10 is not satisfied, the plant model is changed to a rigid body model. The method of changing to a rigid body model is the same as that according to the first embodiment.
　以上、本発明の実施形態について説明したが、本発明は上述した実施の形態の例のみに限定されることなく、適宜の変更を加えることにより様々な態様で実施することができる。
　例えば、上記した実施形態では、２慣性共振系のプラントモデル及び剛体モデルについてのみ説明しているが、一般的な常微分方程式の形でモデル化された他のプラントモデルに対しても、本発明の技術は適用可能である。 Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and can be implemented in various forms by making appropriate changes.
For example, in the above embodiment, only a two-inertia resonant system plant model and a rigid body model are described, but the present invention can also be applied to other plant models modeled in the form of general ordinary differential equations. techniques are applicable.
　　　１　プラントモデル生成装置
　　　４　産業機械
　　　５　ネットワーク
　　　６　フォグコンピュータ
　　　７　クラウドサーバ
　　１１　ＣＰＵ
　　１２　ＲＯＭ
　　１３　ＲＡＭ
　　１４　不揮発性メモリ
　　１５，１８，１９，２０　インタフェース
　　２２　バス
　　７０　表示装置
　　７１　入力装置
　　７２　外部機器
　１１０　シミュレーション条件取得部
　１２０　特性パラメータ取得部
　１３０　安定化処理部
　１４０　係数算出部
　１５０　出力部
　２００　プラントモデル記憶部
　２１０　シミュレーション条件記憶部
　２２０　特性パラメータ記憶部 1 Plant model generation device 4 Industrial machinery 5 Network 6 Fog computer 7 Cloud server 11 CPU
12 ROM
13 RAM
14 Nonvolatile memory 15, 18, 19, 20 Interface 22 Bus 70 Display device 71 Input device 72 External device 110 Simulation condition acquisition section 120 Characteristic parameter acquisition section 130 Stabilization processing section 140 Coefficient calculation section 150 Output section 200 Plant model storage section 210 Simulation condition storage unit 220 Characteristic parameter storage unit

Claims (4)

  1. 　制御対象となるプラントの挙動を所定の式の数値計算で模擬するプラントモデルを、前記数値計算の係数を算出することで生成するプラントモデル生成装置であって、
    　少なくともサンプル時間を含むシミュレーション条件を取得するシミュレーション条件取得部と、
    　前記プラントの特性を示す特性パラメータを取得する特性パラメータ取得部と、
    　前記シミュレーション条件と、前記特性パラメータに基づいて、所定のプラントモデルにおける数値計算が減衰振動を生じる安定化の条件を満足するように所定の特性パラメータを調整する安定化処理部と、
    　前記安定化処理部が調整した所定のプラントモデルの特性パラメータに基づいて、該プラントモデルの係数を算出する係数算出部と、
    を備えたプラントモデル生成装置。     A plant model generation device that generates a plant model that simulates the behavior of a plant to be controlled by numerical calculation of a predetermined formula by calculating coefficients of the numerical calculation,
    a simulation condition acquisition unit that acquires simulation conditions including at least a sample time;
    a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of the plant;
    a stabilization processing unit that adjusts a predetermined characteristic parameter based on the simulation condition and the characteristic parameter so that numerical calculation in a predetermined plant model satisfies a stabilization condition that causes damped vibration;
    a coefficient calculation unit that calculates coefficients of a predetermined plant model based on characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit;
    A plant model generation device equipped with
  2. 　前記安定化処理部は、
    　前記プラントモデルにおける数値計算が減衰振動を生じる安定化の条件を満足する所定の特性パラメータの値が存在する場合、該特性パラメータの値を安定化条件の下限値に予め定めた所定のトレランスを加えた値から、上限値の範囲内に調整し、
    　減衰振動を生じる安定化の条件を満足する所定の特性パラメータの値が存在しない場合には、前記プラントモデルを剛体モデルへと変更する、
    請求項１に記載のプラントモデル生成装置。     The stabilization processing section includes:
    If there is a value of a predetermined characteristic parameter that satisfies the stabilization condition in which the numerical calculation in the plant model causes damped vibration, the value of the characteristic parameter is added to the lower limit of the stabilization condition by a predetermined tolerance. Adjust the value to within the upper limit value,
    If there is no value of a predetermined characteristic parameter that satisfies a stabilization condition that causes damped vibration, changing the plant model to a rigid body model;
    The plant model generation device according to claim 1.
  3. 　前記安定化処理部は、
    　所定の特性パラメータの値を前記プラントモデルにおける数値計算が減衰振動を生じる安定化の条件の下限値にトレランスを加えた値以上に仮調整し、
    　仮調整した場合に、過減衰の安定化の条件を満足する場合、仮調整した特性パラメータの値を調整後の特性パラメータとして扱い、
    　過減衰の安定化の条件を満足しない場合、前記プラントモデルを剛体モデルへと変更する、
    請求項１に記載のプラントモデル生成装置。     The stabilization processing section includes:
    Temporarily adjusting the value of the predetermined characteristic parameter to a value equal to or higher than the lower limit value of the stabilization condition that causes damped vibration by numerical calculation in the plant model plus a tolerance,
    If the condition for stabilizing overdamping is satisfied when the temporary adjustment is made, the value of the temporarily adjusted characteristic parameter is treated as the adjusted characteristic parameter,
    If the overdamped stabilization condition is not satisfied, changing the plant model to a rigid body model;
    The plant model generation device according to claim 1.
  4. 　制御対象となるプラントの挙動を所定の式の数値計算で模擬するプラントモデルを、前記数値計算の係数を算出することで生成するプラントモデル生成装置としてコンピュータを動作させるプログラムを記録したコンピュータ読み取り可能な記録媒体で会って、
    　少なくともサンプル時間を含むシミュレーション条件を取得するシミュレーション条件取得部、
    　前記プラントの特性を示す特性パラメータを取得する特性パラメータ取得部、
    　前記シミュレーション条件と、前記特性パラメータに基づいて、所定のプラントモデルにおける数値計算が減衰振動を生じる安定化の条件を満足するように所定の特性パラメータを調整する安定化処理部、
    　前記安定化処理部が調整した所定のプラントモデルの特性パラメータに基づいて、該プラントモデルの係数を算出する係数算出部、
    としてコンピュータを動作させるプログラムを記録したコンピュータ読み取り可能な記録媒体。     A computer readable computer recording program that operates a computer as a plant model generation device that generates a plant model that simulates the behavior of a plant to be controlled by numerical calculation using a predetermined formula by calculating the coefficients of the numerical calculation. We met on recording media,
    a simulation condition acquisition unit that acquires simulation conditions including at least a sample time;
    a characteristic parameter acquisition unit that acquires characteristic parameters indicating characteristics of the plant;
    a stabilization processing unit that adjusts predetermined characteristic parameters based on the simulation conditions and the characteristic parameters so that numerical calculations in a predetermined plant model satisfy stabilization conditions that cause damped vibration;
    a coefficient calculation unit that calculates coefficients of a predetermined plant model based on characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit;
    A computer-readable recording medium that records a program that operates a computer.
PCT/JP2022/033597 2022-09-07 2022-09-07 Plant model generation device and computer-readable recording medium WO2024053026A1 (en)

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