Plant model generating device and computer-readable recording medium

Abstract

A plant model generation device according to the present disclosure is provided with a simulation condition acquisition unit that obtains a simulation condition containing at least one sampling time; a property parameter acquisition unit that obtains property parameters specifying properties of a plant; a stabilization processing unit that adapts a predetermined property parameter based on the simulation condition and the property parameters such that a numerical calculation in a predetermined plant model fulfills a condition for stabilization leading to damped vibration; and a coefficient calculation unit that calculates a coefficient of the plant model based on the adapted property parameter of the predetermined plant model.

Description

Plant model generating device and computer-readable recording medium

[0001] The present invention relates to a plant model generating device and a computer-readable recording medium.

[0002] Simulators are used to simulate the operation of machines to be controlled (see, for example, Patent Document 1). Simulations are sometimes performed using data collected when the machines are actually operated. Knowledge gained from the simulations is used for the analysis and design of actual controlled objects.

[0003] When simulating the behavior of industrial machinery, for example, a servo system that controls the rotation speed of a spindle or the position of a feed axis to follow desired values ​​is modeled and the simulation is performed. Hereinafter, the spindle or feed axis that is the control target in the servo system will be referred to as the plant, and the model that simulates the plant will be referred to as the plant model. The behavior of industrial machinery can be modeled using, for example, ordinary differential equations. Then, the behavior of industrial machinery can be simulated by updating the state quantities through numerical calculations at predetermined sample times Δt.

[0004] Japanese Patent Application Laid-Open No. 2004-188541

[0005] In a simulation in which the state quantities of a plant, in which the behavior of industrial machinery is modeled using ordinary differential equations, are updated by numerical calculations at a predetermined sample time Δt, the state quantities may become unstable (diverge or oscillate) depending on the system matrix A that constitutes the ordinary differential equations, even if the operation of the actual machine is stable.

[0006] For a servo system simulator, a sample time Δt of approximately 0.5 to 2 times the servo control period is appropriate. In simulators that become unstable despite the fact that the actual machine's operation is stable, the instability can be avoided by shortening the sample time Δt, but this poses the problem of increasing the amount of calculations. For this reason, there is a demand in the field for a way to ensure the stability of the simulation while avoiding an increase in the amount of calculations.

[0007] The plant model generation device according to the present invention solves the above-mentioned problems by ensuring the stability of a resonant system plant model by changing specific mechanical characteristic parameters in a simulator that simulates the behavior of a plant using ordinary differential equations. If stabilization cannot be achieved by adjusting the parameters, the plant model of the resonant system is treated as a rigid body.

[0008] 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 through numerical calculation of a predetermined equation by calculating coefficients of the numerical calculation, the plant model generation device including: a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters that indicate characteristics of the plant; a stabilization processing unit that adjusts the predetermined characteristic parameters based on the simulation conditions and the characteristic parameters so that the numerical calculation in the predetermined plant model satisfies a stabilization condition that causes damped oscillation; and a coefficient calculation unit that calculates coefficients of the plant model based on the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit.

[0009] Another aspect of the present disclosure is a computer-readable recording medium having recorded thereon a program that causes a computer to operate 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 equation by calculating coefficients of the numerical calculation, the computer-readable recording medium having recorded thereon a program that causes a computer to operate as: a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters that indicate characteristics of the plant; a stabilization processing unit that adjusts the predetermined characteristic parameters based on the simulation conditions and the characteristic parameters so that a stabilization condition that causes damped oscillation is satisfied in the numerical calculation of the predetermined plant model; and a coefficient calculation unit that calculates coefficients of the plant model based on the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit.

[0010] According to one aspect of the present disclosure, when constructing a servo system simulator, it is expected that the stability of numerical calculations can be ensured while avoiding an increase in the amount of calculations.

[0011] 1 is a schematic hardware configuration diagram of a diagnostic device according to an embodiment of the present invention; FIG. 2 is a block diagram showing the schematic functions of a diagnostic device according to a first embodiment of the present invention; FIG. 3 is a diagram illustrating an example of a feed axis provided in a plant treated as a control target; FIG. 4 is a diagram illustrating an example of a plant model of a two-inertia resonance system; FIG. 5 is a diagram illustrating an example of a block diagram of a two-inertia resonance system; and FIG. 6 is a flowchart illustrating the flow of processing executed by a stabilization processing unit.

[0012] Hereinafter, an embodiment of the present invention will be described 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 industrial machinery 4 based on a control program. The plant model generation device 1 of the present invention can also be implemented on a personal computer attached to the control device that controls the industrial machinery 4 based on the control program, or on a personal computer, cell computer, fog computer 6, or cloud server 7 connected to the control device via a wired or wireless network. In this embodiment, an example is shown in which the plant model generation device 1 is implemented on a personal computer connected to the control device of the industrial machinery 4 via a network.

[0013] The CPU 11 included in the plant model generating device 1 of the present invention is a processor that controls the entire plant model generating device 1. The CPU 11 reads a system program stored in the ROM 12 via the bus 22 and controls the entire plant model generating device 1 in accordance with the system program. The RAM 13 temporarily stores temporary calculation data, display data, various data input from outside, and the like.

[0014] The nonvolatile memory 14 is configured, for example, by a memory backed up by a battery (not shown) or an SSD (Solid State Drive), and maintains its stored state even when the power to the plant model generation device 1 is turned off. The nonvolatile memory 14 stores data and programs read from an 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 into the RAM 13 when executed / used. Furthermore, various system programs such as known analysis programs are written in the ROM 12 in advance.

[0015] 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. For example, programs related to the functions of the plant model generation device 1 and various data related to service provision can be read from the external device 72. In addition, programs and various data edited in the plant model generation device 1 can be stored in an external storage means via the external device 72.

[0016] The display device 70 displays various data loaded into the memory, data obtained as a result of executing programs and system programs, etc., output via the interface 18. An input device 71, which is comprised of a keyboard, pointing device, etc., transmits instructions, data, etc., based on operations by an operator, to the CPU 11 via the interface 19.

[0017] The interface 20 is an interface for connecting the CPU 11 of the plant model generation device 1 to the network 5. The network 5 may be a wide area network (WAN) configured with a dedicated line or the like, or a wide area network such as the Internet. Industrial machines 4 such as machine tools and robots installed in a factory, a fog computer 6, a cloud server 7, and the like are connected to the network 5. These devices exchange data with the plant model generation device 1 via the network 5.

[0018] 2 is a schematic block diagram showing functions of the plant model generating device 1 according to the first embodiment of the present invention. Each function of the plant model generating device 1 according to this embodiment is realized by a CPU 11 included in the plant model generating device 1 shown in FIG. 1 executing a system program and controlling the operation of each unit of the plant model generating device 1.

[0019] The plant model generating device 1 of this embodiment includes a simulation condition acquiring unit 110, a characteristic parameter acquiring unit 120, a stabilization processing unit 130, a coefficient calculating unit 140, and an output unit 150. The RAM 13 to the nonvolatile memory 14 of the plant model generating device 1 are provided with a plant model storage unit 200, which is an area in which a template of a plant model is stored in advance, a simulation condition storage unit 210, which is an area for storing the simulation conditions acquired by the simulation condition acquiring unit 110, and a characteristic parameter storage unit 220, which is an area for storing the characteristic parameters acquired by the characteristic parameter acquiring unit 120.

[0020] The simulation condition acquisition unit 110 identifies conditions required for executing a simulation using a plant model based on a template of the plant model stored in the plant model storage unit 200. The identified simulation conditions are then acquired and stored in the simulation condition storage unit 210. The simulation conditions include at least a sample time Δt in the simulation. The simulation condition acquisition unit 110 may, for example, display a screen on the display device 70 prompting the user to input the simulation conditions, and acquire the simulation conditions through input from the input device 71. Alternatively, the simulation conditions may be read and acquired from an 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.

[0021] The characteristic parameter acquisition unit 120 identifies characteristic parameters required for executing a simulation using a plant model based on a plant model template stored in the plant model storage unit 200. The characteristic parameters of the identified plant model are then acquired and stored in the characteristic parameter storage unit 220. The characteristic parameters of a plant model vary depending on the plant model. For example, consider the configuration of a feed axis provided in a plant treated as a controlled object, as illustrated in FIG. 3 . In the example of FIG. 3 , the feed axis reduces the rotation of a motor using a belt pulley and converts it into linear motion using a ball screw to drive a table (work table). Such a controlled object can be modeled as a two-inertia resonant system, in which the rotor inertia of the motor and the rigid body inertia of the table are coupled by a single spring element, as illustrated in FIG. 4 . The single spring element refers to the system from the belt pulley to the ball screw as a single spring element.

[0022] Figure 5 shows a block diagram of a model of a two-inertia resonant system. In Figure 5, u is the torque input to the motor as the manipulated variable of the servo system, v M is the motor speed, v L is the table speed, J M is the rotor moment of inertia, J L is the table moment of inertia, C M is the viscous friction (damping) of the motor, C T is the damping 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 moment of inertia J L and rotor moment of inertia J M is the inertia ratio. Also, 1 / (Z-1) represents the integral element. The block diagram shown in Figure 5 is based on the assumption that viscous friction proportional to the inertia acts on the motor and table.

[0023] For the model shown in the block diagram of FIG. 5, in the state where time t=kΔt, the motor speed v at the time (t+Δt)=(k+1)Δt M , table velocity v L , the extension of the spring element x TThe difference equation for calculating can be expressed as in Equation 1. In Equation 1, A is a system matrix, B is an input matrix, and 1 / (Z-1) is an integral element.

[0024]

[0025] Another example of a plant model is a rigid model. FIG. 6 shows a model in which the controlled object is modeled as a rigid body system in which the rotor inertia of the motor and the table inertia are integrated. In this configuration, in the state of time t = kΔt, the velocity v (= v) of the motor and the table at the time (t + Δt) = (k + 1)Δt is M =v L The difference equation for calculating ) can be shown as Equation 2.

[0026]

[0027] 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 equation representing the plant model, and may also store relational equations that show the relationship between the respective characteristic parameters. For example, in addition to the characteristic parameters included in Equation 1, the characteristic parameters of the two-inertia resonant system model may also include the natural frequency f a , reduction ratio r of belt pulley B , ball screw pitch l S , table mass M L Such characteristic parameters can be used to calculate other characteristic parameters, such as the table moment of inertia J L is the reduction ratio r of the belt pulley B , ball screw pitch l S , table mass M L The spring constant K of a single spring element can be calculated using the following formula 3. T is the natural frequency f of the spring-table when the motor shaft is fixed. a , table moment of inertia J L It can be calculated using the following formula 4.

[0028]

[0029]

[0030] The characteristic parameter acquisition unit 120 identifies necessary characteristic parameters based on the characteristic parameters included in the equations expressing the characteristics of the controlled object and the relational expressions of the respective characteristic parameters. For example, the table moment of inertia J L and the spring constant K of a single spring element T Those that can be calculated from other characteristic parameters such as those described above may be directly acquired or indirectly calculated from the values ​​of other characteristic parameters. The characteristic parameter acquisition unit 120 may acquire the characteristic parameters of such a plant model by, for example, displaying a screen on the display device 70 prompting 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.

[0031] The stabilization processor 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. If a stabilization condition under which damped vibration occurs exists, the stabilization processor 130 generates a plant model in which predetermined characteristic parameters are set within a range under which damped vibration occurs. On the other hand, if a stabilization condition under which damped vibration occurs does not exist, the stabilization processor 130 generates a plant model in which the characteristic parameters are adjusted so that the plant model becomes a rigid body model.

[0032] The plant model generated by the stabilization processor 130 uses a predetermined equation that represents the operation of the controlled object. For example, consider a plant model of a two-inertia resonant system as shown in Equation 1. In such a case, the stabilization condition can be a condition under which divergence or oscillation does not occur when the plant model is numerically calculated. In the case of the plant model shown in Equation 1, the stabilization condition can be found using the eigenvalue λ of the system matrix A.

[0033] In Equation 1, the eigenvalue λ of the system matrix A is expressed by Equation 5 below. A is the composite value of the moment of inertia of the two-inertia resonant system, C A is a composite value of the damping of the two-inertia resonant system. When all eigenvalues ​​λ do not exceed 1, the numerical calculation in the plant model is stable without the state quantity diverging or oscillating.

[0034]

[0035] The stabilization processor 130 determines the stabilization conditions under 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, the simulation conditions or characteristic parameters are adjusted. At this time, the rotor moment of inertia J M , table moment of inertia J L , the spring constant K of a single spring element T These characteristic parameters, etc., represent characteristics that strongly govern the behavior of the industrial machine 4 to be controlled, so adjusting them may result in the objective of the simulation not being achieved. Furthermore, reducing the value of the sample time Δt increases the amount of calculation. Therefore, the stabilization processor 130 adjusts the damping composite value C A , viscous friction of the motor C M , and damping C when torque is transmitted between the motor and the table T By adjusting at least one of the values, the eigenvalue λ is adjusted so that it does not exceed 1.

[0036] The eigenvalues ​​of Equation 5 (1) are the damping coefficient C when torque is transmitted between the motor and the table. T The viscous friction C of the motor is independent of M The stabilization condition for Equation 5 (1) can be expressed by the following Equation 6: M However, since it is not usual for the eigenvalue stabilization condition of Equation (1) to not be satisfied, there is no need to determine whether the eigenvalue stabilization condition is satisfied.

[0037]

[0038] The eigenvalues ​​of Equation 5 (2) and Equation 5 (3) are the combined damping value C A Depending on the above, the plant may experience damped oscillation or may be overdamped. A The condition for the existence of can be expressed by the following equation (7).

[0039]

[0040] In addition, when the formula (7) is satisfied, C satisfies the stabilization condition. A The lower limit value of can be expressed by the following formula 8. In formula 8, δ is a predetermined tolerance value.

[0041]

[0042] Damped vibration C A The upper limit of C can be expressed by the following formula 9. A When exceeds the upper limit expressed by Equation 9, the plant becomes overdamped. Even if it is overdamped, the plant is still stable. Since vibration due to resonance does not occur in overdamped, if a two-inertia resonant system is used as the plant model, C A It is desirable that equation (9) be satisfied.

[0043]

[0044] The flow of the stabilization process executed by the stabilization processor 130 will be described with reference to the flowchart of Fig. 7. The stabilization processor 130 first derives stabilization conditions for the numerical calculation of the plant model based on the simulation conditions and the characteristic parameters of the plant model (step SA01). Then, a combined damping value C A It is determined whether or not the damping composite value C satisfies the condition of the damping vibration occurrence, that is, whether or not the condition of the formula 7, which is the condition for the damping vibration occurrence, is satisfied (step SA02). A If there is a damping combined value C A It is determined whether or not the formula 8 is satisfied (step SA03). If the formula 8 is not satisfied (No in step SA03), that is, CA is less than the lower limit value + the tolerance value δ, the combined damping value C A is K T The damping composite value C is set to Δt+δ. A , viscous friction of the motor C M , and damping C when torque is transmitted between the motor and the table T At least one of the characteristic parameters is adjusted (step SA04).

[0045] The stabilization processor 130 also A is equal to or greater than the lower limit value + the tolerance value δ (Yes in step SA03), the combined damping value C A If the formula 9 is not satisfied (No in step SA05), the combined damping value C A is the upper limit value of 2√(J A K T ) so that the combined damping value C A , viscous friction of the motor C M , and damping C when torque is transmitted between the motor and the table T At least one of the characteristic parameters is adjusted (step SA06).

[0046] Then, the stabilization processing unit 130 calculates a combined damping value C A If there is no such condition (No in step SA02), the plant model is changed to a rigid body model (step SA07). The stabilization condition of the rigid body model is the same as that expressed by equation 6. Therefore, this stabilization condition is usually satisfied.

[0047] 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 body model. Therefore, if the answer is No in step SA05, the stabilization processing unit 130 may set the plant model to a rigid body model (step SA07).

[0048] The coefficient calculation unit 140 calculates each coefficient of an equation representing the plant model based on the plant model determined by the stabilization processing unit 130, characteristic parameters of the plant model that satisfy the stabilization conditions, and simulation conditions. The coefficient calculation unit 140 generates the plant model by calculating each coefficient in the difference equations exemplified by, for example, 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.

[0049] The output unit 150 outputs the plant model generated by the coefficient calculation unit 140 calculating the coefficients. The output unit 150 may, for example, display an equation representing the generated plant model on the display device 70. Alternatively, the output unit 150 may store and output the equation in an external memory device via the external device 72. Furthermore, the output may be transmitted and output 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 a simulation in a simulation device, a digital twin system, or the like.

[0050] The plant model generation device 1 according to this embodiment, which has the above configuration, is expected to ensure the stability of numerical calculations while avoiding an increase in the amount of calculations when constructing a servo system simulator. When selling the simulator, if the plant model is unstable and diverges or oscillates, it may be perceived as a "simulator defect = software bug." However, because the characteristic parameters are adjusted in advance by the stabilization processing unit 130 when calculating the coefficients of the plant model, the numerical calculations of the plant model are stable, contributing to improved product reliability.

[0051] A plant model generating device 1 according to a second embodiment of the present invention will be described below. The plant model generating device 1 according to this embodiment differs from the plant model generating device 1 according to the first embodiment in the stabilization processing performed by the stabilization processor 130.

[0052] The stabilization processing unit 130 according to this embodiment calculates the damping composite value C AIt is determined whether or not the formula 8 is satisfied. If the formula 8 is not satisfied, that is, C A is equal to or less than the lower limit value + tolerance, the combined damping value C A is K T The characteristic parameters are provisionally adjusted to be Δt+δ.

[0053] The stabilization processor 130 then determines whether the temporarily adjusted characteristic parameters satisfy the condition for stabilizing overdamping in the following equation 10. If the condition is satisfied, the stabilization processor 130 outputs the temporarily adjusted characteristic parameters as adjusted characteristic parameters.

[0054]

[0055] On the other hand, if the stabilization condition of Equation 10 is not satisfied, the plant model is changed to a rigid body model in the same manner as in the first embodiment.

[0056] 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 embodied in various forms by adding appropriate modifications. For example, in the above-described embodiments, only a plant model and a rigid body model of a two-inertia resonant system are described, but the technology of the present invention can also be applied to other plant models modeled in the form of general ordinary differential equations.

[0057] REFERENCE SIGNS LIST 1 Plant model generating device 4 Industrial machine 5 Network 6 Fog computer 7 Cloud server 11 CPU 12 ROM 13 RAM 14 Non-volatile memory 15, 18, 19, 20 Interface 22 Bus 70 Display device 71 Input device 72 External device 110 Simulation condition acquisition unit 120 Characteristic parameter acquisition unit 130 Stabilization processing unit 140 Coefficient calculation unit 150 Output unit 200 Plant model storage unit 210 Simulation condition storage unit 220 Characteristic parameter storage unit

Claims

1. A plant model generation device that generates a plant model that simulates the behavior of a plant to be controlled through numerical calculation of a predetermined equation by calculating coefficients of the numerical calculation, the plant model generation device 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 that indicate characteristics of the plant; a stabilization processing unit that adjusts the predetermined characteristic parameters based on the simulation conditions and the characteristic parameters so that the numerical calculation in the predetermined plant model satisfies stabilization conditions that cause damped oscillation; and a coefficient calculation unit that calculates coefficients of the plant model based on the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit.

2. The plant model generation device according to claim 1, wherein the stabilization processing unit, when there exists a predetermined characteristic parameter value that satisfies a stabilization condition that causes a damped oscillation in the numerical calculation of the plant model, adjusts the value of the characteristic parameter to fall within a range from a value obtained by adding a predetermined tolerance to a lower limit value of the stabilization condition to an upper limit value, and when there does not exist a predetermined characteristic parameter value that satisfies the stabilization condition that causes a damped oscillation, changes the plant model to a rigid body model.

3. The plant model generation device according to claim 1, wherein the stabilization processing unit provisionally adjusts the value of a predetermined characteristic parameter to a value equal to or greater than a value obtained by adding a tolerance to a lower limit of a stabilization condition at which a numerical calculation in the plant model produces damped oscillation; if the provisional adjustment satisfies the condition for stabilization of overdamping, the value of the provisionally adjusted characteristic parameter is treated as the adjusted characteristic parameter; and if the condition for stabilization of overdamping is not satisfied, the plant model generation device changes the plant model to a rigid body model.

4. A computer-readable recording medium having recorded thereon a program for operating 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 equation by calculating coefficients of the numerical calculation, the computer-readable recording medium having recorded thereon a program for operating a computer as: a simulation condition acquisition unit that acquires simulation conditions including at least a sample time; a characteristic parameter acquisition unit that acquires characteristic parameters that indicate the characteristics of the plant; a stabilization processing unit that adjusts the predetermined characteristic parameters based on the simulation conditions and the characteristic parameters so that the numerical calculation in the predetermined plant model satisfies the stabilization conditions that cause damped oscillation; and a coefficient calculation unit that calculates coefficients of the plant model based on the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit.

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