JP7343731B1 - Plant model generation device and computer readable recording medium - Google Patents

Abstract

A plant model generation device according to the present disclosure includes a simulation condition acquisition section that acquires simulation conditions including at least a sample time, a characteristic parameter acquisition section that acquires characteristic parameters indicating characteristics of a plant, and a simulation condition acquisition section that acquires simulation conditions that include at least a sample time. , a stabilization processing unit that adjusts a predetermined characteristic parameter so that numerical calculations in a predetermined plant model satisfy stabilization conditions that cause damped vibration; A coefficient calculation unit that calculates coefficients of the model.

Description

The present invention relates to a plant model generation device and a computer-readable recording medium.

2. Description of the Related Art 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.

When performing a simulation that simulates the behavior of an industrial machine, the simulation is performed by modeling a servo system that makes the rotation speed of the main shaft, the position of the feed shaft, etc. follow 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.

Japanese Patent Application Publication No. 2004-188541

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).

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.

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.

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 difference equation 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 predetermined characteristic parameter is adjusted without changing the sample time so that a plant model that simulates the behavior of a plant by numerical calculation of a predetermined difference equation satisfies stabilization conditions that produce damped vibration. A plant comprising: a stabilization processing unit; and a coefficient calculation unit that calculates coefficients of a difference equation in the plant model based on the simulation conditions and characteristic parameters of a predetermined plant model adjusted by the stabilization processing unit. It is a model generation device.

Another aspect of the present disclosure uses 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 difference equation by calculating coefficients of the numerical calculation. A computer-readable recording medium recording a program to be operated, 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. Based on the characteristic parameters, the sample time is set such that the plant model that simulates the behavior of the plant to be controlled by numerical calculation of a predetermined difference equation satisfies the stabilization condition that causes damped vibration. a stabilization processing unit that adjusts predetermined characteristic parameters without changing them; and a stabilization processing unit that adjusts the coefficients of the difference equation in the plant model based on the simulation conditions and the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit. 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.

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

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|shaft with which the plant handled as a control object is equipped. 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.

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.

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 solid state drive (SSD), 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 a program, a system program, 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) configured with 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.

FIG. 2 is a schematic block diagram showing the functions of 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. 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.

The simulation condition acquisition unit 110 specifies conditions required when performing a simulation using the plant model, based on the plant model template stored in the plant model storage unit 200. 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.

The characteristic parameter acquisition unit 120 specifies characteristic parameters required when executing a simulation using the plant model, based on the plant model template stored in the plant model storage unit 200. 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 table) 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. 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 table inertia moment. 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 is based on the assumption that viscous friction proportional to inertia acts on the motor and table.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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 synthesized so that the composite 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).

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).

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.

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. ).

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. 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.

The plant model generation device 1 according to the present embodiment having 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.

Below, 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.

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.

Then, the stabilization processing unit 130 determines whether or not the provisionally adjusted characteristic parameter satisfies the over-damping stabilization condition expressed by Equation 10 below. If the conditions are satisfied, the temporarily adjusted characteristic parameters are output as adjusted characteristic parameters.

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.

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 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)

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 difference equation 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;
Based on the simulation conditions and the characteristic parameters, the plant model that simulates the behavior of the plant to be controlled by numerical calculation of a predetermined difference equation satisfies the stabilization condition that causes damped vibration . a stabilization processing unit that adjusts a predetermined characteristic parameter without changing the sample time ;
a coefficient calculation unit that calculates coefficients of a difference equation in the plant model based on the simulation conditions and the characteristic parameters of the predetermined plant model adjusted by the stabilization processing unit;
A plant model generation device equipped with 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. 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. A computer readout that records 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 difference equation by calculating the coefficients of the numerical calculation. A possible recording medium,
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;
Based on the simulation conditions and the characteristic parameters, the plant model that simulates the behavior of the plant to be controlled by numerical calculation of a predetermined difference equation satisfies the stabilization condition that causes damped vibration . a stabilization processing unit that adjusts predetermined characteristic parameters without changing the sample time ;
a coefficient calculation unit that calculates coefficients of a difference equation in the plant model based on the simulation conditions and the 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.

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