Discreate-time model calculation method

Abstract

To prevent obtaining a local optimum solution for the coefficients used in a discrete-time model, and to accurately calculate the equation of the discrete-time model.SOLUTION: A discrete-time model calculation method determines the coefficients used in a discrete-time model representing the behavior of an object to be controlled such that the difference with the data obtained from the object to be controlled subjected to Fourier transformation is minimized, and when the discrete-time model is converted into a continuous-time model equation, the parameters having physical meanings in the continuous-time model equation is reflected with physical meanings read from the data obtained from the object to be controlled.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present invention relates to a method for calculating a discrete-time model.

Background Art

[0002] Techniques for constructing a mathematical model from input / output data of a control target are known, for example, from Non-Patent Document 1.

[0003] The discrete-time model of the control target can be calculated by determining the coefficients (parameters) used in the discrete-time model by fitting with the acquisition data detected from the control target.

Prior Art Documents

Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, when determining the coefficients used in the discrete-time model by fitting with the acquisition data detected from the control target, there are multiple combinations of the coefficients used in the discrete-time model, and there is a possibility that a local optimum solution of the coefficients used in the discrete-time model may be obtained.

[0006] That is, in the discrete-time model obtained only by fitting with the acquisition data detected from the control target, there is a risk that the control accuracy of the control target may decrease.

[0007] In addition, when changing the operating conditions for acquiring the data of the controlled object, the coefficients used in the discrete-time model change discontinuously. Therefore, in a control device incorporating a discrete-time model, switching control according to the operating conditions becomes necessary, and there is a risk that the control accuracy of the controlled object may decrease under operating conditions where the acquired data from the controlled object is not obtained.

Means for Solving the Problems

[0008] The method for calculating the discrete-time model of the present invention is such that the difference from the acquired data from the controlled object is minimized, and when converted into the equation of the continuous-time model of the controlled object, the parameters having physical meanings in the converted continuous-time model equation reflect the physical meanings read from the acquired data from the controlled object. The coefficients used in the discrete-time model of the controlled object are determined.

Effects of the Invention

[0009] According to the present invention, the fitting between the equation of the discrete-time model of the controlled object and the acquired data from the controlled object is improved, and it becomes possible to obtain a global optimal solution of the coefficients used in the equation of the discrete-time model.

[0010] Therefore, it becomes possible to accurately control the controlled object by the discrete-time model of the controlled object calculated from the acquired data from the controlled object.

[0011] In addition, since the coefficients used in the discrete-time model change continuously according to the operating conditions under which the data of the controlled object is acquired, under operating conditions where the acquired data from the controlled object is not obtained, by interpolating and using the coefficients of the discrete-time model of the controlled object calculated under operating conditions where the acquired data from the controlled object is obtained, it becomes possible to accurately control the controlled object.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Mode for Carrying Out the Invention

[0013] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings.

[0014] FIG. 1 is an explanatory diagram schematically showing the relationship between the input to the controlled object and the output from the controlled object.

[0015] The internal combustion engine (engine) as the controlled object outputs, for example, the air-fuel ratio as the output data as a result when a command value of the fuel injection amount (injection amount) is input as the input data. Also, the electric motor (motor) as the controlled object outputs, for example, the current value flowing through the electric motor as the output data as a result when a command value of the applied voltage is input as the input. That is, the output data of the controlled object represents, for example, the time change of the output signals of various sensors attached to the controlled object, and is obtained as data in pairs of the output signals of the various sensors and the time (timing) at which the output signals are detected.

[0016] In such a control target, the discrete-time model representing the behavior of the control target can be expressed, for example, as in Equation (1). The z in Equation (1) is an independent variable. a0, a1, and b0 in Equation (1) are coefficients (parameters), respectively. The "1" in Equation (1) is a constant, and its value has already been determined in advance in Equation (1). The coefficients and constants used in the discrete-time model do not have physical meanings.

[0017]

Number

[0018] The coefficients a0, a1, and b0 in Equation (1) can be calculated, for example, using the input-output data of the control target. Specifically, the coefficients a0, a1, and b0 in Equation (1) are determined by fitting with the output data of the control target, which is a function of time after Fourier transform. That is, the discrete-time model of the control target can be obtained by determining the combination of coefficients used in the discrete-time model (formula) such that the difference from the acquired data from the Fourier-transformed control target is minimized. The acquired data from the control target is the output data of the control target. Note that, for example, the acquired data from the control target detected by various sensors can be displayed with the horizontal axis representing time. On the other hand, the acquired data from the Fourier-transformed control target can be displayed with the horizontal axis representing frequency.

[0019] Figure 2 is an explanatory diagram schematically showing the correlation between the data obtained by Fourier-transforming the output data of the control target and the discrete-time model (formula) of the control target. The characteristic line P1 shown by the dashed line in Figure 2 is obtained by Fourier-transforming the output data of the control target. The characteristic line P2 shown by the solid line in Figure 2 is the output value obtained by the discrete-time model as shown in Equation (1).

[0020] The discrete-time model of the controlled object can be fitted to the output data of the controlled object by finding a combination of coefficients in the formula of the discrete-time model that overlaps with the characteristic line P1, which is a graph obtained by Fourier-transforming the output data of the controlled object, as shown in, for example, FIG. 2. The discrete-time model of the controlled object is calculated for each operating condition of the controlled object.

[0021] Here, there are multiple combinations of coefficients used in the discrete-time model of the controlled object that overlap (match) with the data obtained by Fourier-transforming the output data of the controlled object (for example, the characteristic line P1), that is, the discrete-time model of the controlled object fitted to the output data of the controlled object.

[0022] That is, among the combinations of coefficients that result in an overlap (match) with the data obtained by Fourier-transforming the output data of the controlled object (for example, the characteristic line P1), there are also local optimal solutions that correspond only to the operating conditions corresponding to the output data of the controlled object and do not guarantee continuity with the operating conditions for which the output data of the controlled object is not obtained.

[0023] Therefore, in the present invention, while calculating a combination of coefficients in the formula of the discrete-time model of the controlled object so as to obtain a characteristic line P2 with the minimum difference from the characteristic line P1, the formula of the discrete-time model using the calculated coefficient values is converted into the formula of the continuous-time model of the controlled object, and it is verified whether the parameters having physical meanings in this converted continuous-time model formula reflect the physical meanings that can be read from the acquired data from the controlled object. Based on this verification result, the combination of coefficients in the formula of the discrete-time model of the controlled object fitted is determined.

[0024] The equation of the continuous-time model of the controlled object can be expressed, for example, as in Equation (2). The s in Equation (2) is an independent variable. The k0 and k1 in Equation (2) are coefficients, respectively. The ζ in Equation (2) is the damping ratio (response waveform) and is a parameter with a physical meaning. The ω in Equation (2) is the natural angular frequency (response speed) and is a parameter with a physical meaning.

[0025]

Number

[0026] In the present invention, the equation of the discrete-time model of the controlled object is determined such that the damping ratio ζ and the natural angular frequency ω in the equation of the continuous-time model obtained by converting the equation of the discrete-time model reflect the physical meaning read from the acquired data from the controlled object.

[0027] For example, the damping ratio ζ in Equation (2) can be read using the acquired data detected from the controlled object, as shown in FIG. 3 for example.

[0028] FIG. 3 is an explanatory diagram schematically showing the procedure for reading the damping ratio ζ used in the equation of the continuous-time model of the controlled object.

[0029] For example, it is possible to read what value of the damping ratio the waveform of the damping ratio of the acquired data, which is the time-series data of the air-fuel ratio as the acquired data of the internal combustion engine as the controlled object, is using the time-series data of the air-fuel ratio.

[0030] Then, in the present invention, the coefficient used in the discrete time representing the behavior of the controlled object is determined such that the difference from the acquired data from the controlled object after Fourier transform is minimized, and the parameters having a physical meaning in the equation of the continuous-time model obtained by converting the equation of the continuous-time model of the controlled object reflect the physical meaning read from the acquired data from the controlled object.

[0031] The coefficients in the equation of the discrete-time model determined in this way are ensured to be continuous with the operating conditions under which the output data of the controlled object is not obtained.

[0032] FIG. 4 is an explanatory diagram showing a comparison between the case where the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object converted from the discrete-time model are not considered and the case where they are considered when obtaining the coefficient a0 in the equation of the discrete-time model of the controlled object by fitting. (a) in FIG. 4 shows an example of the case where the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object converted from the discrete-time model of the controlled object are not considered. (b) in FIG. 4 shows an example of the case where the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object converted from the discrete-time model of the controlled object are considered.

[0033] As shown in FIG. 4(a), when the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object converted from the discrete-time model of the controlled object are not considered, the values obtained by fitting may be local optimal solutions, and there may be cases where the values lack continuity corresponding to changes in the operating conditions under which the output data of the controlled object is not obtained.

[0034] On the other hand, as shown in FIG. 4(b), when the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object converted from the discrete-time model of the controlled object are considered, the values obtained by fitting become global optimal solutions and have continuity corresponding to changes in the operating conditions under which the output data of the controlled object is not obtained.

[0035] FIG. 5 is an explanatory diagram showing a comparison of an example of the identification result, control result, and various estimation results when the controlled object is controlled by incorporating a discrete-time model.

[0036] Figure 5(a) shows the identification result of determining the coefficients used in the discrete-time model equation of the controlled object such that the difference from the output data of the Fourier-transformed controlled object is minimized without considering the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object. The dashed line in the identification result of Figure 5(a) is the output data of the Fourier-transformed controlled object, and the solid line in the identification result is the discrete-time model of the identification result.

[0037] Also, Figure 5(a) shows the results of air-fuel ratio control of an internal combustion engine as the controlled object, air-fuel ratio estimation of the internal combustion engine as the controlled object, and disturbance estimation of the internal combustion engine as the controlled object, using the discrete-time model of the controlled object obtained by fitting so that the difference from the output data of the Fourier-transformed controlled object is minimized without considering the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object.

[0038] Figure 5(b) shows the identification result of determining the coefficients used in the discrete-time model equation of the controlled object such that the difference from the output data of the Fourier-transformed controlled object is minimized while considering the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object according to the present invention. The dashed line in the identification result of Figure 5(b) is the output data of the Fourier-transformed controlled object, and the solid line in the identification result is the discrete-time model of the identification result.

[0039] Also, Figure 5(b) shows the results of air-fuel ratio control of an internal combustion engine as the controlled object, air-fuel ratio estimation of the internal combustion engine as the controlled object, and disturbance estimation of the internal combustion engine as the controlled object, using the discrete-time model of the controlled object obtained by fitting so that the difference from the output data of the Fourier-transformed controlled object is minimized while considering the values of the parameters having physical meanings in the equation of the continuous-time model of the controlled object according to the present invention.

[0040] As shown in Fig. 5(b), by using the discrete-time model of the controlled object according to the present invention that is fitted while considering the values of the parameters having physical meanings in the formula of the continuous-time model of the controlled object converted from the discrete-time model of the controlled object, for example, it is possible to accurately perform the air-fuel ratio control of an internal combustion engine as the controlled object, the air-fuel ratio estimation of the internal combustion engine as the controlled object, and the disturbance estimation of the internal combustion engine as the controlled object.

[0041] As described above, in the present invention, the difference from the acquired data from the controlled object after Fourier transform is minimized, and when converted into the formula of the continuous-time model of the controlled object, the parameters (damping ratio ζ, natural angular frequency ω) having physical meanings in this continuous-time model formula are determined so as to reflect the physical meanings read from the acquired data from the controlled object. The coefficients used in the discrete-time model representing the behavior of the controlled object are determined.

[0042] As a result, in the present invention, the fitting between the formula of the discrete-time model of the controlled object and the acquired data from the controlled object is improved, and it becomes possible to obtain a global optimal solution of the coefficients used in the discrete-time model of the controlled object, and the accuracy of the formula of the discrete-time model of the controlled object can be improved. Therefore, in the present invention, it becomes possible to accurately control the controlled object by using the formula of the discrete-time model of the controlled object calculated from the acquired data from the controlled object.

[0043] In addition, according to the present invention, since the accuracy of the formula of the discrete-time model of the controlled object is improved, if the discrete-time model of the controlled object is incorporated into the control device, the control accuracy of the controlled object by the control device is improved.

[0044] In the present invention, since the coefficients used in the formula of the discrete-time model of the control object have continuity corresponding to the operating conditions under which the output data of the control object is not obtained, the behavior of the control object can be predicted by so-called interpolation and extrapolation. That is, if the discrete-time model of the control object is calculated under several operating conditions as described above, the behavior of the control object under the operating conditions for which the discrete-time model of the control object has not been calculated can be accurately predicted.

[0045] As a result, in the present invention, instead of switching the control according to the operating conditions, the calculated discrete-time model can be used to continuously control the control object according to the operating conditions, and the control accuracy of the control object is improved.

[0046] Further, in the present invention, the coefficients used in the formula of the discrete-time model of the control object can be treated as having continuity corresponding to changes in the operating conditions. When incorporating the discrete-time model of the control object into the control device, the number of operating conditions in the table for incorporating the discrete-time model can be reduced, and the amount of memory used can be decreased.

[0047] Note that, as a method of incorporating the discrete-time model of the control object into the control device, it is also possible to use an approximate formula instead of a table. Even in this case, the amount of memory used by the control device when incorporating the discrete-time model can be decreased.

[0048] Also, by reducing the number of operating conditions, it is possible to reduce the man-hours for data acquisition of the control object and coefficient determination of the discrete-time model.

[0049] As described above, specific embodiments of the present invention have been described. However, the present invention is not limited to the above-described embodiments, and various modifications are possible without departing from the spirit thereof.

[0050] For example, the formula of the discrete-time model of the control object is not limited to a quadratic formula, but in many cases, a quadratic formula is sufficient also in terms of suppressing overfitting.

Claims

1. The coefficient used in the discrete-time model of the control object is determined such that the difference from the acquired data from the control object is minimized, and the parameters having a physical meaning in the converted continuous-time model equation when converted into the equation of the continuous-time model of the control object reflect the physical meaning read from the acquired data from the control object. A method for calculating a discrete-time model, characterized in that.

2. The method for calculating a discrete-time model according to claim 1, wherein the parameters having a physical meaning in the equation of the continuous-time model are the natural angular frequency and the damping ratio.

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