Estimation system, estimation method, and program

Abstract

The purpose of the present invention is to estimate an output of a control object without limiting the number of types of input data. This estimation system (1) estimates the output of a control object (30) on the basis of experimental data acquired by a closed-loop control system that outputs output data corresponding to input data from a control device (20) to the control object (30) and feeds back the output data to the control device (20). The estimation system (1) includes: an experimental data storage unit (41) that stores experimental data; an input unit (42) to which arbitrary input data is input; and a calculation unit (43) that calculates the estimated output data on the basis of the following numbers 1 and 2.

Description

Estimation system, estimation method, and program

[0001] The present invention relates to an estimation system, an estimation method, and a program.

[0002] Conventionally, control systems that use a physical model of a controlled object are known. However, it is difficult to generate a physical model of a controlled object with high accuracy, and the generation cost is high. Therefore, the inventors of the present application have proposed a convolution-based data-driven simulation (CDDS) method that estimates an output without using a physical model of the controlled object, as disclosed in Non-Patent Document 1 below.

[0003] Naoki Kameya, Yasutaka Fujimoto, Yu Hosoyamada, and Toyoaki Suenaga “Convolution-Based Data-Driven Simulation and Controller Design Method” IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, pages:1-10, 2023

[0004] Here, the method of Non-Patent Document 1 is limited in its applicability to cases where the number of types of input data for the control target is one.

[0005] An object of the present invention is to provide an estimation system, an estimation method, and a program that are capable of estimating the output of a controlled object without any restriction on the number of types of input data.

[0006] The invention disclosed in this application to solve the above problems has various aspects, and representative aspects thereof are outlined below.

[0007] (1) An estimation system that outputs output data corresponding to input data from a control device to a controlled object and estimates an output of the controlled object based on experimental data acquired by a closed-loop control system that feeds back the output data to the control device, the estimation system including: an experimental data storage unit that stores the experimental data; an input unit that receives input data; and a calculation unit that calculates estimated output data based on the following equations 1 and 2.

[0008] (2) In (1), the estimation system, wherein the number of types of input data input to the controlled object is two or more.

[0009] (3) An estimation method for estimating an output of a controlled object based on experimental data acquired by a closed-loop control system that outputs output data corresponding to input data from a control device to the controlled object and feeds the output data back to the control device, the estimation method including the steps of: storing the experimental data; inputting arbitrary input data; and calculating estimated output data based on the following equations 3 and 4.

[0010] (4) A program for estimating the output of a controlled object based on experimental data acquired by a closed-loop control system that outputs output data corresponding to input data from a control device to the controlled object and feeds the output data back to the control device, the program causing a computer to execute the following steps: storing the experimental data; inputting arbitrary input data; and calculating estimated output data based on the following equations 5 and 6.

[0011] According to the above aspects (1) to (4), the output of the controlled object can be estimated without any limitation on the number of types of input data.

[0012] 7C is a functional block diagram showing the hardware configuration of an estimation system according to the present embodiment. FIG. 7D is a functional block diagram showing the functions implemented by the estimation device. FIG. 7E is a flowchart showing the calculation process of estimated output data. FIG. 7F is a block diagram showing an example in which an output 1 and an output 2 are output when an input 1 and an input 2 are input to a control object whose transfer function matrix is ​​represented by P(z). FIG. 7G is a diagram showing an example of experimental data. FIG. 7H is a diagram showing an example of an estimation result using the experimental data shown in FIG. 5. FIG. 7I is a diagram showing a two-input, two-output two-inertia actuator. FIG. 7J is a block diagram of another simulation of the present embodiment. FIG. 7J is a diagram showing an example of experimental data. FIG. 7I is a block diagram showing an example of an estimation result using the experimental data shown in FIG. 7C. FIG. 7F is a functional block diagram showing the functions implemented by a parameter adjustment device. FIG. 7G is a block diagram showing an example of a data-driven model and a reference model. FIG. 7H is a block diagram showing an example in which closed-loop characteristics are matched to a corresponding reference model instead of being matched to a reference model. FIG. 7I is a block diagram showing an example in which a feedback signal is replaced with the output of a reference model. FIG. 7I is a response graph of data acquisition experiment 1. FIG. 7I is a response graph of data acquisition experiment 2. FIG. 7J is a diagram showing calculated control gains. FIG. 7J is a diagram showing a reference trajectory and a response when control is performed using the calculated control gains.

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

[0014] [Overview] An estimation system 1 according to this embodiment employs a data-driven simulation (CDDS) method based on a time-domain convolution operation using experimental data of inputs and outputs to a controlled object (plant) 30 in a discrete-time closed-loop control system, to estimate the output of the controlled object 30 with multiple inputs and multiple outputs (Multi-In Multi-Out: MIMO). The estimation system 1 can estimate the output of the controlled object 30 without using a physical model of the controlled object 30. Furthermore, because the estimation system 1 is a simulation system using only the controlled object 30, a nonlinear controller with a nonlinear input-output relationship can also be applied as the control device 20.

[0015] An example application of the estimation system 1 is a multi-axis robot such as a manipulator as the control target 30. When a multi-axis robot is used as the control target 30, data relating to the current values ​​supplied to the motors that drive the axes may be input as input data, and data relating to the rotational position, angular velocity, rotational torque, etc. of the motors that drive the axes may be output as output data.

[0016] [Hardware Configuration] Fig. 1 is a block diagram showing the hardware configuration of an estimation system according to this embodiment. As shown in Fig. 1, the estimation system 1 includes a closed-loop control system that acquires output data corresponding to input data to a control target 30 from a control device (controller) 20 and feeds back the output data to the control device 20. The control device 20 is preferably driven by commands from a host control device 10.

[0017] The estimation device 40 is a device that estimates an output using experimental data of inputs and outputs of the controlled object 30. The estimation device 40 is a computer including at least one processor. The estimation device 40 includes at least one of a volatile memory and a non-volatile memory, and a program stored in the memory is executed by the processor. The estimation device 40 may include at least one of a communication interface for wired communication and a communication interface for wireless communication. The program stored in the estimation device 40 may be supplied via a network. The estimation device 40 may also include a reading unit (e.g., a memory card slot) that reads a computer-readable information storage medium, or an input / output unit (e.g., a USB terminal) for connecting to an external device. In this case, the program stored in the information storage medium may be supplied via the reading unit or the input / output unit.

[0018] 1 is an example and is not intended to be limiting. The estimation system 1 may include at least one computer. For example, the estimation device 40 may be configured with two or more computers.

[0019] 2 is a functional block diagram showing functions realized by the estimation device 40. The estimation device 40 includes an experimental data storage unit 41, an input unit 42, and a calculation unit 43. The input unit 42 and the calculation unit 43 are mainly realized by a processor included in the estimation device 40. The experimental data storage unit 41 is mainly realized by a memory included in the estimation device 40.

[0020] The experimental data storage unit 41 stores experimental data relating to the input and output of the controlled object 30 in the closed-loop control system shown in Fig. 1. The experimental data storage unit 41 preferably stores r sets of experimental input data and experimental output data. Arbitrary input data is input to the input unit 42. The calculation unit 43 calculates estimated output data based on equations (11-1) and (13) described below.

[0021] [Estimation of Output Data] In this embodiment, the number of input data is m and the number of output data is p. Note that m and p are natural numbers equal to or greater than 1. Furthermore, in this embodiment, the number of experiments is r, and the system is a discrete system with time k = 0, 1, ..., T. An r-dimensional vector V(z) is introduced as an intermediate variable into the relationship between an arbitrary input and an estimated output and the relationship with the experimental data, thereby obtaining an estimated output y(k) in the time domain. Note that the experimental data refers to experimental input data and experimental output data obtained by actually driving the control object 30. In the following formulas, arbitrary input data and estimated output data estimated based on the input data are represented by adding a hat symbol "^" to the parameters representing them. Furthermore, in the following formulas, input / output data related to the experiment are represented by adding a tilde symbol "~" to the parameters representing them.

[0022] When the time k=0, 1, ..., T, and the input data input to the control target 30 in the j-th experiment is expressed as an m-dimensional vector and the output data obtained at that time as a p-dimensional vector, the input and output data are related by the following formula (1). Also, the Z transform of the input data is given by the following formula (2-1), and the Z transform of the output data is given by the following formula (2-2). Here, U ｊ (z) is the input data, Y ｊ(z) is the output data, and P(z) is a transfer function matrix representing a physical model of the control object 30 with m inputs and p outputs. It is also assumed that the total number of experiments is r, where r is equal to or greater than m.

[0023]

[0024]

[0025] The relationship between the experimental input data U tilde and the experimental output data Y tilde for the number of experiments r in the above formula (1) can be expressed in matrix form as the following formula (3), where the experimental input data in formula (3) is a matrix expressed by the following formula (4-1) or (4-3), and the experimental output data is a matrix expressed by the following formula (4-2) or (4-4).

[0026]

[0027]

[0028] Here, the estimated output data when any input data is given at time k can be expressed by the following formula (5). Note that input data U is the Z transform of any input data u, and is expressed by the following formula (6-1). Also, output data Y is the Z transform of estimated output data y, and is expressed by the following formula (6-2).

[0029]

[0030]

[0031] Here, an r-dimensional vector V(z) is introduced as an intermediate variable that satisfies the following formula (7). Furthermore, when the following formula (7), which is an intermediate variable introduction formula, is expressed in the time domain by performing a time domain convolution operation, it becomes the following formula (8). * is a convolution operator in discrete time. It is assumed that input data u in the time domain is related by an inverse Z transform and expressed by the following formula (9-1). It is also assumed that vector v(k) in the time domain is related by an inverse Z transform and expressed by the following formula (9-2). The bold R in the following formulas (9-1) and (9-2) represents the real number space, and R m×ｒ (R is in bold) is a matrix with m rows and r columns, R r(R is in bold) represents an r-dimensional vector.

[0032]

[0033]

[0034]

[0035] Here, when the convolution operation of the above formula (8) is written down, the following formula (10) is obtained using the internal variable i of the discrete time.

[0036]

[0037] Here, assuming that u (0) is the full row rank, which is the maximum rank of the matrix, solving equation (10) for v(k) gives the following equation (11-1). Note that full row rank refers to a property that holds when the number of rows in a matrix is ​​equal to the number of linearly independent rows among those rows.

[0038]

[0039]

[0040] Furthermore, the above equation (5) can be expressed as the following equation (12) by eliminating the transfer function matrix P(z) of the controlled object 30 using the above equations (3) and (7).

[0041]

[0042] Then, when the above equation (12) is converted into an equation in the time domain, the following equation (13) is obtained.

[0043]

[0044] From the above, the estimated output data y hat can be obtained by calculating the above equation (13) using the above equation (11-1).

[0045] 3 is a flowchart showing the process of calculating estimated output data. Here, an example will be described in which r sets of experimental data have already been acquired and stored in the memory of the estimation device 40. First, arbitrary input data is input to the estimation device 40 (S1). The estimation device 40 uses the input data to calculate estimated output data based on the above formulas (11-1) and (13) (S2).

[0046] [Simulation Results] Here, specific simulation results of this embodiment will be described with reference to Figs. 4 to 6. Here, an example of a controlled object 30 with two inputs and two outputs will be described. Fig. 4 shows a case where an input 1 (u １ ) and input 2 (u ２ ) is input, the output 1 (y １ ) and output 2 (y ２ 5 shows an example of experimental data. FIG. 6 shows an example of an estimation result using the experimental data shown in FIG. 5.

[0047] The waveforms in the upper left (Exp. #1) and upper right (Exp. #1) of Figure 5 show the waveforms of Output 1 and Output 2 in the first experiment, in which the amplitude of Input 1 (Exp. #1) is 1 and the amplitude of Input 2 (Exp. #1) is 2. The waveforms in the upper left (Exp. #2) and upper right (Exp. #2) of Figure 5 show the waveforms of Output 1 and Output 2 in the second experiment, in which the amplitude of Input 1 (Exp. #2) is 2 and the amplitude of Input 2 (Exp. #2) is 1.

[0048] 6 shows the actual output waveform (thin, thick line: Actual) from the controlled object 30 and the estimated output waveform (thick, thin line: CDDS) by the estimating device 40 when arbitrary input data is input using the two sets of experimental data (input / output data) shown in FIG. 6. As shown by the waveforms in the upper part of FIG. 6, it can be confirmed that the output waveforms estimated by the estimating device 40 are almost identical to the actual output waveforms from the controlled object 30 for both Output 1 and Output 2. In other words, it can be confirmed that the estimation system 1 according to this embodiment can reproduce the output estimation with high accuracy.

[0049] 7A to 7D, other simulation results of this embodiment will be described. Here, an example will be described in which the two-input, two-output, two-inertia actuator shown in FIG. 7A is used as the controlled object 30. A block diagram of this simulation is shown in FIG. 7B, and the experimental conditions are shown in Table 1 below.

[0050]

[0051] The waveforms in the upper right (Exp. #1) and upper left (Exp. #1) of Figure 7C show the waveforms of Output 1 and Output 2 in the first experiment when the torque of Input 1 is set to 0.35 [Nm] as shown in the waveform in the lower right (Exp. #1) and the torque of Input 2 is varied from -0.1 [Nm] to 0 [Nm] as shown in the waveform in the lower left (Exp. #1). The waveforms in the upper right (Exp. #2) and upper left (Exp. #2) of Figure 7C show the waveforms of Output 1 and Output 2 in the second experiment when the torque of Input 1 is set to 0.45 [Nm] as shown in the waveform in the lower right (Exp. #2) and the torque of Input 2 is varied from -0.2 [Nm] to 0 [Nm] as shown in the waveform in the lower left (Exp. #2).

[0052] 7D shows the actual output waveform (thin, thick line: Actual) from the controlled object 30 and the estimated output waveform (thick, thin line: CDDS) by the estimating device 40 when arbitrary input data is input using the two sets of experimental data (input / output data) shown in FIG. 7C. As shown by the waveforms in the upper part of FIG. 7D, it can be confirmed that the output waveforms estimated by the estimating device 40 are almost identical to the actual output waveforms from the controlled object 30 for both Output 1 and Output 2. In other words, it can be confirmed that the estimation system 1 according to this embodiment can reproduce the output estimation with high accuracy.

[0053] [Summary] The estimation system 1 according to the present embodiment described above can estimate the output of the controlled object 30 without any limitation on the number of types of input data. The estimation system 1 is particularly useful when the number of types of input data is two or more. Furthermore, as expressed by the above formulas (11-1) and (13), the estimation system 1 does not require a transfer function representing a physical model of the controlled object 30, and therefore can estimate the output of the controlled object 30 without constructing a physical model of the controlled object 30. Furthermore, as expressed by the above formulas (11-1) and (13), the estimation system 1 can estimate the output of the controlled object 30 regardless of parameters related to the control device 20, and therefore can be used with both linear and nonlinear control devices 20.

[0054] Although the embodiments of the present invention have been described above, the specific configurations shown in these embodiments are merely examples and are not intended to limit the technical scope of the present invention. Those skilled in the art may modify these disclosed embodiments as appropriate, and it should be understood that the technical scope of the invention disclosed in this specification also includes such modifications.

[0055] [Comparative Example] Here, as a comparative example, another calculation example of estimated output data will be described. In the above embodiment, the above formula (12) was obtained by introducing an r-dimensional vector V(z) that satisfies the above formula (7). The reason for introducing the r-dimensional vector V(z) in this manner is that, although it would be desirable to eliminate P(z) from the above formulas (3) and (5) to find the relationship between U tilde (z), U hat (z), Y tilde (z), and Y hat (z), each of these parameters is expressed as a determinant assuming multiple inputs and multiple outputs, which makes the calculation complicated. However, although the calculation becomes more complicated, it is possible to calculate estimated output data without introducing the r-dimensional vector V(z).

[0056] An example will be described below in which estimated output data is calculated for a two-input, two-output control object 30 without introducing an r-dimensional vector V(z) that is an intermediate variable.

[0057] [Comparative Example 1] In this example, estimated output data is calculated by devising input data. When two experiments are performed, only the jth input data is given, and the other input data is set to 0, the first experimental data set shown in the following formula (14-1) and the second experimental data set shown in the following formula (14-2) are obtained, and the following formula (15) is obtained from these. Furthermore, the following formula (16) is obtained from formula (15).

[0058]

[0059]

[0060]

[0061] The estimated output data when any input data is input to the controlled object 30 is expressed by the following formula (17): Furthermore, by substituting the following formula (17) into the above formula (16), the following formula (18) is obtained.

[0062]

[0063]

[0064] Here, when each estimated output data is expressed by the following equation (19), the relational expression of the following equation (20) is obtained.

[0065]

[0066]

[0067] Then, estimated output data for each experiment can be calculated from the above formula (18) and formula (20), as shown in the following formula (21).

[0068]

[0069] [Comparative Example 2] In this example, estimated output data is calculated based on an inverse matrix calculation. Two experiments are performed, and different waveforms are applied to the input data during the experiments. In this case, a first experimental data set shown in the following formula (22-1) and a second experimental data set shown in the following formula (22-2) are obtained, from which the following formula (23) is obtained. Furthermore, the following formula (24) is obtained from formula (23). However, it is assumed that delta (z) in the following formula (24) is the following formula (25).

[0070]

[0071]

[0072]

[0073]

[0074] Furthermore, the estimated output data when any input data U hat is input to the controlled object 30 is expressed by the following equation (26).

[0075]

[0076] Then, by substituting the above formula (26) into the above formula (24), the following formula (27) is obtained. Furthermore, the following formula (27) can be replaced as in the following formula (28). However, it is assumed that W(z) in formula (28) is expressed by the following formula (29).

[0077]

[0078]

[0079]

[0080] Moreover, the above equation (28) is expressed in the time domain as the following equation (30): Each element in the following equation (30) is expressed by the following equation (31).

[0081]

[0082]

[0083] Moreover, when the above formula (30) is expressed as a specific calculation formula, it becomes the following formula (32).

[0084]

[0085] Then, estimated output data can be calculated from the above equation (32) as shown in the following equation (33).

[0086]

[0087] As described above, as shown in Comparative Example 1 and Comparative Example 2, it is possible to calculate estimated output data without introducing the r-dimensional vector V(z), which is an intermediate variable, but the calculation is complicated. Furthermore, while Comparative Example 1 and Comparative Example 2 show relatively simple examples with two inputs and two outputs, the calculation becomes even more complicated as the number of inputs and outputs increases.

[0088] [Design Method of Control Device 20] Next, a design method of control device 20 using parameter adjustment device 50 will be described for a general control device, a control device whose objective function is differentiable with respect to control parameters, and a control device whose control parameters are linearly separable. As shown in FIG. 1 , estimation system 1 may include parameter adjustment device 50.

[0089] 8 is a functional block diagram showing functions implemented in the parameter adjustment device 50. The parameter adjustment device 50 includes an estimated output data acquisition unit 51, a parameter generation unit 52, and a parameter output unit 53. Each of these functions is mainly implemented by a processor included in the parameter adjustment device 50.

[0090] The estimated output data acquisition unit 51 acquires estimated output data output from the estimation device 40. The parameter generation unit 52 calculates and generates optimal parameters based on the estimated output data. The parameter output unit 53 outputs the generated optimal parameters to the control device 20.

[0091] The parameter adjustment device 50 is not limited to being a separately provided computer, and the functions realized by the parameter adjustment device 50 may be realized in the upper control device 10 or the control device 20.

[0092] [A. General Control Device 20] First, let W∈R ｐ×ｐ is a positive definite symmetric matrix representing the weights, y ｄ (k)∈R ｐ is an arbitrary reference trajectory (target trajectory) of the output, θ∈R ｑ is a control parameter (parameter vector of the control device 20), and the objective function J(θ) is defined by the following equation (34).

[0093]

[0094] Estimated input data u ∈ R ｍ is assumed to be generated through an arbitrary control device, including nonlinearities such as saturation, based on a feedback signal of the estimated output data y, assuming the implementation of an actual control device. Using this control device 20 and the above equations (11-1) and (13), the objective function J(θ) for a certain control parameter θ can be evaluated by equation (34). Therefore, the optimal parameter θ that minimizes the objective function J(θ) shown in equation (34) can be calculated by ＊ can be calculated by the following equation (35) using an appropriate optimization solver. ｄ (k) may be given as a function, or may be generated using a reference model M(z) described later in the case where the control parameter θ is linearly separable.

[0095]

[0096] Moreover, the objective function J(θ) may be expressed using an arbitrary convex function f() as shown in the following equation (36) other than the quadratic form shown in equation (34).

[0097]

[0098] [B. When the control parameters are differentiable] If the gradient of the objective function J(θ) can be calculated, various gradient methods can be used to efficiently find the optimal parameter θ ＊ The gradient ∂J(θ) / ∂θ of the objective function J(θ) can be expressed by the following equation (37).

[0099]

[0100] Here, the gradient of y(k;θ) with respect to θ expressed by the above formula (13) can be calculated as in the following formula (38). However, the left side of the lower part of the following formula (38) is a matrix representing the gradient of v(k;θ) with respect to θ.

[0101]

[0102] Furthermore, when the above formula (37) is differentiated with respect to θ, the Hessian matrix H(θ)∈R is obtained as shown in the following formula (39): ｑ×ｐ The second term on the right side of the following equation (39) can be transformed based on the following equation (40).

[0103]

[0104]

[0105] However, if it is difficult to calculate the second term on the right side of equation (39), it may be ignored and approximated as shown in equation (41) below.

[0106]

[0107] Optimal parameter θ ＊ is the appropriate initial solution θ ０ Starting from this, it can be obtained by repeating calculations using Newton's method shown in the following equation (42).

[0108]

[0109] [C. When the control parameters of the control device 20 are linearly separable] The virtual input U is linearly separated. ｂ (z; θ)∈Q[z] ｍ×ｐand the feedforward controller C ｆ (z; θ)∈Q[z] ｍ×ｐ Consider the case where R(z)∈Q[z] is determined as in the following equation (43). ｐ is the Z transform of the target signal. Also, Q[z] is a set representing the entire set of advantageous functions.

[0110]

[0111] C(z;θ) is C ｂ (z; θ) and C ｆ (z; θ) and is expressed by the following equation (44).

[0112]

[0113] When the equation (44) is written in the time domain, it can be expressed by the following equation (45): ｆ (z;θ)=Z -１ {C ｆ (z; θ)}∈R ｍ×ｐ And, C ｂ (z;θ)=Z -１ {C ｂ (z; θ)}∈R ｍ×ｐ is the impulse response of the control device 20, and r(k)=Z -１ {R(z)}∈R ｐ is the target signal and * is the convolution operator.

[0114]

[0115] Furthermore, consider the case where the control parameters of the control device 20 can be linearly separated as shown in the following equation (46).

[0116]

[0117] The response of the closed loop system is expressed by the following equation (48) by solving the following equation (47): where I is a unit matrix.

[0118]

[0119]

[0120] Also, consider the following equation (49) as the response of the reference model M(z).

[0121]

[0122] Let us consider finding the control parameters that minimize the above equation (34). That is, the closed loop characteristic (I+P(z)C ｂ (z;θ) －１ P(z)C ｆ The control parameter θ is determined so that (z; θ) is closest to the reference model M(z). This can be represented by a block diagram as shown in Figure 9.

[0123] Instead of matching the closed-loop characteristics to a reference model M(z), consider matching them to a corresponding reference model, as shown in Figure 10A. This replaces the feedback signal Y(z;θ) with the reference model output Y(z), as shown in Figure 10B. The target open-loop characteristics can be expressed by the following equation (50) by solving equation (47).

[0124]

[0125] Here, the transfer function P(z)C(z;θ) from the signal X(z;θ) to the output Y(z;θ) has an open loop characteristic. The corresponding open loop reference model is M ０ (z). That is, a model M that satisfies the following formula (51) ０ Consider (z).

[0126]

[0127] Transforming equation (51) yields equation (52) below.

[0128]

[0129] Then, the following equation (53) is established from equation (52) and the above equation (49).

[0130]

[0131] Also, X ｄ (z) is expressed by the following equation (54) using equation (52).

[0132]

[0133] Also, Xｄ (z) is expressed by the following formula (55) using the above formula (52).

[0134]

[0135] X represented by formula (55) ｄ (z), the open loop characteristics P(z)C(z;θ) of the control device 20 and the controlled object 30 are calculated as an open loop reference model M ０ In other words, X ｄ (z) and evaluate the deviation of the output. ｄ Output Y of the control device 20 and the controlled object 30 when (z) is input ０ hat (z; θ) is expressed by the following equation (56), and the open-loop reference model M ０ Output Y ｏｄ (z) is expressed by the following formula (57).

[0136]

[0137]

[0138] The output Y of the open-loop reference model ｏｄ (z) is the original reference trajectory output Y ｄ The fact that it is equal to (z) can be confirmed by the following equation (58).

[0139]

[0140] The above formula (56) can be rearranged as the following formula (59) using the above formula (46). ｏ０ (z), Y hat ｏ０ｉ (z), U-hat ｏ０ｉ (z) are expressed by the following formula (60).

[0141]

[0142]

[0143] Furthermore, Y-Hat ｏ０ｉ (z) is a vector V that satisfies the following equation (61), similar to the above equation (12). ｏ０ｉ When (z) is introduced, it is expressed by the following equation (62).

[0144]

[0145]

[0146] When the above equations (59) to (61) are expressed in the time domain, they are expressed as the following equation (63).

[0147]

[0148] Furthermore, u ｏ０ｉ Hat is expressed by the following formula (64) in the same way as the above formula (11-1).

[0149]

[0150] Also, the output Y of the open-loop reference model ｏｄ The time domain signal of (z) is expressed by the following equation (65) from the above equation (58).

[0151]

[0152] Furthermore, the time domain signal of the input Xd(z) in the open loop reference model is expressed by the following equation (66) from the above equation (55). ｏ０ (k) = Z -1 {Y ｏｄ (z)}∈R ｐ , x ｄ (k) = Z -１ {X ｄ (z)}∈R ２ｐ , m ０ (k) = Z -１ {M ０ (z)}∈R ｐ×２ｐ , m(k)=Z -１ {M(z)}∈R ｐ×ｐ is.

[0153]

[0154] Therefore, the control parameter θ that minimizes the objective function, which is the weighted sum of squares of the deviations of the open-loop output shown in the following equation (67), can be calculated by solving ∂Jo(θ) / ∂θ=0 from the following equations (68) and (69) and using the calculation formula (70) below. When p≧q, † becomes a normal inverse matrix. On the other hand, when p<q, † needs to be calculated as a Moore-Penrose generalized inverse matrix.

[0155]

[0156]

[0157]

[0158]

[0159] In equation (70), the optimal parameter θ is calculated by a calculation that does not include repeated calculations. * Therefore, the calculation cost can be reduced compared to the equation (42) in which calculations are repeated until convergence occurs.

[0160] Here, we will show a numerical example applied to current control of a permanent magnet synchronous motor when the control parameters of the control device 20 are linearly separable. The d-q axis circuit equation of a permanent magnet synchronous motor is expressed by the following equation (71). Here, y1 and y2 are the d-axis and q-axis currents and the output of the controlled object 30, u1 and u2 are the d-axis and q-axis voltages and the input of the controlled object 30, Ld and Lq are the d-axis and q-axis winding inductances, R is the winding resistance, and ω is the rotor rotation speed. ω is assumed to be constant. The parameters are Ld = Lq = R = 1, and ω = 2. A digital control system with a sampling time of Ts = 0.05 and zero-order hold is assumed for the input is assumed.

[0161]

[0162] As a current control system, consider digital PI control (proportional-integral control) and non-interference control expressed by the following equation (72). Non-interference control is control that prevents interference between the d-axis and q-axis currents due to their changes. In the following equation (72), θ1 and θ3 represent proportional control gains, θ2 and θ4 represent integral control gains, and θ5 and θ6 represent non-interference control gains.

[0163]

[0164] Here, the control device 20 can perform linear separation with respect to the control gain as shown in the following equation (73).

[0165]

[0166] Further, as the reference model M(z), a model expressed by the following equation (74) in which the d-axis and q-axis are decoupled is considered.

[0167]

[0168] FIG. 11 is a response graph for data acquisition experiment 1, and FIG. 12 is a response graph for data acquisition experiment 2. Note that FIGS. 11 and 12 show data acquisition experiments 1 and 2, respectively, which were conducted with only proportional control gain θ1 = θ3 = 1 (i.e., θ2 to θ6 = 0). FIG. 13 shows the results of determining control gains θ1 to θ6 according to the procedure of the proposed method using the data shown in FIGS. 11 and 12. The right graph in FIG. 14 shows the response when control is performed using the determined control gains θ1 to θ6. Because this is nearly identical to the response of the reference model M(z) (left graph in FIG. 14), it can be confirmed that the proposed method described above, which assumes that the control parameters of the control device 20 are linearly separable, can determine control gains that achieve the response of the reference model M(z).

Claims

1. An estimation system that outputs output data corresponding to input data from a control device to a control target, and estimates the output of the control target based on experimental data obtained by a closed-loop control system that feeds back the output data to the control device, the estimation system including: an experimental data storage unit that stores the experimental data; an input unit to which arbitrary input data is input; and a calculation unit that calculates estimated output data based on the following equations (1) and (2).

2. The estimation system according to claim 1, wherein the number of types of the input data input to the control target is 2 or more.

3. An estimation method for estimating the output of a control target based on experimental data obtained by a closed-loop control system that outputs output data corresponding to input data from a control device to the control target and feeds back the output data to the control device, the estimation method including: a procedure for storing the experimental data; a procedure for inputting arbitrary input data; and a procedure for calculating estimated output data based on the following equations (3) and (4).

4. A program for estimating the output of a control target based on experimental data obtained by a closed-loop control system that outputs output data corresponding to input data from a control device to the control target and feeds back the output data to the control device, the program causing a computer to execute procedures for storing the experimental data, procedures for inputting arbitrary input data, and procedures for calculating estimated output data based on the following equations (5) and (6).

5. The estimation system according to claim 1, further comprising a parameter generation unit that generates an optimal parameter of the control device based on the following equation (7), wherein the control target is controlled by the control device in which the control parameter is adjusted to the optimal parameter. θ ＊ : Optimal parameter θ: Parameter vector of the control device y ｄ : Arbitrary reference trajectory of the output W: Positive definite symmetric matrix representing the weight N: Arbitrary natural number 6. A parameter generation unit that generates an optimal parameter of the control device by performing iterative calculation of Newton's method based on the following formula 8, and the control target is controlled by the control device in which the control parameter is adjusted to the optimal parameter. The estimation system according to claim 1. θ: Parameter vector of the control device H: Hessian matrix m: Number of types of input data J: Objective function 7. A parameter generation unit that generates an optimal parameter of the control device based on the following equation (9), wherein the control target is controlled by the control device in which the control parameter is adjusted to the optimal parameter, the estimation system according to claim 1. θ ＊ : Optimal parameter θ: Parameter vector of the control device ŷ ｏ０ : Estimated output data of the reference model represented in the time domain y ｄ : Any reference trajectory of the output data W: Positive definite symmetric matrix representing the weight N: Any natural number 8. An estimation system for estimating the output of a control target based on experimental data obtained by a closed-loop control system that outputs output data corresponding to input data from a control device to the control target and feeds back the output data to the control device, an experimental data storage unit that stores the experimental data; an input unit to which arbitrary input data is input; a calculation unit that calculates estimated output data based on a calculation formula having as a variable the input data in the time domain obtained by performing a convolution operation in the time domain on an intermediate variable introduction formula for the input data introducing an intermediate variable represented by an r-dimensional vector (r is the number of experiment times).

9. The estimation system according to claim 8, wherein the number of types of the arbitrary input data input to the control target is 2 or more.

10. The estimation system according to claim 8 or 9, further comprising a parameter generation unit that generates an optimal parameter of the control device based on the estimated output data, wherein the control target is controlled by the control device whose control parameter is adjusted to the optimal parameter.

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