Information processing device, information processing method, and program

Abstract

The present invention provides appropriate LUT parameters that improve the tracking of the output of the controlled object to the target response. [Solution] In gain-scheduled PID control, the information processing device 200 sets the LUT parameters of the LUT to be the LUT parameters that include a first term expressed by the L2 norm of the difference between the second output of the controlled object 104 and the third output of the reference model, a second term expressed by the L2 norm of the difference between two adjacent LUT parameters in the LUT, and a third term expressed by the L2 norm of the LUT parameters, and that minimize an evaluation function with the LUT parameters as variables.

Description

[Technical Field]

[0001] The present invention relates to an information processing device, an information processing method, and a program for adjusting LUT parameters of a controller in a feedback control system. [Background technology]

[0002] In feedback control such as PID (Proportional Integral Differential) control for controlling a controlled object, a technique is known in which a control gain such as a PID gain is changed according to the state of the controlled object based on look-up table (LUT) parameters in order to achieve desired control performance. Generally, adjusting the LUT parameters requires a great deal of effort, but Patent Document 1 discloses a technique for automatically adjusting the LUT parameters from acquired data. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-181937 Summary of the Invention [Problem to be solved by the invention]

[0004] However, if the acquired data contains noise, the LUT parameters may become large. In this case, the control gain becomes too large, causing the feedback system to become unstable. Furthermore, if the controlled object is linearized for each operating point and the LUT parameters are adjusted, the difference between adjacent LUT parameters becomes extremely large, causing the feedback system to become unstable. On the other hand, for controlled objects whose characteristics change suddenly, the desired control performance cannot be achieved unless the control gain is changed locally. In other words, it is necessary to deal with noise and appropriately set the smoothness of the LUT parameters.

[0005] The present invention has been made in view of these points, and has as its object to provide appropriate LUT parameters that improve the ability of the output of the controlled object to follow the target response. [Means for solving the problem]

[0006] In a first aspect of the present invention, there is provided an information processing device for determining LUT parameters for adjusting the control gain of the PID control in a control system including a controller that performs PID control, a controlled object that receives a first output of the controller as an input, a gain scheduler that adjusts a control gain of the controller, and a reference model that is a transfer function of a target value and a reference response of the controlled object, and in which a second output of the controlled object is fed back to an input of the controller, the information processing device includes an acquisition unit that acquires the first output of the controller and the second output of the controlled object when the first output is input, and an acquisition unit that acquires the first output of the controller and the second output of the controlled object when the first output is input, in a space having one or more states related to the controlled object as axes. Provided is an information processing device having: a storage unit that stores a lookup table in which a plurality of the LUT parameters used for calculating a control gain are arranged; and an adjustment unit that sets the LUT parameters of the lookup table to the LUT parameters that include a first term expressed by the L2 norm of the difference between the second output and a third output of the reference model based on the first output and the LUT parameters, a second term expressed by the L2 norm of the difference between two adjacent LUT parameters in the lookup table, and a third term expressed by the L2 norm of the LUT parameters, and that minimize an evaluation function with the LUT parameters as variables.

[0007] The adjustment unit may set the LUT parameters of the lookup table to the LUT parameters that minimize the evaluation function including the first term, the second term expressed by the L2 norm of the product of the difference between the LUT parameters and a vector representing a weight corresponding to the difference between the LUT parameters, and the third term.

[0008] The adjustment unit may set the LUT parameters of the lookup table to the LUT parameters that minimize the evaluation function including the first term, the second term expressed by the L2 norm of the product of the difference between the LUT parameters and a vector representing the weight determined according to a system gain indicating a ratio of the first output to the second output, and the third term.

[0009] The lookup table may be defined in a space having axes representing the rotation speed of an engine mounted on a vehicle and the amount of fuel injected into a combustion chamber of the engine, the acquisition unit may acquire the rotation speed and the amount of fuel, and the adjustment unit may change the weight according to the system gain corresponding to an operating point on the lookup table determined by the acquired rotation speed and amount of fuel.

[0010] The adjustment unit may decrease the weight as the system gain of the operating point increases.

[0011] The difference between the third output and the second output in the first term, the difference between the LUT parameters in the second term, and the LUT parameters in the third term may be expressed as vectors, the L2 norm of the first term may be expressed as the square root of the sum of the squares of each of the multiple differences between the third output and the second output included in the vector representing the difference between the third output and the second output, the L2 norm of the second term may be expressed as the square root of the sum of the squares of each of the multiple differences between the LUT parameters included in the vector representing the LUT parameter differences, and the L2 norm of the third term may be expressed as the square root of the sum of the squares of each of the multiple LUT parameters included in the vector representing the LUT parameters.

[0012] In a second aspect of the present invention, there is provided an information processing method executed by a computer for determining an LUT parameter for adjusting the control gain of the PID control in a control system including a controller that performs PID control, a controlled object that receives a first output of the controller as an input, a gain scheduler that adjusts a control gain of the controller, and a reference model that is a transfer function of a target value and a reference response of the controlled object, wherein a second output of the controlled object is fed back to an input of the controller, the information processing method including the steps of: acquiring the first output of the controller and the second output of the controlled object when the first output is input; and setting the LUT parameters of the lookup table to the LUT parameters that minimize an evaluation function with the LUT parameters as variables, the LUT parameters including: a first term expressed by the L2 norm of the difference between the second output and a third output of the reference model based on LUT parameters; a second term expressed by the L2 norm of the difference between two adjacent LUT parameters in a lookup table in which the LUT parameters used to calculate the control gain are arranged in a space whose axes are one or more states related to the controlled object; and a third term expressed by the LUT norm of the LUT parameters.

[0013] In a third aspect of the present invention, in a control system including a controller that performs PID control, a controlled object that receives a first output of the controller as an input, a gain scheduler that adjusts a control gain of the controller, and a reference model that is a transfer function of a target value and a reference response of the controlled object, wherein a second output of the controlled object is fed back to an input of the controller, the program for determining LUT parameters for adjusting the control gain of the PID control includes, in a computer mounted on a vehicle, an acquisition unit that acquires the first output of the controller and the second output of the controlled object when the first output is input, and a program for calculating LUT parameters for adjusting the first output and the LUT parameters. a first term expressed by the L2 norm of the difference between the second output and a third output of the reference model based on the parameter; a second term expressed by the L2 norm of the difference between two adjacent LUT parameters in a lookup table in which the LUT parameters used for calculating the control gain are arranged in a space whose axes are one or more states related to the controlled object; and a third term expressed by the L2 norm of the LUT parameters, and the LUT parameters of the lookup table are set to the LUT parameters that minimize an evaluation function whose variables are the LUT parameters. [Effects of the Invention]

[0014] The present invention provides an advantage in that it is possible to provide appropriate LUT parameters that improve the ability of the output of a controlled object to follow a target response. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a schematic diagram for explaining a gain schedule control system according to an embodiment of the present invention; [Figure 2] FIG. 1 is a schematic diagram for explaining a speed-type PID controller. [Figure 3] FIG. 1 is a diagram illustrating a configuration of an information processing device. [Figure 4] FIG. 1 is a schematic diagram of a two-dimensional grid-based LUT. [Figure 5]10A and 10B are diagrams for explaining the area after determining the surrounding nodes of the current operating point; [Figure 6] 10 is a flowchart illustrating an example of a process for adjusting LUT parameters. DETAILED DESCRIPTION OF THE INVENTION

[0016] [Gain-Scheduled Control Overview] An overview of the gain schedule control according to this embodiment will be described. The gain schedule control is a control method for changing the parameters (control gains) of a controller in accordance with the state of a controlled object to achieve desired control performance.

[0017] 1 is a schematic diagram illustrating a gain-scheduled control system according to this embodiment. In the following description, the gain-scheduled control system will be referred to as a control system S. The control system S is a closed-loop system. The control system S includes a controller 102, a controlled object 104, a gain scheduling unit 106, a reference model 108, and an information processing device 200. The control system S is a control system in which a second output of the controlled object 104 is fed back to an input of the controller 102.

[0018] The controller 102 is a controller that performs PID control. A first output u of the controller 102 is input to the controlled object 104. The gain scheduler 106 adjusts each control gain (proportional gain, integral gain, and differential gain) of the controller 102. The gain scheduler 106 is sometimes referred to as a gain scheduler. The reference model 108 is a transfer function between a target value r of the controlled object 104 and a reference response.

[0019] x∈R nxis a scheduling parameter and a measurable state of the controlled plant 104 input to the gain scheduler 106. u∈R is a first output of the controller 102 and a control input to the controlled plant 104. y∈R is a second output of the controlled plant 104. r∈R is a target value of the controlled plant 104. e∈R is the error between the target value and the output defined by e=ry. ρ(t)∈R m is a LUT parameter that is a function of time. t∈Z is discrete time. C(z,ρ) is a controller given as u=C(z,ρ)e. f(x,w) is a scheduling function given as ρ=f(x,w) and expressed as a look-up table (hereinafter referred to as "LUT"). Details of LUT will be described later. w∈R nw are tuning parameters (hereinafter referred to as "LUT parameters") that configure the scheduling function.

[0020] The control target 104 is a control object for verifying the control of the database, and is expressed by the following formula (1).

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[0021] f p is an unknown nonlinear function. u and n y are unknown orders of the input and output. In this embodiment, it is assumed that the system of the controlled object 104 is stable and can be linearized at any equilibrium point. Candidates for the LUT parameters of the LUT are associated with the output y of the controlled object 104. A general nonlinear system needs to be linearized to perform gain-scheduled control. However, in the present invention, gain-scheduled control is performed without system identification and linearization.

[0022] When gain schedule control is performed without system identification and linearization, the tuning parameters of the LUT are adjusted directly. In other words, the LUT is used as a gain scheduler. The tuning parameters of the LUT are determined by adjusting the closed-loop characteristics from the target value r to the output y using a user-defined reference model M. d The information processing device 200 adjusts the parameter so that it coincides with the parameter. Details of the information processing device 200 will be described later. In this embodiment, tuning parameters are determined that minimize an evaluation function expressed by the following equation (2).

number

[0023] The controller 102 is expressed by a function that uses parameters used for control as arguments. The gain of the parameters used for control changes according to the scheduling function of PID control. Specifically, the controller 102 is expressed by the following equation (3). Furthermore, the symbol in equation (3) is expressed by equation (4).

number

[0024] The controller 102 performs PID control. The controller 102 is a velocity-type PID controller. FIG. 2 is a schematic diagram for explaining a velocity-type PID controller. In FIG. 2, e(t) is an error. ρ p (t), ρ i (t), ρ d (t) are the proportional gain, integral gain, and differential gain, respectively. △ is 1-z -1 represents z -1 represents a backward operator. Gain-scheduled PID control is expressed by the following equation (5). Furthermore, each symbol in equation (5) is defined in equations (6) to (9).

number

[0025] [Configuration of information processing device 200] 3 is a diagram illustrating the configuration of the information processing device 200. The information processing device 200 has a storage unit 210 and a control unit 220. The storage unit 210 is a storage medium including a ROM (Read Only Memory), a RAM (Random Access Memory), a hard disk, etc. The storage unit 210 stores a program executed by the control unit 220.

[0026] The control unit 220 is a computational resource including a processor such as a CPU (Central Processing Unit). The control unit 220 executes a program stored in the storage unit 210 to realize the functions of an acquisition unit 221 and an adjustment unit 222.

[0027] FIG. 4 is a schematic diagram of a two-dimensional grid-based LUT. The two-dimensional grid-based LUT is configured in a space with two states as its axes. The vertical axis indicates a weighting coefficient representing the height of the complementary node. The LUT is stored in the storage unit 210. In the LUT, multiple LUT parameters used to calculate the control gain are arranged in a space with two states of the controlled object 104 as its axes. For example, the LUT parameters are arranged in a space with the rotation speed of an engine mounted on a vehicle and the amount of fuel injected into the engine's combustion chamber as its axes. As a specific example, in FIG. 4, Input 1 represents the engine rotation speed, and Input 2 represents the amount of fuel. However, the correspondence between Input 1 and Input 2 and the engine rotation speed and the amount of fuel may be reversed. The LUT is not limited to two states, and multiple parameters may be arranged in a space with one state as its axis or a space with three or more states as its axes.

[0028] The size of the LUT in this embodiment is M1 x M2, where M1 and M2 represent the number of interpolation nodes in each axis direction. x1 and x2 are user-defined inputs to the LUT. 1,k (c 1,1 , …, c 1,M1 ) and c 2,l (c 2,1 , …, c 2,M2 ) is a user-defined completion node. k,l ∈R (k=1 to M1, 1 to M2) is a weighting coefficient representing the height of the complementary node, and is the LUT parameter of the LUT to be adjusted. M1×M2 is θ k,l FIG. 5 is a diagram for explaining the area after determining the peripheral nodes of the current operating point. The shaded area in FIG. 5 represents the area after determining the four peripheral nodes of the current operating point x. x∈R 2is a vector consisting of x1 and x2.

[0029] The output ρ of the LUT after determining the four surrounding nodes of the current operating point is expressed by the following equation (10): Furthermore, each symbol in equation (10) is expressed by equation (11).

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[0030] To obtain the general formula (10), the basis function φ k,l (x,c) is introduced. Basis function φ k,l (x, c) is a function for finding the four surrounding nodes surrounding the current operating point and calculating the normalized area corresponding to the current operating point using equation (11). The output of the generalized LUT is expressed by the following equation (12). Equation (12) can be transformed into equation (13). w and φ in equation (13) are expressed by equations (14) and (15). The elements included in each of equations (14) and (15) are expressed by equation (16).

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[0031] Note that w and θ are both LUT parameters of the LUT, but are expressed as a vector and a matrix, respectively. Similarly, φ tilde and θ differ only in their representation. In the description of this embodiment, Equation (13) will be used in consideration of mathematical ease of handling.

[0032] Data-driven adjustment of the LUT parameters of the LUT will be described. VRFT (virtual reference feedback tuning) of this embodiment adjusts the LUT parameters directly from input / output data of the control system S without system identification and linearization. In other words, the information processing device 200 adjusts the LUT parameters so that the reference model and the control system S have the same characteristics. The process of adjusting the LUT parameters will be described below.

[0033] The acquisition unit 221 acquires input / output data. For example, the acquisition unit 221 acquires a first output of the controller 102 and a second output of the controlled object 104 when the first output is input. Specifically, the acquisition unit 221 acquires initial plant input / output data D={u0(t), y0(t)|t=1,...,N}. Note that the reference model M d Assume that a desired closed-loop system model is set by the user.

[0034] Furthermore, the acquisition unit 221 acquires the state x of the control object 104. For example, the acquisition unit 221 acquires the rotation speed of the engine mounted on the vehicle and the amount of fuel injected into the combustion chamber of the engine as the state x of the control object 104.

[0035] Here, the virtual reference signal and the virtual control input of the VRFT of this embodiment will be described. The virtual reference signal is a reference model M d Based on the output y0(t), it is expressed by the following equation (17).

number

number

number

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[0036] Each control gain of PID control ρ j (j=p, i, d) is expressed by the following equation (22) based on equation (13). ρj is expressed by equation (23), and φ tilde is expressed by the following equation (24).

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[0037] The evaluation function of equation (25) is convex. Therefore, by using the LS (least squares method), the LUT parameters that can minimize the value of the evaluation function of equation (25) are calculated using equation (29). In the following description, minimizing the value of the evaluation function is sometimes referred to as an optimization problem. Z and D in equation (29) are expressed by equations (30) and (31), respectively.

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[0038] When the LS method is applied, the LUT parameters of the LUT are obtained, but the difference between adjacent LUT parameters can become extremely large. If the difference between the LUT parameters becomes large, when the operating point changes, each control gain of the PID in the control system S changes significantly, which may cause the output of the controlled object 104 to become unstable. Therefore, in order to suppress the fluctuation of the control gain, the adjustment unit 222 determines LUT parameters that minimize the difference between adjacent LUT parameters and an evaluation function including the L2 norm of the LUT parameters, i.e., an evaluation function with regularization.

[0039] The evaluation function including the L2 norm is expressed by the following formula (32). The evaluation function of formula (32) is a function with the LUT parameters as variables. The optimization problem of the evaluation function of formula (32) is called generalized ridge regression.

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[0040] The second term is expressed as the L2 norm of the difference between two adjacent LUT parameters in the lookup table. Specifically, the L2 norm of the second term is expressed as the square root of the sum of the squares of the differences between multiple LUT parameters included in the vector representing the LUT parameter differences. More specifically, the second term represents the difference between adjacent LUT parameters and is expressed by the following equation (33).

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[0041] The third term is expressed as the L2 norm of the LUT parameters. Specifically, the L2 norm of the third term is expressed as the square root of the sum of the squares of each of the multiple LUT parameters included in the vector representing the LUT parameters. λ in Equation (32) is a design parameter that adjusts the relative strength between the sum of squared error terms and the regularization term, and is a positive constant.

[0042] However, there are cases where the LUT parameters become extremely large due to over-learning caused by noise or other factors. This problem can be avoided by introducing the L2 regularization term, the third term in equation (32). Furthermore, if there is insufficient training data, the problem of adjacent LUT parameters not being smoothed when the LUT parameters are calculated using equation (29) can arise. Particularly when the control target has nonlinear characteristics, there is no guarantee that sufficient training data has been obtained. By introducing equation (33), it becomes possible to adjust the smoothness of adjacent LUT parameters.

[0043] The adjustment unit 222 uses an optimization solver to calculate LUT parameters that minimize Equation (32), where λ1 and λ2 are hyperparameters. These hyperparameters are directly determined to be optimal λ1 and λ2 using k-fold cross-validation.

[0044] The adjustment unit 222 stores the calculated LUT parameters in the storage unit 210. Specifically, the adjustment unit 222 updates the LUT parameters stored in the storage unit 210 with the calculated LUT parameters.

[0045] As mentioned above, the introduction of equation (33) makes it possible to smooth the LUT. However, there are cases where it is desirable to adjust the LUT parameters locally. For example, in regions (operating points) where the characteristic fluctuations of the controlled object are large, it is necessary to increase the difference between adjacent LUT parameters, and in regions (operating points) where the characteristic fluctuations are small, it is necessary to decrease the difference between adjacent LUT parameters.

[0046] Therefore, the adjustment unit 222 adjusts λ. In this case, λ1 is expressed as a vector representing a weight corresponding to the difference between the LUT parameters. For example, λ1 is expressed by the following equation (34).

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[0047] The adjustment unit 222 determines each element of Λ according to the characteristics or prior information of the controlled object 104. For example, the adjustment unit 222 changes the weight according to the system gain of the controlled object corresponding to an operating point on the LUT determined by the engine speed and the amount of fuel. The system gain is a value indicating the ratio of the first output u to the second output y. Specifically, the adjustment unit 222 decreases the weight as the system gain of the operating point increases. The adjustment unit 222 may also change the weight to achieve a desired system gain. The desired system gain is determined in advance through experiments or the like. For example, the desired system gain is determined as the ratio of the second output y to the first output u when an experiment is conducted by changing the engine speed and the amount of fuel injection.

[0048] This allows the adjuster 222 to handle a controlled object whose characteristics change suddenly. The adjuster 222 can also handle the problem of LUT parameters becoming large due to overlearning caused by noise or other influences due to the effect of λ2. This allows the adjuster 222 to suppress significant fluctuations in the control gain.

[0049] The adjustment unit 222 may use Λ determined by an experiment or the like. For example, the adjustment unit 222 determines the weight of each element by referring to Λ stored in the storage unit 210. For example, Λ can be set by a user of the control system S according to this embodiment based on the engine speed and the amount of fuel injected into the engine combustion chamber. In this way, the adjustment unit 222 can use a weight according to the difference between adjacent LUT parameters, and it becomes possible to set the difference between adjacent LUT parameters more appropriately than when a single λ (scalar) is used.

[0050] [simulation] A simulation using the information processing device 200 according to this embodiment will be described below. The controlled object 104 is a Hammerstein model. The plant is expressed by the following equation (35).

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[0051] Next, the grid spacing of the LUT is set to 1.0, and the LUT size is set to M1 = 13 (range: -5 to 7 inclusive) and M2 = 11 (range: -5 to 5 inclusive). That is, c1 = [-5, -4, ..., 6, 7] and c2 = [-5, -4, ..., 4, 5]. The prefilter L is M d is used.

[0052] The LUT parameters are then adjusted based on the input and output data. The LUT is ρj (j=p,i,d) axis, w ρj is the LUT parameter for each PID gain. ρj The lengths of and w are 143 (M1M2) and 429 (3M1M2), respectively. The obtained λ is 0.5. By this operation, many parameters were adjusted.

[0053] Finally, the controller is implemented. The PID gains are adjusted according to x using the obtained LUT (see equation (22)). The PID gains obtained by the classical PID gain tuning method, the CHR method, are p =0.059, K i = 0.058, and K d =0.0038. The fixed PID gain obtained by standard VRFT is K p =0.0862, K i = 0.1597, and K d =0.0037.

[0054] The cost function that indicates the tracking error performance is explained below. The value of the cost function that indicates the tracking error performance of the CHR method is 1.548×10 -1 The cost function value showing the tracking error performance of the standard VRFT was 5.562 × 10 -2 The value of the cost function indicating the tracking error performance of the LUT-VRFT-LS according to this embodiment was 2.557×10 -2 The value of the cost function indicating the tracking error performance of the LUT-VRFT-Ridge according to this embodiment was 1.132×10 -2 It was.

[0055] The response of the CHR method was very slow compared to the standard VRFT, LUT-VRFT-LS, and LUT-VRFT-Ridge. The PID gains of the CHR method and standard VRFT were fixed, which is thought to be the cause of the poor response. On the other hand, the LUT-VRFT-LS and LUT-VRFT-Ridge have PID gains that change based on the scheduling parameters, so their response was faster than the CHR method and standard VRFT, and they were confirmed to follow the desired response.

[0056] [Process to adjust LUT parameters] 6 is a flowchart showing an example of a process for adjusting the LUT parameters. The process for adjusting the LUT parameters is executed while the control target 104 is operating.

[0057] First, the acquisition unit 221 acquires the first output u of the controller 102 (step S1). Next, the acquisition unit 221 acquires the second output y of the controlled object 104 (step S2).

[0058] The adjustment unit 222 determines LUT parameters that minimize an evaluation function with the LUT parameters as variables, based on the first output u and the second output y (step S3). Specifically, the adjustment unit 222 determines LUT parameters that minimize the evaluation function expressed by equation (32). The adjustment unit 222 updates the LUT with the determined LUT parameters (step S4). The control unit 220 of the information processing device 200 repeatedly executes the above process while the control target 104 is operating.

[0059] [Effects of the information processing device 200] As described above, in gain-scheduled PID control, the information processing device 200 sets the LUT parameters of the LUT to be LUT parameters that include: a first term expressed by the L2 norm of the difference between the second output of the controlled object 104 and the third output of the reference model; a second term expressed by the L2 norm of the difference between two adjacent LUT parameters in a lookup table (LUT) in which a plurality of LUT parameters used to calculate a control gain are arranged; and a third term expressed by the L2 norm of the LUT parameters, and that minimize an evaluation function with the LUT parameters as variables.

[0060] The evaluation function of this embodiment includes the L2 norm of the LUT parameters. Therefore, LUT parameters that reduce the squared value of the LUT parameters are determined, thereby preventing overlearning of each LUT parameter. Furthermore, the evaluation function includes the L2 norm of adjacent LUT parameters. Therefore, the difference between LUT parameters is also reduced, thereby reducing changes in the LUT parameters and control gains in response to changes in the state of the controlled object 104. Furthermore, since Λ is determined according to the system gain for each operating point of the controlled object, it is possible to appropriately adjust the smoothness of the LUT. This allows the information processing device 200 of this embodiment to provide appropriate LUT parameters that improve the tracking of the output of the controlled object 104 to the target response.

[0061] The present invention has been described above using embodiments, but the technical scope of the present invention is not limited to the scope described in the above embodiments, and various modifications and changes are possible within the scope of the gist of the present invention. For example, all or part of the device can be configured by functionally or physically distributing or integrating any unit. Furthermore, new embodiments resulting from any combination of multiple embodiments are also included in the embodiments of the present invention. The effects of the new embodiments resulting from the combination also have the effects of the original embodiments. [Explanation of symbols]

[0062] S Control System 102 Controller 104 Control Object 106 Gain Schedule Section 108 Reference Model 200 Information processing device 210 Storage section 220 Control Unit 221 Acquisition Department 222 Adjustment section

Claims

1. 1. An information processing device for calculating LUT parameters for adjusting the control gain of a control system including: a controller that performs PID control; a controlled object that receives a first output of the controller as an input; a gain scheduler that adjusts a control gain of the controller; and a reference model that is a transfer function of a target value of the controlled object and a reference response, wherein a second output of the controlled object is fed back to an input of the controller, an acquisition unit that acquires the first output of the controller and a second output of the controlled object when the first output is input; a storage unit that stores a lookup table in which a plurality of the LUT parameters used for calculating the control gain are arranged in a space having one or more states related to the controlled object as axes; an adjustment unit that sets the LUT parameters of the lookup table to the LUT parameters that minimize an evaluation function that uses the LUT parameters as variables, the LUT parameters including: a first term expressed by an L2 norm of a difference between the second output and a third output of the reference model based on the first output and the LUT parameters; a second term expressed by an L2 norm of a difference between two adjacent LUT parameters in the lookup table; and a third term expressed by an L2 norm of the LUT parameters; An information processing device having the above.

2. the adjustment unit sets the LUT parameters of the lookup table to the LUT parameters that minimize the evaluation function, which includes the first term, the second term expressed by the L2 norm of the product of the difference between the LUT parameters and a vector representing a weight corresponding to the difference between the LUT parameters, and the third term. The information processing device according to claim 1 .

3. the adjustment unit sets the LUT parameters of the lookup table to the LUT parameters that minimize the evaluation function including the first term, the second term expressed by the L2 norm of the product of the difference between the LUT parameters and a vector representing the weight determined according to a system gain indicating a ratio of the first output to the second output, and the third term. The information processing device according to claim 2 .

4. the look-up table is defined in a space having axes representing the rotation speed of an engine mounted on a vehicle and the amount of fuel injected into a combustion chamber of the engine, the acquisition unit acquires the rotation speed and the amount of fuel, the adjustment unit changes the weight in accordance with the system gain corresponding to an operating point on the look-up table determined by the acquired rotation speed and the acquired amount of fuel. The information processing device according to claim 3 .

5. the adjustment unit reduces the weight as the system gain of the operating point increases. The information processing device according to claim 4 .

6. a difference between the third output and the second output of the first term, a difference between the LUT parameters of the second term, and the LUT parameters of the third term are expressed as vectors; the L2 norm of the first term is expressed by the square root of the sum of squares of the differences between the third output and the second output included in a vector representing the differences between the third output and the second output, the L2 norm of the second term is expressed as the square root of the sum of the squares of the differences between the plurality of LUT parameters included in the vector representing the differences between the LUT parameters; The L2 norm of the third term is expressed as the square root of the sum of the squares of the LUT parameters included in the vector representing the LUT parameters. The information processing device according to claim 1 .

7. An information processing method executed by a computer for determining LUT parameters for adjusting a control gain of the PID control in a control system including: a controller that performs PID control; a controlled object that receives a first output of the controller as an input; a gain scheduler that adjusts a control gain of the controller; and a reference model that is a transfer function of a target value and a reference response of the controlled object, wherein a second output of the controlled object is fed back to an input of the controller, the method comprising: acquiring the first output of the controller and a second output of the controlled object when the first output is input; a step of setting the LUT parameters of the lookup table to the LUT parameters that minimize an evaluation function having the LUT parameters as variables, the LUT parameters including: a first term expressed by an L2 norm of a difference between the second output and a third output of the reference model based on the first output and the LUT parameters; a second term expressed by an L2 norm of a difference between two adjacent LUT parameters in a lookup table in which the LUT parameters used for calculating the control gain are arranged in a space having one or more states related to the controlled object as axes; and a third term expressed by the LUT norm of the LUT parameters; An information processing method comprising:

8. A control system including a controller that performs PID control, a controlled object that receives a first output of the controller as an input, a gain scheduler that adjusts a control gain of the controller, and a reference model that is a transfer function of a target value of the controlled object and a reference response, wherein a second output of the controlled object is fed back to an input of the controller, the program comprising: The vehicle's onboard computer an acquisition unit that acquires the first output of the controller and a second output of the controlled object when the first output is input; and an adjustment unit that sets the LUT parameters of the lookup table to the LUT parameters that minimize an evaluation function having the LUT parameters as variables, the LUT parameters including: a first term expressed by an L2 norm of a difference between the second output and a third output of the reference model based on the first output and the LUT parameters; a second term expressed by an L2 norm of a difference between two adjacent LUT parameters in a lookup table in which the LUT parameters used for calculating the control gain are arranged in a space having one or more states related to the controlled object as axes; and a third term expressed by the LUT norm of the LUT parameters; A program to realize the function as follows.

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