JP2012113676A - Configuring method, system, and program for controller - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique for automatically configuring a controller with respect to each candidate for a scheduling parameter vector.SOLUTION: An LPV model of a plant is described, the number of scheduling parameters is given, and a maximum value and a minimum value found from a high-order request of restriction conditions are given to each element of a scheduling parameter vector comprising a plurality of elements. Each candidate has a ν gap calculated among Min, Max, and an intermediate value between them respectively, respective candidates are determined as scheduling parameter candidates in the decreasing order of differences between ν gaps. The number of parameters given first is selected and converted into an LMI, the controller is found based on an Hbasis for all combination end points associated with the maximum value and minimum value of the selected scheduling parameter, and a controller for a generalized plant is constituted by bilinear interpolation weighted with the ν gap calculated during the parameter selection.

Description

  The present invention relates to a technique for configuring a controller such as an automobile plant, and more particularly to a technique for performing gain schedule control by describing a plant by a linear parameter variation model and converting it into a linear matrix inequality. .

  Conventionally, as a control for a plant whose configuration parameters change during operation, in many cases, a variable structure control method has been used in which control is performed while adjusting an observer gain using a data map and estimating a state variable. .

  However, incorporating all the possibilities into the data map requires a great deal of labor, and when creating a map experimentally, it is difficult to respond to plant parameter changes.

  Therefore, a plant is described using a linear parameter-variable (LPV) model, and gain scheduling control covering all cases is achieved by converting the fluctuation range constraint into linear matrix inequalities (LMI). Has been considered as a solution.

Japanese Patent Laid-Open No. 10-220475 is designed on an LMI basis to provide a magnetic bearing device capable of optimally and continuously controlling over all rotation speeds for an LPV system in which a strong gyro effect acts. Two H ^∞ compensators K (θ _max ) and K (θ _min ) for different rotational speeds satisfying the convex optimization are arranged, and each H ^∞ compensator is interpolated. Multiply by the coefficients α1 and α2 found by interpolation and connect them in parallel. The outputs of both H ^∞ compensators are added, and the coefficients α1 and α2 are continuously changed so that the sum thereof is 1 and depending on the rotational speed ωz measured by the rotational speed sensor 16, and the radial position sensor A technique for calculating an error between the radial position measured by 8 and the command value r and performing an LMI gain schedule ^H∞ calculation based on the error is disclosed.

  Japanese Patent Application Laid-Open No. 11-110003 discloses a vehicle that obtains control performance that satisfies a target response by deriving a controller by inputting (designating) a target response within a range determined by an upper limit value and a lower limit value of parameter fluctuations. Aiming at providing a control system design method, (A) setting the specifications of the vehicle, disturbance conditions, parameter fluctuation range, and target response, (B) creating a dynamic model of the vehicle 1 ( C) LPV modeling is performed based on the dynamic model of the vehicle 1, (D) the setting condition is formulated as an inverse LMI problem, a controller is derived by the LMI design method, and (E) a step response that is a standard of target response A control system design algorithm with a constraint condition is created with an LMI step-constrained servo system configuration. Performed testimony, if insufficient (G) verification result back to the adjustment of the target response setting, the verification result if sufficient, disclose that complete the control system.

  However, in the above prior art, it is difficult to select a scheduling parameter candidate for obtaining sufficient performance, and the selection is made manually, such as by making a special measurement or subjectively determining while looking at the Bode diagram. Since it relied on, it took time and it was difficult to select an optimal parameter candidate.

By the way, S. Aubouet et al., “H-infinity / LPV observer for an industrial semi-active suspension,” IEEE Proc. Conf. On Control Applications, pp.756-763, 2009 includes the LPV model and each constraint. Describes a technique for expressing a control variation based on the H ^∞ criterion at a combination end point of the maximum value / minimum value of each parameter by expressing the fluctuation range of the parameter in consideration of.

  Also, G. Vinnicombe, “Frequency Domain Uncertainty and the Graph Topology,” IEEE Trans. Automatic Control, Vol. 38, No. 9, pp.1371-1383, 1993 describes the ν gap A technique for computing is described.

Japanese Patent Laid-Open No. 10-220475 Japanese Patent Laid-Open No. 11-110003

S. Aubouet et al., “H-infinity / LPV observer for an industrial semi-active suspension,” IEEE Proc. Conf. On Control Applications, pp.756-763, 2009 G. Vinnicombe, “Frequency Domain Uncertainty and the Graph Topology,” IEEE Trans. Automatic Control, Vol.38, No.9, pp.1371-1383, 1993

  It is an object of the present invention to provide a technique for automatically configuring a controller based on the ν gap calculated for each candidate scheduling parameter vector.

  According to the present invention, the user first describes the plant LPV model and gives scheduling parameters (elements of θ) and their numbers. Each element of the scheduling parameter vector composed of a plurality of elements is given a maximum value and a minimum value that come out from the upper request of the constraint condition. The described LPV model, scheduling parameter vector, and maximum and minimum values of its elements are stored in a system that performs the processing of the present invention.

  For each candidate scheduling parameter vector, the system calculates a ν gap for each of its Min, Max, and their intermediate values.

  Next, the system selects scheduling parameters candidates in descending order of the difference between the ν gaps for each candidate, and selects the number of parameters given first.

The system then converts the LPV model to LMI and determines the controller according to the ^H∞ criterion for all combined endpoints for the maximum and minimum values of the selected scheduling parameter.

  The system then configures the controller to the generalized plant by bilinear interpolation weighted by the ν gap calculated during parameter selection.

  According to the present invention, when there are many constraints, scheduling parameters that have been dependent on the model designer are automatically selected based on objective criteria, and more appropriate controller design than before can be made using this. Therefore, it is possible to reduce the effort for creating the map even when the fluctuation range is only vague.

  In addition, grasping the parameter space characteristics by the ν gap may facilitate the association with the requirement analysis by SysML or the like, and automatically discriminates whether or not the control strategy should be reconsidered when constraints are added later. Can be used to improve the flexibility of modeling design.

  Furthermore, using bilinear interpolation instead of linear interpolation takes into account non-Euclidean geometric geodetic distances, thereby reducing feedback control errors.

It is a general | schematic block diagram of an example control computer used by this invention. It is a functional block diagram of a program or the like for executing processing for determining a controller according to the present invention. It is a figure which shows the flowchart for performing the process which determines a controller according to this invention. It is a figure for demonstrating Hinfinity reference ^| standard controller derivation | leading-out by conversion to LMI. It is a figure for demonstrating conversion from a general plant to a LMI problem.

  Embodiments of the present invention will be described below with reference to the drawings. It should be understood that these examples are for the purpose of illustrating preferred embodiments of the invention and are not intended to limit the scope of the invention to what is shown here. Further, throughout the following drawings, the same reference numerals denote the same objects unless otherwise specified.

  Referring to FIG. 1, a block diagram of the control computer hardware for controlling the controller 118 in accordance with the present invention is shown. In FIG. 1, a CPU 104, a main memory (RAM) 106, a hard disk drive (HDD) 108, a keyboard 110, a mouse 112, and a display 114 are connected to the system bus 102. The CPU 104 is preferably based on a 32-bit or 64-bit architecture, such as Intel Pentium (trademark) 4, Intel Core (trademark) 2 DUO, AMD Athlon (trademark), etc. Can be used. The main memory 106 preferably has a capacity of 2 GB or more, more preferably a capacity of 4 GB or more.

  The hard disk drive 108 stores in advance an operating system, a processing program according to the present invention, and the like (not shown). The operating system may be any compatible with the CPU 104, such as Linux (trademark), Microsoft Windows Vista, Windows XP (trademark), Windows (trademark) 2000, Apple Mac OS (trademark).

  The keyboard 110 and the mouse 112 are used to operate graphic objects such as icons, taskbars, and windows displayed on the display 114 in accordance with a graphic user interface provided by the operating system. The keyboard 110 and the mouse 112 are also used to operate a recording program with data described later.

  The display 114 is preferably, but not limited to, a 32-bit true color LCD monitor with a resolution of 1024 × 768 or higher. The display 114 is used for displaying a waveform or the like of the operation of the plant by the controller 118.

  The hard disk drive 108 further includes an LPV model 204 to be described later, a scheduling parameter 206 for the LPV model 204, a ν gap calculation module 208, an LMI conversion module 210, a controller configuration module 212, and a main unit that integrates the overall processing. A program 202 is stored. The main program 202, the ν gap calculation module 208, the LMI conversion module 210, and the controller configuration module 212 can be created in any existing programming language such as C, C ++, C #, Java®. These modules are appropriately loaded into the main memory 106 and executed by the operation of the operating system. Although not shown, the main program 202 displays a window for the operator to operate on the display 114 with an appropriate GUI, and the operator can start or stop the process using the keyboard 110, the mouse 112, or the like. it can.

  Further, a controller 118 for controlling the plant 402 shown in FIG. 4 is connected to the bus 102 via an appropriate interface board 116 such as PCI or USB. The controller 118 has a register for storing a control matrix K obtained as a result of calculation through the interface board 116.

  The plant 402 is a mechanism device to be controlled such as an engine, a brake, and an air conditioner.

  The plant 402 may be a real machine or a software model created by a simulation modeling tool such as Simulink (R) or Modelica. When the plant 402 is a software model, the module is stored in the hard disk drive 108, and the controller 118 is also a module stored in the hard disk drive 108. Therefore, the interface via the interface board 116 is It is unnecessary.

  Next, with reference to the functional block diagram of FIG. 2, a logical configuration of a program or the like for executing a process for determining a controller according to the present invention will be described.

  The main program 202 functions to control the entire operation including the interface with the user.

ここで、A、B、C、Dは、状態空間モデルの係数行列である。 The linear parameter variation (LPV) model 204 is a model that describes the plant 402 by the following linear equation, and is described in advance by the user in consideration of the dynamic equation and the like.

Here, A, B, C, and D are coefficient matrices of the state space model.

θ(t)の各要素θ_j(t) (j = 1,2,...,r)は、システム要件に従い、予めユーザにより記述される。 The scheduling parameter 206 is a time-varying parameter θ (t) used in the LPV model 204, and is an r-dimensional vector as shown by the following equation.

Each element θ _j (t) (j = 1, 2,..., r) of θ (t) is described by the user in advance according to the system requirements.

In addition, each element θ _j (t) (j = 1,2, ..., r) of θ (t) has the maximum value _i ^max and the minimum value θ _i ^min are determined in advance by the user and stored in the hard disk drive 108 as the scheduling parameter 206.

The ν gap calculation module 208 calculates G. Vinnicombe, “Frequency Domain Uncertainty and the Graph Topology,” from the maximum value θ _j ^max , the minimum value θ _j ^min and the intermediate value θ _j ^mid between them. It has a function to calculate the ν gap by the method described in IEEE Trans. Automatic Control, Vol.38, No.9, pp.1371-1383, 1993. The intermediate value θ _j ^mid is calculated as follows.

The linear matrix inequality (LMI) conversion module 210 has a function of converting the LPV model 204 to LMI and obtaining a controller based on the ^H∞ criterion using the maximum and minimum values of the selected scheduling parameter.

  The controller configuration module 212 configures the controller 118 to the generalized plant by bilinear interpolation weighted by the ν gap calculated at the time of parameter selection. At this time, the controller 118 is configured via the interface board 116 shown in FIG.

  Next, processing for determining a controller according to the present invention will be described with reference to the flowchart of FIG. In FIG. 3, in step 302, a user describes an LPV model and gives scheduling parameters and the number of elements thereof. At this time, the maximum value and the minimum value of each element of the scheduling parameter are also input according to the specification. Each of them is stored in the hard disk drive 108 by the main program 202 as the LPV model 204 and scheduling parameter 206 of FIG.

  In step 304, the main program 202 calls the ν gap calculation module 206, and for each candidate of the scheduling parameter vector coming out of the upper request of the constraint condition, for each of Min, Max and its intermediate value, for example, , G. Vinnicombe, “Frequency Domain Uncertainty and the Graph Topology,” IEEE Trans. Automatic Control, Vol.38, No.9, pp.1371-1383, 1993 is used to calculate the ν gap. .

First, general calculation of the ν gap will be described. If the transfer functions of two plant models are P ₁ (jω) and P ₂ (jω), the ν gap between the two transfer functions is defined by the following equation. Here, ω is an angular frequency.

また、

は、最大特異値をあらわす。 Here, κ (X, Y) is defined as follows.

Also,

Represents the maximum singular value.

In the case of a 1-input 1-output system, the ν gap is as follows.

Here, T _i ^max is the transfer function when the maximum value is substituted for the i-th (i = 1, ..., r) element of θ, and T _i ^min is the transfer function when the minimum value is substituted. . Also, let T _i ^mid be the transfer function when the intermediate value is substituted.

Therefore, the main program 202 calls the ν gap calculation module 206 using the above ν gap calculation formula and calculates the next value.
ν _i _mid_max = δ _ν (T _i ^mid , T _i ^max )
ν _i _min_mid = δ _ν (T _i ^min , T _i ^mid )
ν _i _min_max = δ _ν (T _i ^min , T _i ^max )

The main program 202 is step 306,
(| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) (where i = 1, ..., r), starting from i with the largest value, select the scheduling parameter candidates and select the number of parameters given first. .

  At this time, in the first embodiment, only the first given parameter is selected, and in the second embodiment, the next given parameter is also selected. The first embodiment and the second embodiment will be described later.

In step 308, the main program 202 calls the LMI conversion module 210 to convert the LPV model 204 to LMI and derives an ^H∞ reference controller.

  First, the general theory will be explained. That is, the fluctuation part of the LPV model 204 is regarded as an exogenous signal, and further considered as a large plant, which is defined as a generalized plant 404 as shown in FIG. The internal filter of the exogenous signal and the exogenous signal itself can be automatically determined from their frequency characteristics if it is determined which parameter of the LPV model 204 is selected as the scheduling parameter.

と表現できる一般化プラント４０４において、外生信号wに対して制御量zをなるべく小さく抑えることが制御目的なので、この間の伝達関数G_zwを小さくする制御器Kを設計することになる。ここで、

である。 Therefore,

In the generalized plant 404 that can be expressed as follows, since the control purpose is to keep the control amount z as small as possible with respect to the exogenous signal w, a controller K that reduces the transfer function G _zw during this period is designed. here,

It is.

The ^H∞ norm is used as a measure of the magnitude of G _zw , and this is the ^H∞ standard. The definition is as follows.

は、最大特異値をあらわし、ωは角周波数をあらわす。この定義により、Ｈ^∞制御問題は、一般化プラントGに対し、u = Kyのフィードバック制御により、閉ループ系を内部安定化し、かつ、与えられた正数γに大して、

を満たす制御器Kを求めることと定式化できる。γは任意に与えてもよいが、自動決定する方法も従来技術として存在する。これを解くための一つのアプローチが、ＬＭＩによるものである。 here

Represents the maximum singular value, and ω represents the angular frequency. By this definition, the H ^∞ control problem is to stabilize the closed loop system internally by feedback control of u = Ky for the generalized plant G, and to increase the given positive number γ,

It is possible to formulate a controller K that satisfies the above. γ may be arbitrarily given, but there is a conventional method for automatically determining γ. One approach to solve this is by LMI.

としたとき、ある定理によれば、次の２つの条件は等価となる。
(i) 行列Aは安定で、図５に示すブロックにおいて、

が成立する。
(ii) 次式を満たすX > 0が存在する。

That is, take out only the parts z and w

Then, according to a theorem, the following two conditions are equivalent.
(i) The matrix A is stable and in the block shown in FIG.

Is established.
(ii) There exists X> 0 that satisfies the following formula.

That is, the condition (i) is the above-mentioned H ^∞ criterion, and the matrix X that satisfies the condition is a controller, and when the one that satisfies the linear matrix inequality (LMI) for X in the condition (ii) is obtained, the H ^∞ criterion The controller is required.

  Generally, in the case of feedback control, if it is substituted as it is, it will not become linear with respect to X, so it will be converted into the above form by variable conversion. For technical details, see also S. Aubouet et al., “H-infinity / LPV observer for an industrial semi-active suspension,” IEEE Proc. Conf. On Control Applications, pp. 756-763, 2009. I want.

However, since w cannot be input for all scheduling parameters, the main program 202 calculates a controller based on the ^H∞ criterion using the LMI at the end point by the LMI conversion module 210 in step 308, Next, in step 310, a controller for the generalized plant is configured by bilinear interpolation weighted by the ν gap calculated at the time of parameter selection.

ここで、K⁽ⁱ⁾は、i番目の制御器である。 In the prior art, it has been implicitly assumed that the controller K for the generalized plant can be expressed by affine transformation as follows.

Here, K ⁽ⁱ⁾ is the i-th controller.

One feature of the present invention is that this is replaced by bilinear interpolation weighted by the ν gap calculated at the time of parameter selection as in the following equation.

Here, the embodiment is divided according to how many N are selected. In the first embodiment, only the first given parameter is selected, that is, for that parameter, the controller when K ⁽¹⁾ is fixed to min and K ⁽²⁾ is fixed to max. the controller of time, [nu gap between the transfer function when the [nu gap between the transfer function of the time fixed to the respective min and mid is fixed to each of the [nu _1, mid and max and [nu _2, and p ₁ The controller is constructed by bilinear interpolation by giving p ₂ by the following equation.

In the second embodiment, two parameters, the first given parameter and the next parameter, are selected, that is, a controller designed at the end point of {p1_min, p2_min} for these parameters is represented by K ⁽¹⁾ The controller designed at the end point of {p1_min, p2_max} is K ⁽²⁾ , the controller designed at the end point of {p1_max, p2_min} is designed at the end point of K ⁽³⁾ , {p1_max, p2_max} When the controller is K ⁽⁴⁾ , the ν gap between the transfer functions when fixed at p1_min and p2_min is ν ₁ , and the ν gap between the transfer functions when fixed at p1_min and p2_max is ν ₂ , p1_max And p2_min, the ν gap between the transfer functions when fixed to ν ₃ , and the ν gap between the transfer functions when fixed to p1_max and p2_max, respectively, as ν _4, and p ₁ , p ₂ , p ₃ , p _The controller is constructed by bilinear interpolation by giving ₄ by the following equation.

  In accordance with the features of the present invention, using weighting by ν gaps rather than linear interpolation will take into account non-Euclidean geometric geodesic distances, thereby reducing feedback control errors.

  An embodiment in which the controller is configured by selecting three or more parameters is also conceivable, but if the number of parameters to be selected is increased too much, the controller may become complicated and may not function. It is desirable.

  Although the embodiments of the present invention have been described above, the present invention is not limited to specific hardware and software platforms, and can be implemented on any platform. The merchant will understand.

102 System bus 104 CPU
106 Main memory 108 Hard disk 108 Hard disk drive 114 Display 116 Interface board 118 Controller 202 Main program 204 LPV model 206 Gap calculation module 206 Scheduling parameter 208 Gap calculation module 210 Conversion module 212 Controller configuration module 402 Plant 404 Generalized plant

Claims (12)

A method for constructing a controller from a plant described in an LPV model given scheduling parameters by computer processing, comprising:
Calculating a ν gap for each Min, Max and intermediate value of each candidate plant parameter vector of the LPV model based on constraint requirements;
Selecting the plant parameter vector candidates based on the magnitude of the difference between the ν gaps;
Converting the LPV model into an LMI and obtaining a controller according to the H ^∞ criterion for all combination endpoints for the maximum and minimum values of the selected plant parameter vector;
Configuring a controller to the plant by bilinear interpolation weighted by the ν gap calculated by the selected plant parameter vector.
How to configure the controller. In the step of calculating the ν gap, the transfer function when the maximum value of the i-th element of the scheduling parameter is substituted is T _i ^max , the transfer function when the minimum value is substituted is T _i ^min , and the intermediate value is When the substitution transfer function is T _i ^mid and δ _ν () is a function that calculates the ν gap,
ν _i _mid_max = δ _ν (T _i ^mid , T _i ^max )
ν _i _min_mid = δ _ν (T _i ^min , T _i ^mid )
ν _i _min_max = δ _ν (T _i ^min , T _i ^max )
Calculate
Selecting the plant parameter vector candidates;
The method according to claim 1, wherein the plant parameter vector candidate is selected based on a value of (| ν _i _min_mid−ν _i _mid_max | + ν _i _min_max). Selecting the plant parameter vector candidates;
Only one candidate with the maximum value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) is selected, and the bilinear interpolation is performed at two points with fixed min and max of the selected parameters. The method according to claim 2. Selecting the plant parameter vector candidates;
The candidate with the largest value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) and the next largest candidate are selected, and the bilinear interpolation uses p1 as the largest candidate, The method according to claim 2, wherein when the maximum candidate is p2, p1_min and p2_min, p1_min and p2_max, p1_max and p2_min, and p1_max and p2_max are fixed at four points, respectively. A program that configures a controller from a plant described in an LPV model given scheduling parameters by computer processing,
In the computer,
Calculating a ν gap for each Min, Max and intermediate value of each candidate plant parameter vector of the LPV model based on constraint requirements;
Selecting the plant parameter vector candidates based on the magnitude of the difference between the ν gaps;
Converting the LPV model into an LMI and obtaining a controller according to the H ^∞ criterion for all combination endpoints for the maximum and minimum values of the selected plant parameter vector;
Causing the step of configuring a controller to the plant by bilinear interpolation weighted by the v gap calculated by the selected plant parameter vector;
Controller configuration program. In the step of calculating the ν gap, the transfer function when the maximum value of the i-th element of the scheduling parameter is substituted is T _i ^max , the transfer function when the minimum value is substituted is T _i ^min , and the intermediate value is When the substitution transfer function is T _i ^mid and δ _ν () is a function that calculates the ν gap,
ν _i _mid_max = δ _ν (T _i ^mid , T _i ^max )
ν _i _min_mid = δ _ν (T _i ^min , T _i ^mid )
ν _i _min_max = δ _ν (T _i ^min , T _i ^max )
Calculate
Selecting the plant parameter vector candidates;
6. The program according to claim 5, wherein the plant parameter vector candidate is selected based on a value of (| ν _i _min_mid−ν _i _mid_max | + ν _i _min_max). Selecting the plant parameter vector candidates;
Only one candidate with the maximum value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) is selected, and the bilinear interpolation is performed at two points with fixed min and max of the selected parameters. The program according to claim 6. Selecting the plant parameter vector candidates;
The candidate with the largest value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) and the next largest candidate are selected, and the bilinear interpolation uses p1 as the largest candidate, The program according to claim 6, wherein the program is executed at four points where p1_min and p2_min, p1_min and p2_max, p1_max and p2_min, and p1_max and p2_max are fixed, respectively, when the maximum candidate is p2. A system that configures a controller from a plant described in an LPV model given scheduling parameters by computer processing,
Storage means;
The LPV model and its scheduling parameters stored in the storage means;
Means for calculating a ν gap for each of the Min, Max and intermediate values of each candidate plant parameter vector of the LPV model, based on constraint requirements;
Means for selecting candidate plant parameter vectors based on the magnitude of the difference between the ν gaps;
Means for converting the LPV model into LMI and obtaining a controller according to H ^∞ criteria for all combinational endpoints relating to the maximum and minimum values of the selected plant parameter vector;
Means for configuring a controller to the plant by bilinear interpolation weighted by the v gap calculated by the selected plant parameter vector;
Controller configuration system. The means for calculating the ν gap is T _i ^max for the transfer function when the maximum value of the i-th element of the scheduling parameter is substituted, T _i ^min for the transfer function when the minimum value is substituted, and the intermediate value thereof When the substitution transfer function is T _i ^mid and δ _ν () is a function that calculates the ν gap,
ν _i _mid_max = δ _ν (T _i ^mid , T _i ^max )
ν _i _min_mid = δ _ν (T _i ^min , T _i ^mid )
ν _i _min_max = δ _ν (T _i ^min , T _i ^max )
Calculate
Means for selecting candidate plant parameter vectors
The controller configuration system according to claim 9, wherein candidates for the plant parameter vector are selected based on a value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max). Means for selecting candidate plant parameter vectors
Only one candidate with the maximum value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) is selected, and the bilinear interpolation is performed at two points with fixed min and max of the selected parameters. The system for configuring a controller according to claim 10. Means for selecting candidate plant parameter vectors
The candidate with the largest value of (| ν _i _min_mid-ν _i _mid_max | + ν _i _min_max) and the next largest candidate are selected, and the bilinear interpolation uses p1 as the largest candidate, The controller configuration system according to claim 10, wherein p1_min and p2_min, p1_min and p2_max, p1_max and p2_min, and p1_max and p2_max are fixed at four points, respectively, when the maximum candidate is p2.

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