JP7077667B2 - Control method, control device and program - Google Patents

Description

The present invention relates to control methods, control devices and programs.

A method called Model Predictive Control (MPC) is known as a method for optimally controlling a multivariable system having complicated constraints. In model predictive control, the optimum input is calculated by solving the optimum control problem in a specific period in the future by using the current value of the state quantity of the process for each sampling period. In model predictive control, optimum control is realized by repeatedly executing the observation of this state quantity and the optimization calculation for solving the optimum control problem online (for example, Patent Document 1).

On the other hand, a multiparametric planning method is known as a technique that extends model predictive control. In the multiparametric planning method, the optimal control problem is analyzed offline to obtain the state feedback law for obtaining the optimum input for the state quantity. As a result, in the multi-parametric planning method, online optimization calculation becomes unnecessary, and optimum control can be realized at high speed (for example, Patent Documents 2 to 8, Non-Patent Documents 1 and 2).

Further, methods for expressing problems such as system control and circuit analysis by first-order predicate logic expressions and optimizing the system by solving first-order predicate logic expressions have been conventionally known (for example, non-patented). Document 3).

Specifically, quantifiers represented by universal quantifiers (∀) and existential quantifiers (∃), and logical symbols represented by products (∧) and sums (∨) of equations and inequality of multivariable polynomials. The first-order predicate logical expressions are obtained by combining the combined logical expressions using. Of the variables that appear in the formula, the variables that are bound by the finite symbol are called bound variables, and the variables that are not bound by the finite symbol are called free variables. Of the first-order predicate formulas, the bound variables are eliminated and the logical formulas that the free variables should satisfy are derived for optimization. Of the first-order predicate logical expressions, the method of eliminating the bound variables and deriving the logical expressions that the free variables should satisfy is called the qualifying symbol elimination method.

Further, a method of designing a control system and analyzing a control system by using a qualifying symbol elimination method is known (for example, Patent Document 9). According to this method, the control system analysis / design device formulates the input control problem as a linear Matrix Inequality (LMI) or a Bilinear Matrix Inequality (BMI). .. Then, the constraints such as the design specifications formulated as LMI or BMI are transformed into the constraints in which the inequalities are connected by a logical sum, the control system is converted into the first-order predicate logical formula, and the control system is bound by the qualifying symbol. Analyze the control system from the equation with the variables cleared.

Further, as a technique for analyzing the energy of a plant, a method of generating a first-order predicate logic formula and solving the first-order predicate logic formula is known (for example, Non-Patent Document 4).

Japanese Unexamined Patent Publication No. 2004-20031 Japanese Unexamined Patent Publication No. 2010-12889 Japanese Unexamined Patent Publication No. 2010-12890 Japanese Unexamined Patent Publication No. 2010-13990 Japanese Unexamined Patent Publication No. 2013-101472 Japanese Unexamined Patent Publication No. 2013-134741 International Publication No. 2011/136160 International Publication No. 2013/077007 Japanese Unexamined Patent Publication No. 11-328239

Alberto Bemporad, Manfred Morari, Vivek Dua, Efstratios N. Pistikopoulos "The explicit linear quadratic regulator for constrained systems" Automatica, Vol.38, pp.3-20 Jun-ichi Imura, Shunichi Higashi, Izumi Masubuchi, "Control of Hybrid Systems", Corona Publishing Co., Ltd., 2014, pp. 142-154 Hirokazu Anai, Kazuhiro Yokoyama, "QE Calculation Algorithms and Their Applications Optimization by Mathematical Processing", University of Tokyo Press, 2011, pp. 214-221 Yoshio Tange, Satoshi Kiryu, Tetsuro Matsui, Yoshikazu Fukuyama, "Visualization of Demand-Supply Balance Optimization Problems Using Computer Algebra Technology", 13th ROMBUNNO. 8C2-5

Here, for example, in the model predictive control disclosed in Patent Document 1, the optimum control is realized by solving the optimum control problem by using a mathematical programming method. Therefore, a lot of calculation time is required to search for the optimum solution, and a lot of calculation resources are also required to solve the optimum control problem. Therefore, for example, it may be difficult to solve the optimum control problem with an edge device having limited computational resources, and it may be difficult to control a controlled object having a short control cycle. Further, for example, it was not possible to determine in advance the case where the optimum input cannot be calculated because there is no solution to the optimum control problem. Examples of the edge device include a built-in computing device, a control device such as a PLC (Programmable Logic Controller), and the like.

On the other hand, in the multi-parametric planning method disclosed in, for example, Patent Documents 2 to 8 and Non-Patent Documents 1 and 2, the target value is fixed in the state space model. Further, when the prediction interval becomes long, the region division of the state variable becomes complicated, and it may be difficult to realize it with an edge device having limited computational resources.

Further, in the multiparametric planning method, the optimization calculation is performed when the optimum control problem is analyzed offline and the state feedback law is generated. Therefore, depending on the numerical error and the accuracy of optimization, it may not be possible to generate an accurate optimum control rule (optimal state feedback law). That is, the state feedback law could not be generated in the region of the state quantity for which it was determined by the optimization calculation that there was no feasible solution.

One embodiment of the present invention has been made in view of the above points, and an object thereof is to realize constrained multivariable control accurately and at high speed even in a device having limited computational resources.

In order to achieve the above object, in one embodiment of the present invention, a control method used for multi-variable control in which a plurality of control amounts follow a target value, a variable representing an operation amount in a controlled object and the control amount are used. A model formula representing the relationship with the variable to be represented, an upper / lower limit constraint representing the upper and lower limits of the variable representing the manipulated variable, and an evaluation function for evaluating the difference between the target value and the controlled variable are input. And the generation procedure for generating in advance the relational logical expression representing the relationship that the variable representing the target value and the variable representing the manipulated variable should be satisfied so that the evaluation function satisfies the optimum condition, and the target value is input. Each time, the computer executes a calculation procedure for calculating the operation amount for making the plurality of control amounts follow the target value based on the target value and the relational logic expression. And.

Even with equipment with limited computational resources, constrained multivariable control can be realized accurately and at high speed.

It is a figure which shows an example of the structure of the optimum control device which concerns on 1st Embodiment. It is a figure which shows an example of the hardware composition of the optimum control device which concerns on 1st Embodiment. It is a figure which shows an example of the functional structure of the optimal control processing unit which concerns on 1st Embodiment. It is a flowchart which shows an example of the generation process of the relational formula which concerns on 1st Embodiment. It is a figure which shows an example of the area division represented by the relational formula. It is a flowchart which shows an example of the calculation process of the optimum operation amount which concerns on 1st Embodiment. It is a figure which shows an example of the application example of the optimum control processing part. It is a figure which shows an example of the functional structure of the optimal control processing part which concerns on the 2nd Embodiment. It is a figure which shows an example of a cache. It is a flowchart which shows an example of the calculation process of the optimum operation amount which concerns on 2nd Embodiment. It is a flowchart which shows the other example of the calculation process of the optimum operation amount which concerns on 2nd Embodiment. It is a figure which shows an example of the functional structure of the optimal control processing unit which concerns on 3rd Embodiment. It is a flowchart which shows an example of the visualization process which concerns on 3rd Embodiment. It is a figure which shows an example of the case where the set of evaluation values is visualized. It is a flowchart which shows the other example of the visualization process which concerns on 3rd Embodiment. It is a figure which shows an example of the case where the region where the deviation becomes 0 is visualized. It is a figure which shows an example of the functional structure of the optimal control processing part which concerns on 4th Embodiment. It is a flowchart which shows an example of the generation process of the relational formula which concerns on 4th Embodiment. It is a figure which shows the heat pump model in Example 1. FIG. It is a figure which shows the area division represented by the relational formula in Example 1. FIG. It is a figure which shows an example of the plot result of 1000 target values. It is a figure which shows the comparative example of the calculation time with the prior art. It is a figure which shows the time change of the control amount and the operation amount in Example 2. FIG. It is a figure which shows an example of the area division of each time in Example 2. FIG.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Hereinafter, the optimum control device 10 for calculating the optimum operation amount for the operation target at high speed in the multivariable control in which a plurality of control amounts follow the target value will be described. The optimum control device 10 is an edge device (for example, a built-in computing device, a control device such as a PLC, or the like) having limited computing resources. However, the optimum control device 10 according to the present embodiment may be, for example, various devices or devices having sufficient computational resources, in addition to the edge device.

In the following, the variables representing the manipulated variable in the controlled system are MV ₁ , ..., MV _M , the variables representing the controlled variable are PV ₁ , ..., PV _N , and the target value of the controlled variable is represented. Variables are represented as SV ₁ , ..., SV _N. Note that M and N are constants determined by the configuration of the system to be controlled.

[First Embodiment]
<Configuration of optimal control device 10>
First, the configuration of the optimum control device 10 according to the present embodiment will be described with reference to FIG. FIG. 1 is a diagram showing an example of the configuration of the optimum control device 10 according to the first embodiment.

As shown in FIG. 1, the optimum control device 10 according to the present embodiment has an optimum control processing unit 100. The optimum control device 10 according to the present embodiment calculates the optimum operation amount for the operation target in the multivariable control in which a plurality of control amounts follow the target value by the optimum control processing unit 100. At this time, the optimum control device 10 according to the present embodiment generates a relational formula expressing the relationship that the optimum operation amount should satisfy with respect to the target value offline. That is, the optimal control device 10 according to the present embodiment generates a relational formula in advance before the online execution.

Then, the optimum control device 10 according to the present embodiment calculates the optimum operation amount for making a plurality of control amounts follow the target value online by the relational formula generated in advance. As a result, in the optimum control device 10 according to the present embodiment, accurate and high-speed control can be realized even with a device or device having limited computational resources such as an edge device.

The optimum control processing unit 100 is realized by a process of causing one or more programs installed in the optimum control device 10 according to the present embodiment to be executed by a CPU (Central Processing Unit) 17, which will be described later.

<Hardware configuration of optimal control device 10>
Next, the hardware configuration of the optimum control device 10 according to the present embodiment will be described with reference to FIG. FIG. 2 is a diagram showing an example of the hardware configuration of the optimum control device 10 according to the first embodiment.

As shown in FIG. 2, the optimum control device 10 according to the present embodiment includes an input device 11, a display device 12, an external I / F 13, a communication I / F 14, a ROM (Read Only Memory) 15, and a RAM. It has (Random Access Memory) 16, a CPU 17, and an auxiliary storage device 18. Each of these hardware is connected to each other by a bus 19 so as to be able to communicate with each other.

The input device 11 is, for example, various buttons, a touch panel, a keyboard, a mouse, or the like, and is used to input various operations to the optimum control device 10. The display device 12 is, for example, a display or the like, and displays various processing results by the optimum control device 10. The optimum control device 10 does not have to have at least one of the input device 11 and the display device 12.

The external I / F 13 is an interface with an external device. The external device includes a recording medium 13a and the like. The optimum control device 10 can read and write the recording medium 13a via the external I / F 13. The recording medium 13a includes, for example, an SD memory card, a USB memory, a CD (Compact Disk), a DVD (Digital Versatile Disk), and the like. One or more programs that realize the optimum control processing unit 100 may be stored in the recording medium 13a.

The communication I / F 14 is an interface for the optimum control device 10 to perform data communication with another device. The one or more programs that realize the optimal control processing unit 100 may be acquired (downloaded) from a predetermined server or the like via the communication I / F14.

The ROM 15 is a non-volatile semiconductor memory that can retain data even when the power is turned off. The RAM 16 is a volatile semiconductor memory that temporarily holds programs and data. The CPU 17 is an arithmetic unit that reads programs and data from, for example, the auxiliary storage device 18 and the ROM 15 into the RAM 16 and executes various processes.

The auxiliary storage device 18 is, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), or the like, and is a non-volatile memory for storing programs and data. The programs and data stored in the auxiliary storage device 18 include, for example, one or more programs that realize the optimum control processing unit 100, an OS (Operating System) that is basic software, and various application programs that operate on the OS. be.

By having the hardware configuration shown in FIG. 2, the optimum control device 10 according to the present embodiment can realize various processes described later. Although FIG. 2 shows a hardware configuration example in which the optimum control device 10 is realized by one computer, the optimum control device 10 may be realized by a plurality of computers.

<Functional configuration of optimal control processing unit 100>
Next, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 3 is a diagram showing an example of the functional configuration of the optimum control processing unit 100 according to the first embodiment.

As shown in FIG. 3, the optimal control processing unit 100 according to the present embodiment includes an offline processing unit 110 and an online processing unit 120. In the present embodiment, the case where one optimum control device 10 has both the offline processing unit 110 and the online processing unit 120 will be described, but the present invention is not limited to this. Different devices may have the offline processing unit 110 and the online processing unit 120. In particular, for example, various devices or devices having sufficient computational resources may have an offline processing unit 110, while an edge device or the like having limited computational resources may have an online processing unit 120.

The offline processing unit 110 inputs the model formula 1100, the upper / lower limit constraint 1200, and the evaluation function 1300 offline, and calculates the relational formula 1400.

The model formula 1100 is a model representing the relationship between the manipulated variable and the controlled variable in the system to be controlled. In the model equation 1100, if the function representing the relationship between the variables MV ₁ , ..., MV _M representing the manipulated variable and the variable PV _n representing the controlled variable is f _n , then PV _n : = f _n (MV ₁ ). , ..., MV _M ), (n = 1, ..., N).

The model formula 1100 can be created by regression analysis or the like using, for example, the actual value of the controlled variable with respect to the actual manipulated variable. f _n is not limited to linear, and may be piecewise linear or the like.

Further, the upper and lower limit constraints 1200 are constraints representing the upper limit and the lower limit of each manipulated variable in the system to be controlled. As for the upper and lower limit constraints 1200, if the upper limit of each manipulated variable is HMV ₁ , ..., HMV _M , and the lower limit of each manipulated variable is HMV ₁ , ..., HMV _M , then LMV _m ≤ MV _m ≤ HMV _m , It is represented by (m = 1, ..., M).

The evaluation function 1300 is a function for evaluating the difference between the target value and the controlled variable. If the function for evaluating the difference between the variables SV ₁ , ..., SVN representing the target value and the variables PV ₁ , ..., PV _N representing the control amount is _E , the evaluation function 1300 is assumed. It is represented by the following number 1.

また、関係論理式１４００は、モデル式１１００と上下限制約１２００と評価関数１３００とに基づく最適性条件（ＫＫＴ（Karush-Kuhn-Tucker ）条件）を満たす場合において、目標値を表す変数ＳＶ_１，・・・，ＳＶ_Ｎに対して操作量を表す変数ＭＶ_１，・・・，ＭＶ_Ｍが満たすべき関係を表す論理式である。関係論理式１４００は、目標値を表す変数ＳＶ_１，・・・，ＳＶ_Ｎを各軸とするＮ次元空間をＫ個の領域Ｒｋ（ｋ＝１．・・・，Ｋ）に分割する論理式で表される。なお、分割数Ｋは、限定記号消去法を行うことによって決定される定数である。

Further, the relational formula 1400 is a variable SV ₁ , which represents a target value when the optimum condition (KKT (Karush-Kuhn-Tucker) condition) based on the model formula 1100, the upper / lower limit constraint 1200, and the evaluation function 1300 is satisfied. ..., A logical expression representing the relationship that the variables MV ₁ , ..., MV _M , which represent the manipulated variable with respect to _SVN , should satisfy. The relational formula 1400 is a formula that divides an _N -dimensional space having variables SV ₁ , ..., SVN as each axis representing a target value into K regions Rk (k = 1. ..., K). It is represented by. The number of divisions K is a constant determined by performing the qualifying symbol elimination method.

Here, the offline processing unit 110 includes a first-order predicate logic expression generation unit 111 and a qualifying symbol erasing unit 112. The first-order predicate logic expression generation unit 111 generates the first-order predicate logic expression ψ from the model expression 1100, the upper / lower limit constraint 1200, and the evaluation function 1300. The limited symbol erasing unit 112 generates the relational formula 1400 from the first-order predicate logical formula ψ generated by the first-order predicate logical formula generation unit 111 by the limited symbol erasing method.

The online processing unit 120 inputs the relational formula 1400 and the target value 1500 online to calculate the optimum operation amount 1600.

The target value 1500 is the target value p ₁ , ..., P _N of the variables PV ₁ , ..., PV _N representing the control amount.

The optimum operation amount 1600 is an optimum operation amount s ₁ , ..., S _M for making the control amount follow the target value.

Here, the online processing unit 120 includes an area determination unit 121 and an operation amount calculation unit 122. The area determination unit 121 determines which of the areas Rk (k = 1, ..., K) the target values p ₁ , ..., P _N are included in. The operation amount calculation unit 122 has an optimum operation amount s ₁ , ..., By a function corresponding to the region _Rk including the target values p ₁ , ... s _M is calculated.

<Generation process of relational formula>
Hereinafter, the process of generating the relational formula 1400 will be described with reference to FIG. FIG. 4 is a flowchart showing an example of the generation process of the relational formula 1400 according to the first embodiment. The process shown in FIG. 4 is executed offline in advance, for example, before the process of calculating the optimum operation amount described later.

First, the first-order predicate logic expression generation unit 111 of the offline processing unit 110 inputs the model expression 1100, the upper / lower limit constraint 1200, and the evaluation function 1300 to generate the first-order predicate logic expression ψ (step S101).

Here, the first-order predicate logic expression generation unit 111 generates the first-order predicate logic expression ψ as follows. That is, first, the first-order predicate logic expression generation unit 111 arranges the upper and lower limit constraints 1200 so that the right side becomes 0, that is, LMV _m -MV _m ≤ 0, MV _m -HMV _m ≤ 0. Next, the first-order predicate logic expression generation unit 111 adds an expression obtained by multiplying the LMV _m -MV _m and the MV _m -HMV _m by the Lagrange multipliers (λ1 _m , λ2 _m ) to the evaluation function E as follows. Generates the Lagrange function L of.

次に、一階述語論理式生成部１１１は、ｍ＝１，・・・，Ｍに対して、最適性条件（ＫＫＴ条件）を満たすように以下の条件式を生成する。言い換えれば、一階述語論理式生成部１１１は、制約の数Ｍだけ、最適性条件（ＫＫＴ条件）を満たすように以下の条件式を生成する。

Next, the first-order predicate logic expression generation unit 111 generates the following conditional expressions for m = 1, ..., M so as to satisfy the optimum condition (KKT condition). In other words, the first-order predicate logic expression generation unit 111 generates the following conditional expressions so as to satisfy the optimum condition (KKT condition) by the number of constraints M.

次に、一階述語論理式生成部１１１は、上記で生成した全ての条件式ψ１_ｍ，ψ２_ｍ，ψ３_ｍ及びψ４_ｍを論理積で結合した以下の条件式ψ５を生成する。

Next, the first-order predicate logic expression generation unit 111 generates the following conditional expression ψ5 in which all the conditional expressions ψ1 _m , ψ2 _m , ψ3 _m , and ψ4 _m generated above are combined by a logical product.

そして、一階述語論理式生成部１１１は、条件式ψ５に対して、ラグランジュ乗数（λ１_ｍ，λ２_ｍ）に存在記号（∃）を付与して、以下の一階述語論理式ψを生成する。

Then, the first-order predicate logic expression generation unit 111 adds an existence symbol (∃) to the Lagrange multiplier (λ1 _m , λ2 _m ) with respect to the conditional expression ψ5, and generates the following first-order predicate logic expression ψ. ..

これにより、一階述語論理式生成部１１１により一階述語論理式ψが生成される。

As a result, the first-order predicate logic expression ψ is generated by the first-order predicate logic expression generation unit 111.

Next, the limited symbol erasing unit 112 of the offline processing unit 110 generates the relational formula 1400 from the first-order predicate logical formula ψ by the limited symbol erasing method (step S102). Here, if the relational formula 1400 is expressed as φ, the limited symbol erasing unit 112 generates the following relational formula φ by erasing the Lagrange multiplier by the limited symbol erasing method. For the qualifying symbol elimination method, refer to, for example, Non-Patent Document 3.

ここで、領域Ｒｋ（ｋ＝１，・・・，Ｋ）は分割論理式φ^Ｒｋ（ＳＶ_１，・・・，ＳＶ_Ｎ）が真（Ｔｒｕｅ）となる領域を示している。すなわち、上記の関係論理式φは、ＳＶ_１，・・・，ＳＶ_Ｎを各軸とするＮ次元空間をＫ個の領域Ｒｋ（ｋ＝１．・・・，Ｋ）に分割している。

Here, the region Rk (k = 1, ..., K) indicates a region in which the divided formula φ ^Rk (SV ₁ , ..., _SVN ) is true (True). That is, the above relational formula φ divides the _N -dimensional space having SV ₁ , ..., SVN as each axis into K regions Rk (k = 1. ..., K).

again,

は目標値ｐ_１，・・・，ｐ_Ｎが領域Ｒｋの内部にある場合（すなわち、目標値ｐ_１，・・・，ｐ_Ｎが領域Ｒｋに含まれる場合）における最適な操作量を算出する操作量決定関数を表している。この式は、一階述語論理式ψに対して限定記号消去法を行うことによって決定される。

Calculates the optimal manipulation amount when the target values p ₁ , ..., P _N are inside the region Rk (that is, when the target values p ₁ , ..., P _N are included in the region Rk). Represents an operation amount determination function. This formula is determined by performing the qualifying symbol elimination method for the first-order predicate logic formula ψ.

In this way, the relational formula φ is the divisional formula φ ^Rk (SV ₁ , ..., _SVN ) that divides the space with the variables SV ₁ , ..., _SVN as each axis representing the target value. , ..., p _N is represented by the logical _sum of the logical products of the manipulated variable determination function that calculates the optimum manipulated variable when the region Rk is included.

As a result, the relational formula φ is generated by the limited symbol erasing unit 112. Here, as described above, the relational formula φ divides the _N -dimensional space having SV ₁ , ..., SVN as each axis into K regions Rk (k = 1. ..., K). is doing. Therefore, as an example, in the case of K = 5, the regions R1 to R5 on the plane composed of a certain axis SV _n and SV _{n + 1} are shown in FIG. FIG. 5 is a diagram showing an example of region division represented by a relational formula. As shown in FIG. 5, each region R1 to R5 is represented by a region that divides an _N -dimensional space with SV ₁ , ..., SVN as each axis.

<Calculation processing of optimum operation amount>
Hereinafter, the process of calculating the optimum manipulated variable s ₁ , ..., S _M for the target values p ₁ , ..., P _N using the relational formula 1400 will be described with reference to FIG. .. FIG. 6 is a flowchart showing an example of the calculation process of the optimum operation amount according to the first embodiment. The process shown in FIG. 6 is executed online for each control cycle of the system to be controlled, for example.

First, the online processing unit 120 initializes k for specifying the area Rk (this k is also referred to as a “region number”) to 1 (step S201).

Next, the area determination unit 121 of the online processing unit 120 inputs the relational formula 1400 and the target value 1500, and whether or not the divisional formula φ ^Rk (p ₁ , ..., P _N ) = True. (Step S202). The target value 1500 input to the online processing unit 120 may be different for each control cycle, for example.

That is, the area determination unit 121 substitutes the target values p ₁ ..., P _N for the divided formula φ ^Rk (SV ₁ , ..., _SVN ) included in the relational formula φ, and φ It is determined whether or not ^Rk (p ₁ , ..., P _N ) = True. In other words, the area determination unit ₁₂₁ determines whether or not the target values p1 ..., _PN are included in the area Rk.

When it is determined in step S202 that φ ^Rk (p ₁ , ..., p _N ) = True (that is, when the target values p ₁ , ..., P _N are not included in the region Rk), online. The processing unit 120 adds 1 to the area number k (step S203). Then, the online processing unit 120 returns to the processing of step S202. As a result, the above step S202 is repeatedly executed until φ ^Rk (p ₁ , ..., P _N ) = True for a certain area number k.

When it is determined in step S202 that φ ^Rk (p ₁ , ..., p _N ) = True (that is, when the target values p ₁ , ..., P _N are included in the region Rk), online. The operation amount calculation unit 122 of the processing unit 120 calculates the optimum operation amount s ₁ , ..., S _M by the operation amount determination function corresponding to the region Rk including the target values p ₁ , ..., P _N. (Step S204).

That is, the operation amount calculation unit 122 calculates the optimum operation amount s ₁ , ..., S _M by the following operation amount determination function for each m = 1, ..., M.

これにより、操作量算出部１２２により、制御対象のシステムの制御量を目標値ｐ_１，・・・，ｐ_Ｎに追従させるための最適な操作量ｓ_１，・・・，ｓ_Ｍが算出される。

As a result, the operation amount calculation unit 122 calculates the optimum operation amount s ₁ , ..., S _M for making the control amount of the controlled system follow the target values p ₁ , ..., P _N. To.

As described above, the optimum control device 10 according to the present embodiment generates the relational formula φ in advance offline, and then calculates the optimum operation amount for the target value online. In this way, by generating the relational formula φ in advance offline, the optimal control device 10 according to the present embodiment can operate the optimum amount of operations online at high speed even when computational resources are limited, for example. Can be calculated.

Further, the optimal control device 10 according to the present embodiment generates the relational formula φ by the qualifying symbol elimination method. As a result, the optimal control device 10 according to the present embodiment can generate an accurate optimal control rule (that is, a relational formula φ) without a numerical error.

The relational formula generation process shown in FIG. 4 is performed once before the optimum operation amount calculation process shown in FIG. 6 unless at least one of the model formula 1100, the upper / lower limit constraint 1200, and the evaluation function 1300 is changed. It should be executed.

<Application example of optimal control processing unit 100>
Here, an application example of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIGS. 7 (a) and 7 (b). FIG. 7 is a diagram showing an example of an application example of the optimum control processing unit 100.

In FIG. 7A, the upper controller C11 has an optimum control processing unit 100. The upper controller C11 calculates the optimum operation amount (MV ₁ and MV 2) from the target values (SV ₁ and SV ₂ ) by the optimum control processing unit 100, and outputs the optimum operation amount (MV 1 and MV ₂ ) to the lower controllers C12 and C13. Then, the lower controllers C12 and C13 receive and control the optimum operation amount (MV ₁ and MV ₂ ) as the target value (SV ′ ₁ and SV ′ ₂ ). As described above, the upper controller C11 may pass the optimum operation amount to the lower controllers C12 and C13, and the lower controllers C12 and C13 may control the optimum operation amount as the target value.

In FIG. 7B, the upper controller C11 calculates the optimum operation amount (MV ₁ and MV ₂ ) from the target values (SV ₁ and SV ₂ ) by the optimum control processing unit 100, and the model formula is obtained from this optimum operation amount. The control amounts (PV ₁ and PV ₂ ) calculated by 1100 are output to the lower controllers C12 and C13. Then, the lower controllers C12 and C13 receive and control the control amounts (PV ₁ and PV ₂ ) as target values (SV ′ ₁ and SV ′ ₂ ). As described above, the upper controller C11 may pass a control amount for the optimum operation amount to the lower controllers C12 and C13, and the lower controllers C12 and C13 may perform control using this control amount as a target value.

[Second embodiment]
Next, the second embodiment will be described. In the first embodiment, in the calculation process of the optimum manipulated variable shown in FIG. 6, the regions including the target values p ₁ and ... p _N are searched in order from k = 1 among the regions R1 to RK. .. Therefore, it may take time to search the region including the standard values p ₁ , ... P _N. Therefore, in the second embodiment, a case where the search for the region including the target values p ₁ , ... P _N is performed based on the priority will be described.

In the second embodiment, the differences from the first embodiment will be mainly described, and the description of the components substantially the same as those of the first embodiment will be omitted or simplified.

<Functional configuration of optimal control processing unit 100>
First, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 8 is a diagram showing an example of the functional configuration of the optimum control processing unit 100 according to the second embodiment.

As shown in FIG. 8, the online processing unit 120 of the optimal control processing unit 100 according to the present embodiment further includes a cache mechanism unit 123. In the online processing unit 120 according to the present embodiment, whether or not the target values p ₁ , ..., P _N are included in the area Rk indicated by the area number k corresponding to the priority Y in ascending order of the priority Y. To judge. At this time, the cache mechanism unit 123 refers to the cache 1700 and converts the priority Y into the area number k.

Here, the cache 1700 will be described with reference to FIG. FIG. 9 is a diagram showing an example of the cache 1700.

As shown in FIG. 9, the cache 1700 is associated with the priority Y and the area number k. For example, the priority Y = 1 and the area number k = 5 are associated with each other. Similarly, the priority Y = 2 and the area number k = 4 are associated with each other. The same applies to the case where the priority Y = 3 or higher. From this, the online processing unit 120 according to the present embodiment has a target value p in the area Rk indicated by the corresponding area number k in the order of the area numbers k = 5, 4, 1, 3, 2 according to the priority Y. It can be determined whether or not ₁ , ..., P _N is included.

<Calculation processing of optimum operation amount>
Hereinafter, the calculation process of the optimum operation amount according to the present embodiment will be described with reference to FIG. FIG. 10 is a flowchart showing an example of the calculation process of the optimum operation amount according to the second embodiment. Since steps S202 and S204 of FIG. 10 are the same as those of FIG. 6, the description thereof will be omitted.

First, the online processing unit 120 initializes the priority Y to 1 (step S301). Next, the cache mechanism unit 123 of the online processing unit 120 refers to the cache 1700 and converts the priority Y into the area number k (step S302). That is, the cache mechanism unit 123 refers to the cache 1700 and converts the priority Y into the area number k associated with the priority Y. As a result, in step S202, it is determined whether or not φ ^Rk (p ₁ , ..., P _N ) = True using the region number k. Note that k: = cache [Y] is a function that converts the priority Y into the area number k with reference to the cache 1700.

If it is determined in step S202 that φ ^Rk (p ₁ , ..., p _N ) = True, the online processing unit 120 adds 1 to the priority Y (step S303). Then, the online processing unit 120 returns to the processing of step S302. As a result, the above steps S202 are repeatedly executed in ascending order of priority Y until φ ^Rk (p ₁ , ..., P _N ) = True for a certain area number k.

As described above, in the optimum control device 10 according to the present embodiment, the region Rk including the target values p ₁ , ..., P _N is searched in descending order of priority. As a result, by appropriately creating the cache 1700, it is possible to reduce the time required for searching the region Rk including the target values p ₁ , ..., P _N.

<Other examples of optimum operation amount calculation processing>
Hereinafter, another example of the optimum operation amount calculation process according to the present embodiment will be described with reference to FIG. 11. FIG. 11 is a flowchart showing another example of the optimum operation amount calculation process according to the second embodiment. Since steps S301 to S303 and step S204 in FIG. 11 are the same as those in FIG. 10, the description thereof will be omitted.

When it is determined in step S202 that φ ^Rk (p ₁ , ..., p _N ) = True, the cache mechanism unit 123 updates the cache 1700 so that the area number k has a higher priority. (Step S304).

For example, the cache mechanism unit 123 updates the priority Y associated with the area number k to 1, and decrements 1 from the priority Y associated with the other area number k. As a result, the priority Y of the area number k determined to be φ ^Rk (p ₁ , ..., P _N ) = True in step S202 can be set to the highest.

However, the present invention is not limited to this, and the cache mechanism unit 123 raises the priority Y of the area number k determined as φ ^Rk (p ₁ , ..., p _N ) = True in step S202 by one, for example. You may.

As described above, the optimum control device 10 according to the present embodiment may update the cache 1700 according to the determination result of the area determination unit 121. As a result, the priority Y corresponding to the area number k of the area Rk determined to include the target values p ₁ , ..., P _N can be dynamically increased. Therefore, it can be expected that the time required for searching the region Rk including the target values p ₁ , ..., P _N will be further reduced.

[Third embodiment]
Next, the third embodiment will be described. In the third embodiment, for example, when a target value (that is, a set of target values) for each control cycle i is input, a set of target values and a set of control quantities calculated from an optimum manipulated variable are used. The case of calculating the evaluation value such as the deviation of the above and visualizing the set of the calculated evaluation value will be described. As a result, for example, the user of the optimum control device 10 can confirm the deviation between the control amount and the target value when the operation of the optimum operation amount is performed on the operation target.

In the third embodiment, the differences from the first embodiment will be mainly described, and the description of the components substantially the same as those of the first embodiment will be omitted or simplified.

<Functional configuration of optimal control processing unit 100>
First, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 12 is a diagram showing an example of the functional configuration of the optimum control processing unit 100 according to the third embodiment.

As shown in FIG. 12, the online processing unit 120 of the optimum control processing unit 100 according to the present embodiment inputs the relational formula 1400 and the set of target values 1800 online, and sets the optimum operation amount 1900. Is calculated.

The set of target values 1800 is, for example, a set of target values for each control cycle i, and n = 1, ..., N, i = 1, ..., I.

で表される。

It is represented by.

The set of optimum manipulated variables 1900 is, for example, a set of optimum manipulated variables for each control cycle i, where m = 1, ..., M, i = 1, ..., I.

で表される。

It is represented by.

Further, the optimal control processing unit 100 according to the present embodiment shown in FIG. 12 has a visualization processing unit 130. The visualization processing unit 130 calculates an evaluation value such as a deviation between the control amount calculated from the optimum operation amount and the target value, and visualizes the calculated evaluation value.

Here, the visualization processing unit 130 includes a control amount calculation unit 131, an evaluation value calculation unit 132, and a visualization unit 133. The control amount calculation unit 131 calculates a set of control quantities from the set of optimum manipulated quantities 1900 by the model formula 1100. The set of control quantities is set to n = 1, ..., N, i = 1, ..., I by the model formula 1100.

で算出される。

It is calculated by.

The evaluation value calculation unit 132 calculates a set of evaluation values based on the set of control quantities calculated by the control amount calculation unit 131 and the set of target values 1800. The visualization unit 133 visualizes a set of evaluation values calculated by the evaluation value calculation unit 132.

<Visualization processing>
Hereinafter, a process of calculating a set of evaluation values and then visualizing the set of evaluation values will be described with reference to FIG. 13. FIG. 13 is a flowchart showing an example of the visualization process according to the third embodiment.

First, the online processing unit 120 inputs the target value set 1800 and calculates the optimum operation amount set 1900 (step S401). The online processing unit 120 repeatedly executes the calculation process of the optimum operation amount shown in FIG. 6 for each control cycle i, for example, to calculate the set 1900 of the optimum operation amount.

Next, the control amount calculation unit 131 of the visualization processing unit 130 calculates a set of control quantities from the set of optimal manipulated quantities 1900 by the model formula 1100 (step S402). That is, the control amount calculation unit 131 calculates a set of control amounts by the formula shown in the above equation 11.

Next, the evaluation value calculation unit 132 of the visualization processing unit 130 calculates a set of evaluation values (step S403).

Here, the evaluation values include, for example, (1) the deviation between the target value and the control amount corresponding to the optimum operation amount, (2) root-mean square error (RMSE), and (3) evaluation function E. The function value of can be used.

(1) Deviation between the target value and the control amount corresponding to the optimum operation amount When the deviation is used as the evaluation value, the evaluation value calculation unit 132 uses n = 1, ..., N, i = 1, ... , I, the deviation err _n ⁱ is calculated by the following formula.

これにより、評価値の集合として、偏差ｅｒｒ_ｎ ^ｉの集合が得られる。

As a result, a set of deviations _errn ⁱ is obtained as a set of evaluation values.

(2) Root-mean-squared error (RMSE)
When the mean square error is used as the evaluation value, the evaluation value calculation unit 132 uses i = 1. ..., For I, RMSE ⁱ is calculated by the following formula.

これにより、評価値の集合として、平均二乗誤差ＲＭＳＥ^ｉの集合が得られる。

As a result, a set of root-mean square error RMSE ⁱ is obtained as a set of evaluation values.

(3) Function value of the evaluation function E When the function value of the evaluation function E is used as the evaluation value, the evaluation value calculation unit 132 has i = 1. ..., For I, E ⁱ is calculated by the following formula.

これにより、評価値の集合として、評価関数値の集合Ｅ^ｉが得られる。

As a result, a set ^Ei of evaluation function values is obtained as a set of evaluation values.

Next, the visualization unit 133 of the visualization processing unit 130 visualizes a set of evaluation values calculated by the evaluation value calculation unit 132 (step S404).

Here, FIG. 14 shows an example of a case where a set of evaluation values is visualized. FIG. 14A is a graph that visualizes the deviation err ₁ on a plane composed of SV ₁ and SV ₂ . FIG. 14B is a graph that visualizes the root-mean-squared error RMSE on a plane composed of SV ₁ and SV ₂ . FIG. 14C is a graph that visualizes the evaluation function value E on the plane composed of SV ₁ and SV ₂ .

By visualizing the set of evaluation values in this way, the user or the like of the optimum control device 10 according to the present embodiment can perform deviation, mean square error or evaluation between the target value and the control amount corresponding to the optimum operation amount. You can check the function value. Thereby, for example, the user or the like can specify how much the target value for each i deviates from the target value when the optimum control is performed. Further, the visualization process in the present embodiment can be performed on a set of assumed target values offline before the control is executed. For this reason, visualization makes it possible to grasp in advance the presence or absence of a solution and the situation where control deviation occurs before performing control.

<Other examples of visualization processing>
In the following, as another example of the visualization process, the process of visualizing the region where the evaluation value becomes a predetermined value when the optimum control is performed (that is, when the operation of the optimum operation amount is performed) is shown in the figure. It will be described with reference to 15. FIG. 15 is a flowchart showing another example of the visualization process according to the third embodiment. Hereinafter, as an example, it is assumed that the evaluation value is a deviation. The visualization process shown in FIG. 15 is executed offline, for example.

First, the first-order predicate logic expression generation unit 111 of the offline processing unit 110 generates the first-order predicate logic expression ψ'corresponding to the region where the deviation becomes a predetermined value from the model expression 1100 and the relational logic expression 1400. (Step S501). Hereinafter, as an example, a case where a first-order predicate logic expression corresponding to a region where the deviation is 0 will be generated will be described.

In this case, the first-order predicate logic expression generation unit 111 generates the first-order predicate logic expression ψ'shown in the following equation 15.

なお、例えば、偏差がａとなる領域に対応する一階述語論理式ψ´を生成する場合は、以下の数１６を生成すれば良い。

For example, when generating the first-order predicate logic equation ψ'corresponding to the region where the deviation is a, the following number 16 may be generated.

また、例えば、偏差がａ以上かつｂ以下となる領域に対応する一階述語論理式ψ´を生成する場合は、以下の数１７を生成すれば良い。

Further, for example, when generating the first-order predicate logic equation ψ'corresponding to the region where the deviation is greater than or equal to a and less than or equal to b, the following number 17 may be generated.

次に、オフライン処理部１１０の限定記号消去部１１２は、限定記号消去法により、一階述語論理式ψ´から制御可能論理式φ´（ＳＶ_１，・・・，ＳＶ_Ｎ）を生成する（ステップＳ５０２）。

Next, the limited symbol erasing unit 112 of the offline processing unit 110 generates a controllable logical expression φ'(SV ₁ , ..., SVN) from the first _- order predicate logical expression ψ'by the limited symbol erasing method (SV 1, ..., SVN). Step S502).

Next, the visualization processing unit 130 visualizes the controllable formula φ'(SV ₁ , ..., _SVN ) generated by the qualifying symbol erasing unit 112 (step S503). That is, the visualization processing unit 130 draws a region in which the controllable formula φ'(SV ₁ , ..., SV _N ) is True, so that the controllable logical formula φ'(SV ₁ , ..., SV N) is drawn. , _SVN ) is visualized.

Here, FIG. 16 shows an example of the case where the region where the deviation becomes 0 is visualized. In FIG. 16, a region where the deviation is 0 on a plane composed of SV ₁ and SV ₂ (that is, a region where φ ′ (SV ₁ , ..., _SVN ) = True) is visualized. ..

As a result, the user or the like of the optimum control device 10 according to the present embodiment can confirm the region of the target value at which the deviation is a predetermined value (for example, the deviation is 0). As a result, the user or the like can set an appropriate target value, for example.

[Fourth Embodiment]
Next, a fourth embodiment will be described. In the fourth embodiment, a case where there is a rate of change constraint on the change in the controlled variable will be described. When there is a rate of change constraint, it is necessary to satisfy the rate of change constraint, and changes in the controlled variable (PV _n ) that do not satisfy the rate of change constraint (for example, a sudden temperature rise or a sudden temperature drop) can be performed. Can not.

Therefore, in the fourth embodiment, when the system to be controlled has a change rate constraint, a case of calculating the optimum operation amount satisfying the change rate constraint will be described. However, the fourth embodiment is applied not only when there is a constraint on the change in the controlled variable, but also when there is a rate of change constraint on the manipulated variable or when there is a rate of change constraint on both the manipulated variable and the controlled variable. It is possible.

In the fourth embodiment, the differences from the first embodiment will be mainly described, and the description of the components substantially the same as those of the first embodiment will be omitted or simplified.

<Functional configuration of optimal control processing unit 100>
First, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 17 is a diagram showing an example of the functional configuration of the optimum control processing unit 100 according to the fourth embodiment.

As shown in FIG. 17, the offline processing unit 110 of the optimum control processing unit 100 according to the present embodiment inputs the model formula 1100, the upper / lower limit constraint 1200, the evaluation function 1300, and the rate of change constraint 2000 offline. Then, the relational formula 1400 is calculated.

The rate of change constraint 2000 is a constraint condition indicating a control amount or operation amount that can be changed per unit time when the control amount (PV _n ) or operation amount (MV _m ) in the system to be controlled is changed. .. The rate of change constraint 2000 is n = 1, if the current control amount is P _n ⁰ , the upper limit of the rate of change with respect to the control amount P _n is δ _n ^u , and the lower limit of the rate of change with respect to the control amount P _n is δ _n ^l . ..., For N, it is represented by the following number 18.

本実施形態に係るオフライン処理部１１０の一階述語論理式生成部１１１は、モデル式１１００と上下限制約１２００と評価関数１３００と変化率制約２０００とから一階述語論理式ψを生成する。これにより、変化率制約２０００も考慮した一階述語論理式ψが生成される。そして、限定記号消去部１１２は、限定記号消去法により、変化率制約２０００も考慮した一階述語論理式ψから関係論理式１４００を生成する。

The first-order predicate logic expression generation unit 111 of the offline processing unit 110 according to the present embodiment generates the first-order predicate logic expression ψ from the model expression 1100, the upper / lower limit constraint 1200, the evaluation function 1300, and the rate of change constraint 2000. As a result, the first-order predicate logic equation ψ considering the rate of change constraint 2000 is generated. Then, the limited symbol erasing unit 112 generates the relational formula 1400 from the first-order predicate logical formula ψ in consideration of the rate of change constraint 2000 by the limited symbol erasing method.

<Generation process of relational formula>
Hereinafter, the process of generating the relational formula 1400 from the first-order predicate formula ψ in consideration of the rate of change constraint 2000 will be described with reference to FIG. FIG. 18 is a flowchart showing an example of the generation process of the relational formula 1400 according to the fourth embodiment. The process shown in FIG. 18 is executed offline in advance, for example, before the process of calculating the optimum operation amount.

First, the first-order predicate logic expression generation unit 111 of the offline processing unit 110 inputs the model expression 1100, the upper / lower limit constraint 1200, the evaluation function 1300, and the change rate constraint 2000 to generate the first-order predicate logic expression ψ (. Step S601).

Here, the first-order predicate logic expression generation unit 111 generates the first-order predicate logic expression ψ as follows. That is, first, the first-order predicate logic expression generation unit 111 arranges the upper and lower limit constraints 1200 so that the right side becomes 0, that is, LMV _m -MV _m ≤ 0, MV _m -HMV _m ≤ 0, and changes. The rate constraint 2000 is arranged so that the right side is 0, that is, PV _n ⁰ -δ _n ^l -PV _n ≤ 0 and PV _n -PV _n ⁰ -δ _n ^u ≤ 0. Next, the first-order predicate logic expression generator 111 multiplies LMV _m -MV _m and MV _m -HMV _m by the Lagrange multipliers (λ1 _m , λ2 _m ), respectively, and PV _n ⁰ -δ _n ^l -PV. The following Lagrange function L is generated by adding an equation obtained by multiplying _n and PV _n −PV _n ⁰ −δ _n ^u by a Lagrange multiplier (λ3 _n , λ4 _n ), respectively, to the evaluation function E.

次に、一階述語論理式生成部１１１は、ｍ＝１，・・・，Ｍ、ｎ＝１，・・・，Ｎに対して、最適性条件（ＫＫＴ条件）を満たすように以下の条件式を生成する。言い換えれば、一階述語論理式生成部１１１は、制約の数（ｍ＝１，・・・，Ｍ、ｎ＝１，・・・，Ｎ）だけ、最適性条件（ＫＫＴ条件）を満たすように以下の条件式を生成する。

Next, the first-order predicate logic expression generation unit 111 satisfies the following conditions for m = 1, ..., M, n = 1, ..., N so as to satisfy the optimum condition (KKT condition). Generate an expression. In other words, the first-order predicate logic expression generation unit 111 satisfies the optimality condition (KKT condition) by the number of constraints (m = 1, ..., M, n = 1, ..., N). Generate the following conditional expression.

次に、一階述語論理式生成部１１１は、上記で生成した条件式ψ１_ｍ，ψ２_ｍ，ψ３_ｍ及びψ４_ｍを論理積で結合した以下の条件式ψ５と、上記で生成した条件式ψ６_ｎ，ψ７_ｎ及びψ８_ｎを論理積で結合した以下の条件式ψ９とを生成する。

Next, the first-order predicate logic expression generation unit 111 includes the following conditional expression ψ5 in which the conditional expressions ψ1 _m , ψ2 _m , ψ3 _m and ψ4 _m generated above are combined by a logical product, and the conditional expression ψ6 generated above. The following conditional expression ψ9 is generated by combining _n , ψ7 _n and ψ8 _n by a logical product.

そして、一階述語論理式生成部１１１は、条件式ψ５と条件式ψ９とを論理積で結合した論理式ψ５∧ψ９に対して、ラグランジュ乗数（λ１_ｍ，λ２_ｍ，λ３_ｎ，λ４_ｎ）に存在記号（∃）を付与して、以下の一階述語論理式ψを生成する。

Then, the first-order predicate logical expression generation unit 111 has a Lagrangian multiplier (λ1 _m , λ2 _m , λ3 _n , λ4 _n ) for the logical expression ψ5 ∧ ψ9, which is a combination of the conditional expression ψ5 and the conditional expression ψ9 by a logical product. The existence symbol (∃) is added to to generate the following first-order predicate formula ψ.

これにより、一階述語論理式生成部１１１により一階述語論理式ψが生成される。

As a result, the first-order predicate logic expression ψ is generated by the first-order predicate logic expression generation unit 111.

Next, the limited symbol erasing unit 112 of the offline processing unit 110 generates the relational formula 1400 from the first-order predicate logical formula ψ by the limited symbol erasing method (step S602). Here, if the relational formula 1400 is expressed as φ, the limited symbol erasing unit 112 generates the following relational formula φ by erasing the Lagrange multiplier by the limited symbol erasing method.

これにより、変化率制約２０００を考慮した一階述語論理式ψから関係論理式φが生成される。

As a result, the relational formula φ is generated from the first-order predicate formula ψ in consideration of the rate of change constraint 2000.

Here, PV _n ⁰ is a variable representing the current value of the controlled variable with respect to n = 1, ..., N, and the region R _k (k = 1, ..., K) is the divided formula φ ^Rk . The region where (SV ₁ , ..., SV _N , PV ₁₀ ^,,,, PV _N ⁰ ) is true is shown. That is, the above relational formula _φ has ^K regions _Rk ( _k ⁼ ₁ . ..., K).

Further, in the manipulated variable determination function g _m ^Rk , when the target values p ₁ , ..., P _N and the current values q ₁ , ..., Q _N of the controlled variable are inside the region Rk (that is, the target). Represents an operation amount determination function that calculates the optimum operation amount in the region Rk) where the values p ₁ , ..., P _N and the current value q ₁ , ..., Q _N of the control amount are included in the region Rk. .. This equation is determined by performing the qualifying symbol elimination method for the first-order predicate logic equation ψ in consideration of the rate of change constraint.

In this way, the relational logical expression φ has variables SV ₁ , ..., SV _N representing the target value and variables PV ₁ ⁰ , ..., PV _N ⁰ representing the current value of the controlled variable as axes. The current division logic formula φ ^Rk (SV ₁ , ..., _SVN , PV ₁ ⁰ , ..., PV _N ⁰ ) that divides the space, the target values p ₁ , ..., p _N , and the current control amount. Operation amount determination function g _m ^Rk (SV ₁ , ..., _SVN , PV ₁ ⁰ , ...) To calculate the optimum operation amount when the values q ₁ , ..., q _N are included in the region Rk. ·, It is represented by the logical sum of the logical products of PV _N ⁰ ). As a result, the relational formula φ is generated by the limited symbol erasing unit 112.

<Calculation processing of optimum operation amount>
The area determination unit 121 of the online processing unit 120 inputs the target values p ₁ , ..., P _N and the current values q ₁ , ..., Q _N of the control amount into the division logic formula, and divides the logic. It is determined whether or not the formula φ ^Rk (p ₁ , ..., p _N , q ₁ , ..., Q _N ) = True. The target value 1500 and the current value 2100 input to the online processing unit 120 may be different for each control cycle, for example.

When the area determination unit 121 of the online processing unit 120 determines that the divided formula φ ^Rk (p ₁ , ..., p _N , q ₁ , ..., Q _N ) = True, the online processing unit 120 The operation amount calculation unit 122 has a target value for the operation amount determination function corresponding to the region Rk including the target values p ₁ , ..., P _N and the current values q ₁ , ..., Q _N of the control amount. By substituting p ₁ , ..., p _N and the current value q ₁ , ..., q _N , the optimum manipulated amount s ₁ , ..., s _M is calculated. In the calculation process, the optimum operation amount in consideration of the rate of change constraint 2000 can be calculated. Since the calculation process of the optimum operation amount is the same as that of the first embodiment, the description thereof will be omitted.

As a result of considering the rate of change constraint 2000, even if the operation target is operated with the optimum operation amount, the control amount may not reach the target value in one operation. In such a case, for example, by repeating the calculation of the optimum operation amount and the operation on the operation target for each control cycle, the control amount can reach the target value while satisfying the rate of change constraint 2000. ..

[Example 1]
Hereinafter, the first embodiment of the optimum control device 10 according to the present embodiment will be described. In the first embodiment, a case where the heat pump model shown in FIG. 19 is controlled as the system to be controlled will be described. The heat pump model shown in FIG. 19 includes a compressor 200, an expansion valve 300, a condenser 400, and an evaporator 500. When the operating amount of the compressor 200 (MV ₁ : compressor motor rotation rate) is increased, the controlled amount of the condenser 400 (PV ₁ : condensation temperature) becomes high, and the controlled amount of the evaporator 500 (PV ₂ : evaporation temperature) becomes high. ) Becomes cold. On the other hand, when the operating amount of the expansion valve 300 (MV ₂ : expansion valve opening) is increased, the controlled amount of the condenser 400 (PV ₁ : condensation temperature) becomes low, and the controlled amount of the evaporator 500 (PV ₂ :). Evaporation temperature) becomes high. In the first embodiment, it is assumed that the operation amount of the compressor 200, the operation amount of the expansion valve 300, the control amount of the condenser 400, and the control amount of the evaporator 500 are modeled in the following relationship. ..

このとき、圧縮機２００の操作量と膨張弁３００の操作量とを調整し、凝縮器４００の制御量と蒸発器５００の制御量とを目標値（ＳＶ_１及びＳＶ_２）にする制御を行うものとする。

At this time, the operation amount of the compressor 200 and the operation amount of the expansion valve 300 are adjusted, and the control amount of the condenser 400 and the control amount of the evaporator 500 are controlled to be the target values (SV ₁ and SV ₂ ). It shall be.

Further, the operation amount of the compressor 200 and the operation amount of the expansion valve 300 have upper and lower limit constraints of 1800 ≤ MV ₁ ≤ 3400 and 500 ≤ MV ₂ ≤ 700, respectively, and an error between the target value and the control amount can be obtained. It is assumed that the evaluation function E to be evaluated is as follows.

このとき、図４のステップＳ１０１において、一階述語論理式生成部１１１により、以下のラグランジュ関数Ｌが生成される。

At this time, in step S101 of FIG. 4, the following Lagrange function L is generated by the first-order predicate logic expression generation unit 111.

次に、一階述語論理式生成部１１１により、最適性条件を満たす条件式ψ１_１，ψ１_２，ψ２_１，ψ２_２，ψ３_１，ψ３_２，ψ４_１，ψ４_２が生成される。そして、条件式ψ１_１，ψ１_２，ψ２_１，ψ２_２，ψ３_１，ψ３_２，ψ４_１，ψ４_２が論理積で結合されたψ５が生成され、ラグランジュ乗数に存在記号が付与されることで、一階述語論理式ψ：＝∃λ１_１∃λ１_２∃λ２_１∃λ２_２（ψ５）が生成される。

Next, the first-order predicate logic expression generation unit 111 generates conditional expressions ψ1 ₁ , ψ1 ₂ , ψ2 ₁ , ψ2 ₂ , ψ3 ₁ , ψ3 ₂ , ψ4 ₁ , ψ4 ₂ , which satisfy the optimum condition. Then, ψ5 is generated in which the conditional expressions ψ1 ₁ , ψ1 ₂ , ψ2 ₁ , ψ2 ₂ , ψ3 ₁ , ψ3 ₂ , ψ4 ₁ , ψ4 ₂ are combined by a logical product, and the existence symbol is added to the Lagrange multiplier. , First-order predicate logical expression ψ: = ∃λ1 ₁ ∃λ1 ₂ ∃λ2 ₁ ∃λ2 ₂ (ψ5) is generated.

Then, in step S102 of FIG. 4, the limited symbol erasing unit 112 generates the relational formula φ from the first-order predicate logical formula ψ by the limited symbol erasing method. Here, FIG. 20 shows the region division represented by the divisional formula φ ^Rk of the relational formula φ in the first embodiment. FIG. 20 shows a case where the region is divided into a plurality of regions including the regions R1 to R7. For each region shown in FIG. 20, the manipulated variable determination function gm _Rk for calculating the optimum manipulated ^variable is determined.

Next, a case of determining the optimum operation amount will be described. As an example, the target values are p ₁ = 63 and p ₂ = 0. In this case, in step S202 of FIG. 6, the area determination unit 121 determines that the target values (p ₁ , p ₂ ) are included in the area R7. Therefore, the operation amount calculation unit 122 calculates the optimum operation amount by the following formula.

上記の数２７に示す操作量決定関数のＳＶ_１及びＳＶ_２に対して、目標値（ｐ_１＝６３，ｐ_２＝０）を代入することで、以下の最適な操作量ｓ_１及びｓ_２が算出される。

By substituting the target values (p ₁ = 63, p ₂ = 0) for the operation amount determination functions SV ₁ and SV ₂ shown in the above equation 27, the following optimum operation amounts s ₁ and s ₂ are substituted. Is calculated.

なお、逆に、操作量ＭＶ_１及びＭＶ_２がそれぞれ（５６９５０００４）／２５８７７及び（４５１２９７３３）／７７６３１である場合、制御量ＰＶ_１及びＰＶ_２はそれぞれ６３及び０となり、目標値と一致する。

On the contrary, when the manipulated quantities MV ₁ and MV ₂ are (5695004) / 25877 and (45129733) / 77631, the controlled quantities PV ₁ and PV ₂ are 63 and 0, respectively, which match the target values.

Here, in the first embodiment, 1000 target values SV ₁ and SV when the optimum control amount (that is, the optimum operation amount) is calculated by the optimum control device 10 using a certain 1000 target values. The plot result in which ₂ is plotted is shown in FIG. Further, FIG. 22 shows an example of comparison with the prior art at this time. As shown in FIG. 21, it can be seen that these plot results are concentrated in a specific region. Therefore, for example, when the cache mechanism unit 123 is used, it becomes easy to hit a region having a higher priority, and high speed can be expected. Further, in the example shown in FIG. 22, the optimum operation amount is calculated by the optimization function (Mathematica) using the interior point method as a conventional technique, and the optimum operation amount is calculated by the optimum control device 10 according to the present embodiment. It shows the case of calculation. As shown in FIG. 22, it is 0.022212 [sec] in the conventional technique, whereas it is 0.000255 [sec] in the optimum control device 10 according to the present embodiment, and the calculation time is about 1/87. You can see that it has been shortened. As described above, according to the optimum control device 10 according to the present embodiment, the optimum operation amount for making the control amount follow the target value can be calculated at high speed as compared with the conventional technique.

When the optimum control device 10 according to the present embodiment had the cache mechanism unit 123, it was 0.000203 [sec], which was 1.26 times faster.

[Example 2]
Hereinafter, the second embodiment of the optimum control device 10 according to the present embodiment will be described. In the second embodiment, a case where the control amount of the heat pump model of the first embodiment has a rate of change constraint will be described. This rate of change constraint shall be as follows.

この変化率制約は、具体的には、制御量（ＰＶ_１及びＰＶ_２）が１制御周期で１℃しか変化しないものとした制約条件である。なお、ＰＶ_１ ^０及びＰＶ_２ ^０は、それぞれ制御時点でのＰＶ_１及びＰＶ_２の値を表す。

Specifically, this rate of change constraint is a constraint condition in which the controlled quantities (PV ₁ and PV ₂ ) change only 1 ° C. in one control cycle. Note that PV ¹⁰ and PV _{20 represent the values of PV 1 and} ^PV ₂ at the time of control, _respectively .

At this time, in step S101 of FIG. 4, the following Lagrange function L is generated by the first-order predicate logic expression generation unit 111.

次に、一階述語論理式生成部１１１により、最適性条件を満たすように条件式ψ１_１，ψ１_２，ψ２_１，ψ２_２，ψ３_１，ψ３_２，ψ４_１，ψ４_２，ψ５，ψ６_１，ψ６_２，ψ７_１，ψ７_２，ψ８_１，ψ８_２，ψ９が生成される。そして、ψ５とψ９とを論理積で結合したψ５∧ψ９に対して、ラグランジュ乗数（λ１_１，λ１_２，λ２_１，λ２_２，λ３_１，λ３_２，λ４_１，λ４_２）に存在記号が付与されることで、一階述語論理式ψ：＝∃λ１_１∃λ１_２∃λ２_１∃λ２_２∃λ３_１∃λ３_２∃λ４_１∃λ４_２（ψ５∧ψ９）が生成される。

Next, the first-order predicate logic expression generation unit 111 uses the conditional expressions ψ1 ₁ , ψ1 ₂ , ψ2 ₁ , ψ2 ₂ , ψ3 ₁ , ψ3 ₂ , ψ4 ₁ , ψ4 ₂ , ψ5, ψ6 ₁ so as to satisfy the optimum condition. , Ψ6 ₂ , ψ7 ₁ , ψ7 ₂ , ψ8 ₁ , ψ8 ₂ , ψ9 are generated. Then, for ψ5 ∧ ψ9, which is a logical product of ψ5 and ψ9, the existence symbol is in the Lagrange multiplier (λ1 ₁ , λ1 ₂ , λ2 ₁ , λ2 ₂ , λ3 ₁ , λ3 ₂ , λ4 ₁ , λ4 ₂ ). By being given, the first-order predicate logical expression ψ: = ∃λ1 ₁ ∃λ1 ₂ ∃λ2 ₁ ∃λ2 ₂ ∃λ3 ₁ ∃λ3 ₂ ∃λ4 ₁ ∃λ4 ₂ (ψ5 ∧ ψ9) is generated.

Then, in step S102 of FIG. 4, the limited symbol erasing unit 112 generates the relational formula φ from the first-order predicate logical formula ψ by the limited symbol erasing method. As a result, in the calculation process of the optimum manipulated variable, the optimum manipulated variable satisfying the rate of change constraint is calculated.

Here, FIG. 23 shows a time change when the control amount is controlled by repeatedly executing the calculation process of the optimum operation amount for each control cycle. 23 (a) shows the time change of PV ₁ , FIG. 23 (b) shows the time change of PV ₂ , FIG. 23 (c) shows the time change of MV ₁ , and FIG. 23 (d) shows the time change of MV ₂ . There is. As shown in FIGS. 23 (a) to 23 (d), the manipulated variable at each time is adjusted so that the controlled variable approaches the target value while satisfying the rate of change condition (the change in the controlled variable is within 1 ° C.). It has been calculated.

Further, FIG. 24 shows a case where the divisional formula φ ^Rk of the relational formula φ is visualized for each control cycle t when the optimum control by the optimum control device 10 according to the present embodiment is repeatedly executed for each control cycle t. show. In the example shown in FIG. 24, the case where the current value of the controlled variable in each control cycle t is observed and the divided formula φ ^Rk to which the observed value is substituted is visualized is shown. From t = 1 to t = 4, it can be seen that, for example, the region R1 changes significantly. On the other hand, in t = 5 to t = 7, the region R1 hardly changes. This is because PV ₁ and PV ₂ approach the target values p ₁ and p ₂ at t = 5 to t = 7, as shown in FIGS. 23 (a) and 23 (b). be.

<Summary>
As described above, the optimal control device 10 according to the present embodiment generates a relational formula offline and then online the relational formula and the target in the multivariable control in which a plurality of controlled quantities follow the target value. The optimum operation amount is calculated from the value. As a result, the optimal control device 10 according to the present embodiment can perform multivariable control even with a device having relatively few computational resources such as an edge device.

Further, the optimal control device 10 according to the present embodiment generates the relational formula by using the qualifying symbol elimination when the relational formula is generated. As a result, the optimal control device 10 according to the present embodiment can generate an accurate optimal control rule (that is, a relational formula φ) without a numerical error.

The present invention is not limited to the above-described embodiment disclosed specifically, and various modifications and modifications can be made without departing from the scope of claims.

10 Optimal control device 100 Optimal control processing unit 110 Offline processing unit 111 First-order predicate logic expression generation unit 112 Limited symbol erasing unit 120 Online processing unit 121 Area judgment unit 122 Operation amount calculation unit

Claims (12)

It is a control method used for multivariable control that makes multiple control quantities follow the target value.
A model expression that expresses the relationship between a variable that represents an operation amount in a controlled object and a variable that represents the control amount, an upper / lower limit constraint that expresses the upper and lower limits of the variable that represents the operation amount, and the target value and the control amount. When an evaluation function for evaluating the difference is input, a relational logical expression representing the relationship to be satisfied between the variable representing the target value and the variable representing the manipulated variable so that the evaluation function satisfies the optimum condition. And the generation procedure to generate in advance
Each time the target value is input, a calculation procedure for calculating the operation amount for making the plurality of control amounts follow the target value based on the target value and the relational formula, and a calculation procedure.
The computer runs ,
The generation procedure is
A Lagrange function is generated from the model formula, the upper and lower limit constraints, the evaluation function, and the Lagrange multiplier.
The Lagrange function generates a conditional expression that satisfies the optimum condition,
An existence symbol is added to the Lagrange multiplier of the conditional expression to generate a first-order predicate logic expression.
The first-order predicate formula is applied with the qualifying symbol elimination method to divide the space composed of variables representing the target values into a plurality of regions, and the optimum formula for each divided region. A control method comprising generating the relational formula composed of an operation amount determination function for calculating an operation amount . The calculation procedure is
The operation amount is obtained by searching for a region including the target value among a plurality of regions divided by the division formula and substituting the target value into the operation amount determination function corresponding to the searched region. The control method according to claim 1 , wherein the calculation is performed. The generation procedure is
The Lagrange function is generated from the model formula, the upper and lower limit constraints, the evaluation function, the Lagrange multiplier, and the rate of change constraint of the controlled amount per unit time.
A split logic formula that applies the qualifying symbol elimination method to the first-order predicate formula to divide the space composed of the variable representing the target value and the variable representing the current value of the control amount into a plurality of regions. , Generate the relational formula composed of the manipulated variable determination function,
The calculation procedure is
Of the plurality of regions divided by the division formula, the region including the target value and the current value of the control amount is searched, and the target value and the target value and the operation amount determination function corresponding to the searched region are used. The operation amount is calculated by substituting the current value of the control amount.
The control method according to claim 1, wherein the control method is characterized by the above. The generation procedure is
A Lagrange function is generated from the model formula, the upper and lower limit constraints, the evaluation function, the Lagrange multiplier, and the rate of change constraint of the manipulated variable over a unit time.
A divided formula that applies the qualifying symbol elimination method to the first-order predicate formula to divide the space composed of the variable representing the target value and the variable representing the current value of the manipulated variable into a plurality of regions. , Generate the relational formula composed of the manipulated variable determination function,
The calculation procedure is
Of the plurality of regions divided by the division formula, the region including the target value and the current value of the manipulated variable is searched, and the target value and the manipulated variable are used in the manipulated variable determination function corresponding to the searched region. The operation amount is calculated by substituting the current value of the operation amount.
The control method according to claim 1, wherein the control method is characterized by the above. The calculation procedure is
Referencing the cache in which the priority of the area to be searched is stored, and searching for the area including the target value among the plurality of areas divided by the division formula according to the priority. The control method according to any one of claims 2 to 4 . The fifth aspect of claim 5 , wherein when the area including the target value is searched, the computer executes an update procedure for updating the cache so that the searched area has a higher priority. Control method. The visualization procedure of calculating a predetermined evaluation value from the operation amount calculated by the calculation procedure, the control amount calculated using the model formula, and the target value, and visualizing the calculated evaluation value is described above. The control method according to any one of claims 1 to 6 , wherein the control method is executed by a computer. When the optimum control is performed from the relational formula and the model formula, a first-order predicate logical formula corresponding to a region where the deviation becomes a predetermined value is generated, and the region corresponding to the region where the deviation becomes a predetermined value is generated. By applying the qualifying symbol elimination method to the first-order predicate formula, a controllable formula representing a region where the deviation becomes a predetermined value is generated, and a visualization procedure for visualizing the generated controllable formula is described above. The control method according to any one of claims 1 to 6 , wherein the control method is executed by a computer. An output procedure for outputting either the operation amount calculated by the calculation procedure or the control amount calculated by using the operation amount and the model formula to another device connected to the computer. The control method according to any one of claims 1 to 8 , wherein the control method is executed. The model formula is any one of claims 1 to 9 , wherein the model formula is generated by regression analysis using the actual value of the manipulated variable and the actual value of the controlled variable corresponding to the actual value of the manipulated variable. The control method according to paragraph 1. It is a control device that performs multivariable control to make multiple control quantities follow the target value.
A model expression that expresses the relationship between a variable that represents an operation amount in a controlled object and a variable that represents the control amount, an upper / lower limit constraint that expresses the upper and lower limits of the variable that represents the operation amount, and the target value and the control amount. When an evaluation function for evaluating the difference is input, a relational logical expression representing the relationship to be satisfied between the variable representing the target value and the variable representing the manipulated variable so that the evaluation function satisfies the optimum condition. And the generation means to generate in advance,
Each time the target value is input, a calculation means for calculating the operation amount for making the plurality of control amounts follow the target value based on the target value and the relational formula, and a calculation means.
Have,
The generation means is
A Lagrange function is generated from the model formula, the upper and lower limit constraints, the evaluation function, and the Lagrange multiplier.
The Lagrange function generates a conditional expression that satisfies the optimum condition,
An existence symbol is added to the Lagrange multiplier of the conditional expression to generate a first-order predicate logic expression.
The first-order predicate formula is applied with the qualifying symbol elimination method to divide the space composed of variables representing the target values into a plurality of regions, and the optimum formula for each divided region. A control device for generating the relational formula composed of an operation amount determination function for calculating an operation amount . For computers that perform multivariable control that makes multiple control quantities follow the target value
A model expression that expresses the relationship between a variable that represents an operation amount in a controlled object and a variable that represents the control amount, an upper / lower limit constraint that expresses the upper and lower limits of the variable that represents the operation amount, and the target value and the control amount. When an evaluation function for evaluating the difference is input, a relational logical expression representing the relationship to be satisfied between the variable representing the target value and the variable representing the manipulated variable so that the evaluation function satisfies the optimum condition. Pre-generated generation procedure,
A calculation procedure for calculating the operation amount for making the plurality of control amounts follow the target value based on the target value and the relational formula each time the target value is input.
To execute ,
The generation procedure is
A Lagrange function is generated from the model formula, the upper and lower limit constraints, the evaluation function, and the Lagrange multiplier.
The Lagrange function generates a conditional expression that satisfies the optimum condition,
An existence symbol is added to the Lagrange multiplier of the conditional expression to generate a first-order predicate logic expression.
The first-order predicate formula is applied with the qualifying symbol elimination method to divide the space composed of variables representing the target values into a plurality of regions, and the optimum formula for each divided region. A program characterized by generating the relational formula composed of an operation amount determination function for calculating an operation amount .

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