Control system, system design tool, control method, and computer program

Abstract

To provide a technology of guaranteeing safety of an output of a control object under a requirement that a model error and constraint requirement are present in a control system that controls the control object.SOLUTION: A control system includes a target determination machine that uses a condition observation machine, which observes a condition of a control object including a model error expressed with formulae (3) and (4) and estimates disturbance expressed with a formula (5), and an optimization problem, which takes account of a linear inequality constraint concerning an input target, an estimate value of disturbance, and an outside signal, to correct the input target and determine a correction input target, and that is expressed with formulae (6) and (7), and a controller that controls a control object, uses the correction input target determined by the target determination machine to control the control object, and is expressed with a formula (9). α included in the formulae (3) and (5), β included in the formula (6), and γ included in the formula (9) are determined at each time.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a control system, a system design tool, a control method, and a computer program.

Background Art

[0002] Conventionally, a control system for controlling a controlled object using a model representing the relationship between an input to the controlled object and an output from the input controlled object has been known (for example, Patent Documents 1 and 2, and Non-Patent Documents 1 to 3).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0004]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, even with the prior art as described above, in a control system for controlling a controlled object, there is still room for improvement in the technology for ensuring the stability of the output of the controlled object under conditions where there are model errors and constraint conditions.

[0006] The present invention has been made to solve the above-described problems, and an object thereof is to provide a technique for ensuring the stability of the output of a controlled object under conditions where there are model errors and constraint conditions in a control system for controlling the controlled object.

Means for Solving the Problems

[0007] The present invention has been made to solve the above-described problems and can be realized in the following forms.

[0008] (1) According to one aspect of the present invention, there is provided a control system for controlling a linear system to which an unknown disturbance is added to the output, the linear system being represented by equations (1) and (2). This control system observes the state of the control target including the model error represented by equations (3) and (4), and estimates the disturbance represented by equation (5). Using a state observer, linear inequality constraints regarding the input target, and an optimization problem considering the estimated value of the disturbance estimated by the state observer and an external signal, the input target is corrected, and a corrected input target is determined by a target determiner represented by equations (6) and (7). The control system further includes a controller for controlling the control target, which uses the corrected input target determined by the target determiner to control the control target, and is represented by equation (9). Here, α included in equations (3) and (5), β included in equation (6), and γ included in equation (9) are determined at each time.

Number

Number

Number

Number

[0009] According to this configuration, within the achievable range considering the model error between the model and the control object estimated using the state observer and the input constraint, the input target is corrected to an optimal target according to the external signal \(r\), and a target determiner that determines the corrected input target is provided. For example, when the external signal \(r\) is the output target, the target determiner determines, within the range that satisfies the constraints, a corrected input target such that the output closest to the output target can be obtained in the steady state. The controller controls the control object using the corrected input target determined by the target determiner. At this time, \(\alpha\) included in Equation (3) and Equation (5), \(\beta\) included in Equation (6), and \(\gamma\) included in Equation (9) are adaptively determined at each time. Thereby, even in the presence of model errors and constraint conditions, the stability of the output of the control object can be guaranteed.

[0010] (2) In the control system of the above form, \(\alpha\), \(\beta\), and \(\gamma\) may be subject to the condition of Equation (12) as an inequality using Equation (10) and Equation (11). [Number] where \(\kappa\) is a positive scalar value that converges to 0 as time passes. According to this configuration, scalar values \(\alpha\), \(\beta\), \(\gamma\) that satisfy the condition of Equation (12) can always exist under appropriate assumptions and settings of \(S\). b

[0011] (3) In the control system of the above form, the target determiner determines the corrected input target using the optimization problem represented by Equation (13), and \(\delta\) * that satisfies the requirements of Equation (6) may be Equation (15) and Equation (16).

Mathematics

Mathematics

Mathematics

[0012] ​(4) According to still another aspect of the present invention, there is provided a control method for a linear system to which an unknown disturbance is added to an output, the control method controlling the linear system represented by Formula (1) and Formula (2). This control method includes a state observation step of observing the state of the control target including a model error represented by Formula (3) and Formula (4) and estimating the disturbance represented by Formula (5); a linear inequality constraint regarding an input target; and an optimization problem in which an estimated value of the disturbance estimated in the state observation step and an external signal are taken into account, and uses these to correct the input target and determine a corrected input target, which is a target determination step represented by Formula (6) and Formula (7); and a controller that controls the control target, the controller using the corrected input target determined in the target determination step to control the control target, which is a control step represented by Formula (9). Here, α included in Formula (3) and Formula (5), β included in Formula (6), and γ included in Formula (9) are determined at each time.

Number

Number

Number

Number

[0013] (5) According to another form of the present invention, there is provided a system - design tool for designing a control system for a linear system to which an unknown disturbance is added to the output, with the linear system represented by Equation (1) and Equation (2) as the controlled object. This system - design tool has a state - observation function for observing the state of the controlled object including the model error represented by Equation (3) and Equation (4) and estimating the disturbance represented by Equation (5), a linear - inequality constraint regarding the input target, and an optimization problem in which the estimated value of the disturbance estimated by the state - observation function and an external signal are considered, and uses these to correct the input target and determine the corrected input target, a target - determination function represented by Equation (6) and Equation (7), and a controller for controlling the controlled object, which controls the controlled object using the corrected input target determined by the target - determination function, a control function represented by Equation (9). The design unit is provided with a design unit that designs such that α included in Equation (3) and Equation (5), β included in Equation (6), and γ included in Equation (9) are determined at each time. [Number] However, x is in an n-dimensional state, u is an n-dimensional input, y is an n-dimensional output, θ is an n-dimensional disturbance, A and B are n×n matrices, + (plus) represents the value at the next time step. The true values of x, θ, A, and B are unknown, and the values of u and y are known. [Number] However, ^(hat) represents the estimated value, α is a non-negative scalar value, and L x , L θ is the observer gain of an n×n matrix. Each of  and B̂ is a matrix that reproduces A and B and may contain the model error θ. [Number] However, K̂ is represented by Equation (8), [Number] β is a non-negative scalar value, r is an external signal, and δ * is a function that determines the update amount of the input target ū. [Number] However, γ takes a scalar value, and ũ *~ is an arbitrary n-dimensional vector value. According to this configuration, in each of the state observation function for estimating the model error between the model and the control object designed for the control system, the target determination function for determining the corrected input target, and the control function for controlling the control object using the corrected input target, α included in Equation (3) and Equation (5), β included in Equation (6), and γ included in Equation (9) are adaptively determined at each time step. Thereby, it is possible to design a control system that guarantees the stability of the output of the control object even under conditions where model errors and constraint conditions exist.

[0014] (6) According to yet another aspect of the present invention, there is provided a computer program for causing a computer to control a control target which is a linear system to which an unknown disturbance is added to the output and which is the linear system represented by formulas (1) and (2). This computer program observes the state of the control target including the model error represented by formulas (3) and (4), and estimates the disturbance represented by formula (5), and uses a state observation function, a linear inequality constraint regarding an input target, and an optimization problem in which the estimated value of the disturbance estimated by the state observation function and an external signal are considered, to correct the input target and determine a corrected input target, a target determination function represented by formulas (6) and (7), and a control function for controlling the control target, which controls the control target using the corrected input target determined by the target determination function and is represented by formula (9), to be executed by the computer, and α included in formulas (3) and (5), β included in formula (6), and γ included in formula (9) are determined at each time.

Number

Number

Number

Number

Equation

[0015] Note that the present invention can be realized in various forms, for example, a method for correcting an input target, a system including a device controlled by a control system and the control system, a design tool for designing a control system, a computer program executed in these systems or design tools, a server device for distributing the computer program, a non - transient storage medium storing the computer program, etc.

Brief Description of the Drawings

[0016]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Mode for Carrying Out the Invention

[0017] <First Embodiment> FIG. 1 is a schematic diagram showing the configuration of the control system 1 of the first embodiment. The control system 1 of the present embodiment uses the model of the control target 5 to control the input corresponding to the output target toward the control target 5 so as to stably control the control target 5 with a linear system to which a model error (disturbance) is added to the output as the control target 5. In the present embodiment, the “model” is a state equation that can approximately represent the time change of the output of the control target with respect to the input to the control target, which is created by learning data obtained by experiments or simulations on the control target 5. In the present embodiment, the control target 5 of the control system 1 is represented by the following equations (1) and (2).

Equation

[0018] Examples of the control target 5 controlled by the control system 1 of the present embodiment include drive engines such as internal combustion engines, hybrid engines, and power trains, fuel cells, induction motors, etc., and equipment attached to these devices. Specifically, when assuming a hybrid engine of an internal combustion engine and a motor as the control target 5, the model is a state equation that takes the accelerator opening, brake operation amount, and vehicle acceleration as inputs and outputs the output value of the internal combustion engine, the output value of the motor, the battery power storage amount, and the power storage amount limit value output from the hybrid engine. Also, when assuming a fuel cell as a system, the model is a state equation that takes the amount of supplied fuel as an input and outputs the generated power.

[0019] The control system 1 is, for example, a personal computer (PC), and includes a CPU 110, a storage unit 120, a ROM / RAM 130, a communication unit 140, and an input / output unit 150. Each part of the control system 1 is interconnected by a bus.

[0020] The CPU 110 controls each part of the control system 1 by expanding and executing a computer program stored in the ROM 130 in the RAM 130. The CPU 110 has a state observation unit 111, a target determination unit 112, and a control unit 113.

[0021] The state observation unit 111 observes the state of the controlled object including the model error and estimates the model error. Specifically, the state observation unit 111 uses the model of the controlled object 5 stored in the storage unit 120 to obtain the relationship between the estimated value of the state x of the controlled object 5, the estimated value of the model error θ, and the estimated value of the output y. The estimated value of the state x of the controlled object 5, the estimated value of the model error θ, and the estimated value of the output y are respectively represented by the following equations (3) to (5).

Equation

[0022] The target determination unit 112 corrects the input target and determines the corrected input target. Specifically, as shown in the following equations (6) and (7), the target determination unit 112 corrects the input target $\bar{u}$ by approaching the solution of an optimization problem that takes into account the linear inequality constraints regarding the input target $\bar{u}$, the model error $\hat{\theta}$ estimated by the state observation unit 111, and the target value of the output with respect to the input (output target) $r$ given from the outside.

Equation

Equation

[0023] In this embodiment, the target determination unit 112 corrects the input target $\bar{u}$ using the optimization problem represented by the following equation (13).

Equation

Equation

[0024]

Number

Number

Number

[0025] In Equation (6), the function δ * is a function that determines the update amount of the input target ū (bar). The function δ * becomes δ * = 0 when the input target ū (bar) is the solution of the optimization problem of Equation (13). On the other hand, when the input target ū (bar) is not the solution, it is a function that returns a vector approaching the solution of Equation (13), and the sum of the function δ * and the input target ū (bar) satisfies the linear inequality constraint of Equation (13). That is, it is a function that satisfies the following Equation (20).

Number

[0026] Examples of the function δ * that satisfy the requirements of Equation (6) and Equation (7) include Equation (15) and Equation (16).

Number

[0027] The control unit 113 inputs the corrected input target u, which is the input target ū(bar) corrected by the target determination unit 112, to the controlled object 5 and controls the controlled object 5. In the present embodiment, the control unit 113 is represented by Equation (8). + ￣(bar) is input to the controlled object 5 to control the controlled object 5. In the present embodiment, the control unit 113 is represented by Equation (8).

Number

Number

[0028] In the control system 1 of the present embodiment, each of the gain α included in Equations (3) and (5), the gain β included in Equation (6), and the gain γ included in Equation (9) is a time-varying gain determined at each time. In the present embodiment, each of the time-varying gains α, β, and γ is subject to the condition of Equation (12) as an inequality using Equations (10) and (11).

Number

[0029] The storage unit 120 is a storage medium composed of a hard disk, a flash memory, a memory card, etc. The storage unit 120 has a model storage unit 121. The model storage unit 121 stores a model used for obtaining the relationship between the estimated value x^(hat) of the state x of the control target 5 by the state observation unit 111, the estimated value θ^(hat) of the model error θ, and the estimated value y^(hat) of the output y.

[0030] The communication unit 140 controls communication via a communication interface between the control system 1 and other devices. Examples of other devices include the control target 5 controlled by the control system 1 and other information processing devices. The input / output unit 150 is various interfaces used for input and output of information by the user. Examples of the input / output unit 150 include a touch panel, a keyboard, a mouse, operation buttons, a microphone as an input unit, and a touch panel, a monitor, a speaker, an LED (Light Emitting Diode) indicator as an output unit.

[0031] Figure 2 is a flowchart of the control method of the first embodiment. The control method of the control target 5 by the control system 1 is executed, for example, by a request from the user such as the activation of a predetermined application.

[0032] In the control method of the first embodiment, first, the state observation unit 111, the target determination unit 112, and the control unit 113 are initialized (step S11). In step S11, each of the state observation unit 111, the target determination unit 112, and the control unit 113 sets the set variables to predetermined initial values and stores the parameters in the storage unit 120.

[0033] Next, control of the control target 5 is executed (step S12). In step S12, the state observation unit 111 inputs the input u at the current time into the model of the control target 5. At this time, the state observation unit 111 observes the output y of the control target 5 at the current time and the target value r of the output (step S13). As a result, the state observation unit 111 can obtain the relationship between the estimated value x^ (hat) of the state x of the control target 5, the estimated value θ^ (hat) of the model error θ, and the estimated value y^ (hat) of the output y, and estimate the model error θ.

[0034] Next, the time-varying gains α, β, and γ of the state observation unit 111 are calculated (step S14). In step S14, the target determination unit 112 calculates the time-varying gains α, β, and γ that satisfy the above-described equations (10) to (12). As a result, the target determination unit 112 determines the corrected input target u + ￣(bar) obtained by correcting the input target u￣(bar). Note that the time-varying gains α, β, and γ may have mathematical formulas for calculation prepared in advance, or may be obtained by searching for settings that satisfy the conditions. Further, the time-varying gains α, β, and γ may be obtained by optimization.

[0035] Next, the states of the model and the control unit 113 are updated (step S15). In step S15, using the calculation results in step S14, the respective variables of the model and the control unit 113 are updated according to equations (3) to (9) and equations (13) to (16). At this time, for the update of the function δ included in equations (6) and (7) by the target determination unit 112, optimization operations such as equations (15) and (16) are performed. Since equations (15) and (16) are quadratic programming problems (QP), a general-purpose QP solver can be used. In the input update of equation (9) by the control unit 113, u * ~(tilde) is arbitrary. As a result, the control unit 113 controls the control target using the corrected input target u + ￣(bar).

[0036] Next, it is determined whether to continue the current control method (step S16). In step S16, the control unit 113 determines whether to continue the control of the control target 5 according to whether to continue driving the control target 5. If the control unit 113 determines to continue the control of the control target 5, the process proceeds to step S12, and the control of the control target 5 is re-executed (step S12). If the control unit 113 determines not to continue the control of the control target 5, that is, to end the driving of the control target 5, the process proceeds to step S17, and the current control method ends.

[0037] Figure 3 is a diagram for explaining the change in the achievable output range due to the model error. Next, the effects of the control system 1 of the present embodiment will be described. Figure 3 shows, for a control target that outputs "Output 1" and "Output 2" with respect to an input, the range LM of the output achievable under a predetermined input constraint using a model, that is, the physical limit on the model of the control target, and the range LR of the actually achievable output, that is, the physical limit in the actual control target. In model-based control for a linear system, as shown in Figure 3, the range LM of the output achievable under a predetermined input constraint using a model can be calculated. However, when there is a model error Me (disturbance) in the model of the control target, since the actually achievable output range is the range LR, there is a possibility that even a target value achievable on the model may not be actually achievable. Specifically, as shown in Figure 3, the target value A0 is included in the range LM indicating the physical limit on the model of the control target, but is not included in the range LR indicating the physical limit in the actual control target. That is, the target value A0 cannot be achieved. In such a case, it is ideal to estimate the output variation due to the model error Me as a fixed disturbance, calculate the best target value A1 close to the target value A0 from within the range LR achievable under the condition of the estimated fixed disturbance, and converge the actual output thereto. However, as shown in Figure 3, when there are physical limits on the input in addition to the model error Me, it has been difficult to calculate the optimal target value A1 in real time within the actual physical limits considering the model error Me and ensure the stability of the control target.

[0038] The control system 1 of this embodiment includes a target determination unit 112 that sequentially calculates the optimal target value closest to the original target within the achievable range considering the model error θ between the model and the control target and the constraints on the input u estimated using the state observation unit 111. In the control system 1, the control unit 113 controls the input toward the target value corrected by the target determination unit 112. At this time, in the control system 1, the stability of the control target can be ensured by adaptively determining the set time-varying gains α, β, γ within a range that satisfies given conditions.

[0039] The effect of the control system 1 of this embodiment will be further described. The control method by the control system 1 satisfies the condition shown in the following formula (22), namely, the dissipativity condition.

Number

Number

Number

[0040] Here, when the combined system of formulas (1) to (5) is stable for a fixed input u, there must exist a positive definite symmetric matrix P and a setting of the function S b such that the following formula (27) holds for a certain constant λ > 0.

Number

[0041] Furthermore, when the function V is defined by formula (28), the following formula (29) is obtained.

Number

Equation

Equation

[0042] Next, a simulation experiment when the control system 1 of this embodiment is applied to the intake and exhaust system control of an engine will be described. In this test, among the intake and exhaust system controls of the engine, an experiment of the control by the control system 1 was conducted for the purpose of minimizing the pump loss. As a comparative example, the control results by a control system (hereinafter referred to as "control system of the comparative example") in which the gains α, β, and γ are fixed at constant values in the control system 1 will be described together.

[0043] FIG. 4 is a diagram showing the control result by the control system of the comparative example. Each of the three graphs shown in FIG. 4 shows time (unit: second) on the horizontal axis and the magnitude of pump loss on the vertical axis. FIG. 4(a) shows the time change of the output value (pump loss) corresponding to before correction, that is, the target value of pump loss. FIG. 4(b) shows the time change of the target value of pump loss corresponding to the corrected input target calculated in the control system of the comparative example. FIG. 4(c) shows the time change of pump loss when the corrected input target is input as the control result. As shown in FIG. 4(b), the corrected target calculated in the control system of the comparative example does not satisfy the above-mentioned dissipativity because the gains α, β, and γ are fixed. Therefore, the corrected input target diverges and the continuation of the calculation becomes impossible. For this reason, the continuation of the calculation is also impossible in the control result shown in FIG. 4(c).

[0044] FIG. 5 is a diagram showing the control result by the control system 1 of the present embodiment. Each of the three graphs shown in FIG. 5 shows time (unit: second) on the horizontal axis and the magnitude of pump loss on the vertical axis, similar to FIG. 4. FIG. 5(a) shows the time change of the target value of pump loss corresponding to the input target before correction. FIG. 5(b) shows the time change of the target value of pump loss corresponding to the corrected input target calculated in the control system 1 of the present embodiment. FIG. 5(c) shows the time change of pump loss when the corrected input target is input as the control result. Different from the case of the control system of the comparative example shown in FIG. 4, the control system 1 of the present embodiment calculates the corrected target while variably changing the gains α, β, and γ so as to satisfy dissipativity. Therefore, it can be seen that the corrected target converges (see FIG. 5(b)). As a result, as shown in FIG. 5(c), the control result becomes stable.

[0045] According to the control system 1 of the present embodiment described above, within the achievable range considering the model error between the model and the control target 5 and the input constraint estimated using the state observation unit 111, the input target is corrected to the optimal target closest to the input target, and the target determination unit 112 that determines the corrected input target is provided. The control unit 113 controls the control target 5 using the corrected input target determined by the target determination unit 112. At this time, the gain α included in equations (3) and (5), the gain β included in equation (6), and the gain γ included in equation (9) are adaptively determined at each time. Thereby, even under conditions where there are model errors and constraint conditions, the stability of the output of the control target 5 can be ensured.

[0046] Also, according to the control system 1 of the present embodiment, for the gains α, β, and γ, the condition of equation (12) is imposed as an inequality using equations (10) and (11). Thereby, the gains α, β, and γ that satisfy the condition of equation (12) can always exist under appropriate premise and S b settings.

[0047] Also, according to the control system 1 of the present embodiment, the target determination unit 112 determines the corrected input target using the optimization problem represented by equation (13), and the function δ * that satisfies the requirement of equation (6) is equations (15) and (16). Thereby, under the setting of appropriate β, it is guaranteed that the input target converges to the local optimal solution of equation (13), so that divergence of the control result can be suppressed.

[0048] Also, according to the control method of the present embodiment, in each of the step S13 of estimating the model error between the model and the control target 5, the step S14 of determining the corrected input target, and the step S15 of controlling the control target using the corrected input target, the gain α included in equations (3) and (5), the gain β included in equation (6), and the gain γ included in equation (9) are adaptively determined at each time. Thereby, even under conditions where there are model errors and constraint conditions, the stability of the output of the control target 5 can be ensured.

[0049] Also, according to the computer program of the present embodiment, in each of a state observation function for estimating a model error between the model and the control target 5, a target determination function for determining a corrected input target, and a control function for controlling the control target 5 using the corrected input target, the gain α included in Expression (3) and Expression (5), the gain β included in Expression (6), and the gain γ included in Expression (9) are adaptively determined at each time. Thereby, even under conditions where a model error or constraint conditions exist, the stability of the output of the control target 5 can be ensured.

[0050] <Second Embodiment> FIG. is a schematic diagram showing the configuration of the second embodiment. The system design tool 2 of the second embodiment includes a CPU 210 having a design unit 211. The system design tool 2 is connected to a control system 7 including a control device 6 and a control target 5 controlled by the control device 6, and is a personal computer electrically connected to the control device 6 that controls the control target 5. The system design tool 2 includes a CPU 210, a storage unit 220, a ROM / RAM 230, a communication unit 240, and an input / output unit 250. Each unit of the system design tool 2 is interconnected by a bus. The system design tool 2 designs a system capable of executing a control method for ensuring the stability of the output of the control target 5.

[0051] The CPU 210 designs the control system 7 by expanding and executing a computer program stored in the ROM 230 in the RAM 230. The CPU 110 has a design unit 211.

[0052] The design department 211 designs the process of the control method so that the control device 6 has an observation function, a target determination function, and a control function. The observation function is a function capable of obtaining the relationship between the estimated value of the state x of the control target 5, the estimated value of the model error θ, and the estimated value of the output y by using the model of the control target 5, similar to the state observation unit 111 included in the control system 1 of the first embodiment. The target determination function is a function capable of correcting the input target ū (bar) by approaching the solution of the optimization problem in consideration of the linear inequality constraint regarding the input target ū (bar), the model error θ̂ (hat) estimated by the observation function, and the target value r of the output, similar to the target determination unit 112 included in the control system 1 of the first embodiment. The control function is the corrected input target u + ū (bar), which is the input target ū (bar) corrected by the target correction function, is input to the control target 5 to control the control target 5.

[0053] According to the system design tool 2 of the present embodiment described above, in each of the state observation function for estimating the model error between the model and the control target 5 designed for the control device 6, the target determination function for determining the corrected input target, and the control function for controlling the control target using the corrected input target, the gain α included in equations (3) and (5), the gain β included in equation (6), and the gain γ included in equation (9) are adaptively determined at each time. Thereby, the system design tool 2 of the present embodiment can design a control system that guarantees the stability of the output of the control target 5 even under conditions where there are model errors and constraint conditions.

[0054] <Modification Example of the Present Embodiment> The present invention is not limited to the above-described embodiments, and can be implemented in various forms without departing from the gist thereof. For example, the following modifications are possible. Also, in the first embodiment, at least a part of the configuration implemented by hardware may be replaced with software, or conversely, a part of the configuration implemented by software may be replaced with hardware. For example, by replacing all of the configuration implemented by hardware with software, it is possible to obtain a design tool for designing a control system for controlling a control target.

[0055] [Modification Example 1] In the above-described embodiment, the time-varying gains α, β, and γ are set such that the condition of Equation (12) is imposed as an inequality using Equations (10) and (11). However, the method for determining the time-varying gains α, β, and γ is not limited to this. It may change according to the time.

[0056] [Modification Example 2] In the above-described embodiment, the target determination unit 112 corrects the input target using the optimization problem represented by Equation (13). However, the method for correcting the input target in the target determination unit 112 is not limited to this.

[0057] [Modification Example 3] In the above-described embodiment, in the target determination unit 112, as an example of the function δ * that satisfies the requirements of Equations (6) and (7), Equations (15) and (16) are given. However, the function δ * is not limited to this.

[0058] [Modification Example 4] In the above embodiment, the target determination unit 112 corrects the input target \(\bar{u}\) by approaching the solution of an optimization problem that takes into account linear inequality constraints regarding the input target \(\bar{u}\), the model error \(\hat{\theta}\) estimated by the state observation unit 111, and the target value \(r\) of the output. However, \(r\) included in Equation (6) is not limited to the target value of the output. Any signal input from the outside (external signal) may be used.

[0059] As described above, the present aspect has been described based on the embodiment and the modification example. However, the embodiments of the above-described aspects are for facilitating the understanding of the present aspect and do not limit the present aspect. The present aspect can be changed and improved without departing from the spirit and scope of the claims, and equivalents thereof are included in the present aspect. Also, if the technical features are not described as essential in this specification, they can be deleted as appropriate.

[0060] <Application Example 1> A control system for controlling a linear system to which an unknown disturbance is added to the output, the linear system represented by Equations (1) and (2) being the control target, a state observer that observes the state of the control target including the model error represented by Equations (3) and (4) and estimates the disturbance represented by Equation (5); a target determiner that corrects the input target by using a linear inequality constraint regarding the input target and an optimization problem that takes into account the estimated value of the disturbance estimated by the state observer and an external signal, and determines a corrected input target, represented by Equations (6) and (7); a controller that controls the control target, represented by Equation (9), and that controls the control target by using the corrected input target determined by the target determiner; and \(\alpha\) included in Equations (3) and (5), \(\beta\) included in Equation (6), and \(\gamma\) included in Equation (9) are determined at each time. A control system.

Equation

Number

Number

Number

Number

Number

Number

Number

Number

Number

Number

Number

Number

Number

Number

Equation

Equation

[0061] 1…Control system 2…System design tool 5…Controlled object 111…State observation unit 112…Target determination unit 113…Control unit 211…Design unit

Claims

1. A control system for a linear system to which an unknown disturbance is added to the output, the control system controlling the linear system represented by equations (1) and (2), a state observer that observes the state of the control target including a model error represented by equations (3) and (4) and estimates the disturbance represented by equation (5); a target determiner that modifies the input target and determines a modified input target by using a linear inequality constraint regarding the input target and an optimization problem in which the estimated value of the disturbance estimated by the state observer and an external signal are considered, represented by equations (6) and (7); a controller that controls the control target, the controller controlling the control target by using the modified input target determined by the target determiner, represented by equation (9); and α included in equations (3) and (5), β included in equation (6), and γ included in equation (9) are determined at each time. A control system. 【Number 1】 However, x is in an n-dimensional state, u is an n-dimensional input, y is an n-dimensional output, θ is an n-dimensional disturbance, A and B are n×n matrices, ＋ (plus) represents the value at the next time step. The true values of x, θ, A, and B are unknown, and the values of u and y are known. 【Number 2】 However, ^ (hat) represents an estimated value, α is a non - negative scalar value, and L ｘ , L θ is an observer gain of an n×n matrix, and each of  (hat) and B̂ (hat) is a matrix that reproduces A and B and may include a model error θ. 【Number 3】 However, K^ (hat) is represented by equation (8), [Number 4] β is a non - negative scalar value, r is an external signal, and δ ＊ is a function that determines the update amount of the input target ū (bar), 【Number 5】 However, γ takes a scalar value, and u ＊～ (tilde) is an arbitrary n-dimensional vector value.

2. The control system according to claim 1, wherein α, β, and γ are subject to the condition of equation (12) as an inequality using equations (10) and (11). A control system. 【Number 6】 However, κ is a positive scalar value that converges to 0 as time elapses.

3. The control system according to claim 1 or claim 2, wherein the target determiner determines the modified input target by using the optimization problem represented by equation (13). δ that satisfies the requirements of Equation (6) ＊ is given by Equations (15) and (16). A control system. 【Number 7】 However, Equation (13) is an optimization problem that minimizes the objective function f under the linear inequality constraints regarding the input target shown in Equation (14). ｒ It is an optimization problem to minimize 【Number 8】 C is an m×n matrix, and d is an n-dimensional vector. 【Number 9】

4. A control method for a linear system to which an unknown disturbance is added to the output, the control method controlling the linear system represented by equations (1) and (2), a state observation step of observing the state of the control target including a model error represented by equations (3) and (4) and estimating the disturbance represented by equation (5); a target determination step of modifying the input target and determining a modified input target by using a linear inequality constraint regarding the input target and an optimization problem in which the estimated value of the disturbance estimated in the state observation step and an external signal are considered, represented by equations (6) and (7); a control step of controlling the control target, the control step controlling the control target by using the modified input target determined in the target determination step, represented by equation (9). α included in Formula (3) and Formula (5), β included in Formula (6), and γ included in Formula (9) are determined at each time, control method. 【Number 10】 However, x is in an n-dimensional state, u is an n-dimensional input, y is an n-dimensional output, θ is an n-dimensional disturbance, A and B are n×n matrices, ＋ (plus) represents the value at the next time step. The true values of x, θ, A, and B are unknown, and the values of u and y are known. 【Number 11】 However, ^ (hat) represents an estimated value, α is a non - negative scalar value, and L ｘ , L θ is the observer gain of an n×n matrix, and each of  (hat) and B̂ (hat) is a matrix that reproduces A and B and may include the model error θ. 【Number 12】 However, K^ (hat) is represented by Formula (8), 【Number 13】 β is a non - negative scalar value, r is an external signal, and δ ＊ is a function that determines the update amount of the input target ū (bar), 【Number 14】 However, γ takes a scalar value, and u ＊～ (tilde) is an arbitrary n-dimensional vector value.

5. A system design tool for designing a control system that controls a linear system to which an unknown disturbance is added to the output and uses the linear systems represented by Formulas (1) and (2) as a control target, a state observation function that observes the state of the control target including the model error represented by Formulas (3) and (4) and estimates the disturbance represented by Formula (5); a target determination function represented by Formulas (6) and (7) that corrects the input target and determines a corrected input target by using a linear inequality constraint regarding the input target and an optimization problem considering the estimated value of the disturbance estimated by the state observation function and an external signal; a design unit that designs a controller that controls the control target and uses the corrected input target determined by the target determination function to control the control target, the design unit including a control function represented by Formula (9); the design unit designs such that α included in Formulas (3) and (5), β included in Formula (6), and γ included in Formula (9) are determined at each time, system design tool. 【Number 15】 However, x is in an n-dimensional state, u is an n-dimensional input, y is an n-dimensional output, θ is an n-dimensional disturbance, A and B are n×n matrices, ＋ (plus) represents the value at the next time step. The true values of x, θ, A, and B are unknown, and the values of u and y are known. 【Number 16】 However, ^ (hat) represents an estimated value, α is a non - negative scalar value, and L ｘ , L θ is an observer gain of an n×n matrix, and each of  (hat) and B̂ (hat) is a matrix that reproduces A and B and may include a model error θ. 【Number 17】 However, K^ (hat) is represented by Formula (8), 【Number 18】 β is a non - negative scalar value, r is an external signal, and δ ＊ is a function that determines the update amount of the input target ū (bar), 【Number 19】 However, γ takes a scalar value, and u ＊～ (tilde) is an arbitrary n-dimensional vector value.

6. A computer program for causing a computer to control a linear system to which an unknown disturbance is added to the output and which is the linear system represented by Formulas (1) and (2), a state observation function that observes the state of the control target including the model error represented by Formulas (3) and (4) and estimates the disturbance represented by Formula (5); a target determination function represented by Formulas (6) and (7) that corrects the input target and determines a corrected input target by using a linear inequality constraint regarding the input target and an optimization problem considering the estimated value of the disturbance estimated by the state observation function and an external signal; causing the computer to execute a control function that controls the control target and uses the corrected input target determined by the target determination function to control the control target, the control function being represented by Formula (9); α included in Formulas (3) and (5), β included in Formula (6), and γ included in Formula (9) are determined at each time, computer program. 【Number 20】 However, x is in an n-dimensional state, u is an n-dimensional input, y is an n-dimensional output, θ is an n-dimensional disturbance, A and B are n×n matrices, ＋ (plus) represents the value at the next time step. The true values of x, θ, A, and B are unknown, and the values of u and y are known. 【Number 21】 However, ^ (hat) represents an estimated value, α is a non - negative scalar value, and L ｘ , L θ is an observer gain of an n×n matrix, and each of  (hat) and B̂ (hat) is a matrix that reproduces A and B and may include a model error θ. 【Number 22】 However, K^(hat) is represented by Equation (8), 【Number 23】 β is a non - negative scalar value, r is an external signal, and δ ＊ is a function that determines the update amount of the input target, [24 Points] However, γ takes a scalar value, and u ＊～ (tilde) is an arbitrary n-dimensional vector value.

Images