Input / output estimation method, designing method for controller, and control method

Abstract

To provide a data estimation method that is able to estimate input / output data even when a control target is changed in system, and to provide a control method using the estimated data.SOLUTION: In an input / output estimation method according to the present invention, pseudo reference input of an FRIT is generated based on: a control target having the system fluctuation which is a change in characteristic over time; an initial target value which is a target value when a control parameter of a controller is set to a predetermined initial parameter; initial input which is control input; and initial output which is output of the control target. In addition, an FIR filter is generated by using the pseudo reference input, and input / output at the time when the control parameter of the controller is different from the initial parameter is estimated by using the FIR filter.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present invention relates to an input / output prediction method, a controller design method, and a control method.

Background Art

[0002] Conventionally, for a system whose structure and parameters are not fully understood, a data-driven control system design method has been proposed that directly calculates control parameters from operation data without going through modeling.

[0003] The database-driven control method is a method of adjusting parameters of a controller such as PID gain by referring to data stored in a database. Therefore, if more operation data can be stored in the database, further improvement in control performance can be expected. As a method for predicting input / output data of a control system for storage in a database, a method using the ERIT (Estimated Response Iterative Tuning) method (Non-Patent Document 1), a method based on the principle of superposition (Non-Patent Document 2), etc. have been proposed.

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, since the ERIT method makes predictions when the controller is changed, it cannot predict the response when the controlled object varies over time. In addition, since the superposition principle assumes a linear time-invariant control system, it is difficult to simply apply it to a time-varying control system.

[0006] The present invention has been made in view of the above circumstances, and an object thereof is to provide an input / output prediction method, a controller design method, and a control method capable of predicting an input / output response even when the controlled object varies in the system.

Means for Solving the Problems

[0007] In order to achieve the above object, in the input / output prediction method according to the first aspect of the present invention, a controlled object having a system variation which is a characteristic change over time represented by the following formula, and

Equation

Equation

Equation

Equation

[0008] In addition, the controller realizes a reference trajectory represented by the following formula.

Number

Number

Number

Number

[0009] In the method for designing a controller according to the second aspect of the present invention, Using the predicted input-output predicted by the data prediction method according to the first aspect and the prediction deviation represented by the following formula,

Number

Number

Number

[0010] In the control method according to the third aspect of the present invention, Storing in a database an information vector including the PID gain optimized by the design method according to the second aspect, the predicted input and predicted output corresponding to the optimized PID gain, and a target value, Based on the information vector stored in the database and the required points representing the current state of the system, calculate a control parameter to be updated. Based on the calculated control parameter, control the controlled object by database-driven control.

Effect of the Invention

[0011] According to the data prediction method and control method of the present invention, even when the state of the controlled object fluctuates, it is possible to predict input / output data.

Brief Description of the Drawings

[0012]

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[0013] Hereinafter, with reference to the drawings, an input / output prediction method, a controller design method, and a control method according to embodiments of the present invention will be described.

[0014] As shown in FIG. 1, a control system 1 according to the present embodiment includes a controller 10 and a control target 20. The controller 10 is a database-driven controller including a database 11 (not shown). Also, the control target 20 is a control target whose characteristics change over time. Hereinafter, the characteristic change of the control target 20 over time is also referred to as system variation.

[0015] Further, in the present embodiment, in the control system 1 having a system-varying control target, a plurality of input / output responses are predicted from data of a closed-loop response acquired in advance and stored in the database 11, thereby designing a controller 10 with high control performance. The closed-loop response acquired in advance consists of a control input (initial input) and an output of the control target (initial output) obtained by setting the control parameters of the controller to predetermined initial parameters and giving a predetermined target value (initial target value). Hereinafter, the method for predicting input / output data as data to be stored in the database will be described step by step.

[0016] <Prediction of Closed-Loop Response in an Arbitrary Controller> First, consider an input / output prediction method without considering system variations. In the prior art (for example, Non-Patent Document 2), in the FRIT method, a closed-loop response is predicted based on the principle of superposition using a pseudo-reference input ~r(t).

[0017] In this embodiment, similar to the prior art, a pseudo-reference input r(t) is used, and taking advantage of the fact that the transfer function block of the linear time-invariant system is interchangeable, a closed-loop response is predicted using a FIR filter (Figs. 1, 2). Also, the controlled plant G(z -1 ) to be handled in this embodiment is an unknown single-input single-output discrete-time linear time-invariant (LTI) system. At this time, the initial input / output data of the closed loop and the target values {u0(t), y0(t), r(t)} t=0,1,2,···,N-1 (N: number of data) are assumed to be acquired in advance, and the controller at this time is denoted as C0(z -1 ).

[0018] The following pseudo-reference input r(t) in the FRIT method is introduced.

Equation

Equation

[0019] Subsequently, design of the FIR filter used for closed-loop response prediction is performed. Specifically, an FIR filter F α (z -1 ) that satisfies the following relationship of Equation (4) is introduced.

Equation

Equation

[0020] Subsequently, the above-mentioned FIR filter F α (z -1 ) is used to predict the closed-loop response. Using the FIR filter F α (z -1 ), as shown in Figure 2, the predicted output ^y(t), which is the response when the controller ~C(0)(z -1 ) is implemented, can be calculated by the following equation (10).

Equation

[0021] Also, the predicted input ^u(t) can be calculated by the following equation (11) in the same procedure.

Equation

[0022] <Prediction of Closed-Loop Response Considering System Variation> Subsequently, consider the prediction of the closed-loop response assuming a linear time-varying system that varies with the passage of time. Specifically, consider the multiplicative system variation G Δ (z -1 ) as follows.

[0023]

Equation

[0024] In this embodiment, based on the method using the above FIR filter, the response of ~G(z -1 ) after system variation is predicted. Specifically, ~r(t) included in Equation (8) is replaced with the following equation.

Equation

[0025] By constructing Equation (8) using Equation (13) and applying Equations (6) and (10), the closed-loop predicted output ^y(t) in the case of the controlled object ~G(z -1 ) and the controller ~C(0)(z -1 ) can be calculated. Note that the predicted input is calculated by the following Equation (15).

Equation

[0026] Note that since the above-described method of predicting closed-loop input-output holds for a linear time-invariant system, in this embodiment, the system variation G Δ (z -1 ) is assumed to be given by an FIR-type model. For example, when assuming that system variation occurs at a certain time t n , it is set as follows.

Equation

[0027] <Design of a Controller to Achieve Desired Control Performance> In the above, the method of predicting the closed-loop response when an arbitrary controller ~C(z -1 ) is given has been described. Hereinafter, a method of designing a controller that realizes a desired reference trajectory y ref (t) will be described (Fig. 3).

[0028] Reference orbit y ref (t) is the reference model G as shown in the following equation m (z -1 ) is expressed using

Number

[0029] Furthermore, P(z -1 ) is a polynomial of the reference model and is expressed by the following equation.

Number

[0030] In the above, the multiplicative system variation G Δ (z -1 ) was given by an FIR-type transfer function. Therefore, in order to correspond to the system variation of G Δ (z -1 ), ideally the controller should also be of the FIR type. As shown in Figure 3, in the FRIT method, the inverse system of the controller is used, so the inverse system is expressed in the FIR type of the following equation.

Number

[0031] The evaluation criterion J of the FRIT method shown in Figure 3 FIR is as follows.

Number

[0032] At this time, each variable included in the above equation (22) is as follows.

Number

[0033] Therefore, the control parameter θ that minimizes Equation (22) * can be calculated by applying the least squares method to the following equation.

Equation

Equation

[0034] <Controller C * FIR (z -1 ) Design of a PID controller that mimics the characteristics of Considering the system variation G Δ (z -1 ) designed above, the controller C * FIR (z -1 ) will be a high-order controller. Therefore, as a more suitable controller for implementation, C * FIR (z -1 ) Design a PID controller C PID (z -1 ) that mimics the characteristics of (Figure 4).

[0035] Since the target value r(t) is known, the predicted deviation ^e(t) is obtained using the predicted output ^y(t) calculated in the design of the above-mentioned controller C * FIR (z -1 ).

Equation

[0036] Here, u in Figure 4 PID is calculated by the following equation.

Number

Number

[0037] At this time, since J PID can be linearly described with respect to the PID gain, the least squares method can be applied. However, in this embodiment, since a time-varying system variation G Δ (z -1 ) is assumed, it is also useful to apply the gradient method, the recursive least squares method, etc. For example, considering a system variation as in formula (16), with time t n as the boundary, it can be divided into two systems before and after t n . Therefore, (1) for the time interval from 0 to (t n -1), and (2) for the time interval from t n to (N-1), the least squares method can be applied to the data in each interval, and the PID gain suitable for each interval can be calculated.

[0038] <Database-Driven PID Control Using Prediction Data> In the above-described PID controller design method, the time when the system varies is assumed in advance. However, in an actual control system used in industry, the time when the state varies is unknown. Therefore, it is preferable to provide a mechanism for adaptively adjusting the control parameters according to the state of the controlled object. Accordingly, the controller 10 according to this embodiment constitutes a controller 10 that can exhibit high control performance regardless of the occurrence time of system variations by using a database-driven control method.

[0039] Specifically, the controller 10 is a database-driven PID controller, and the above-described predictive input / output data and PID gains are stored in the database 11 in advance in the form of an information vector φ(t) shown below.

Number

[0040] As the control method using a database-driven controller, a known method can be used. Hereinafter, an example of database-driven control according to the present embodiment will be specifically described with reference to the flowchart of FIG. 5.

[0041] When the control is started, the similarity S between the required point acquired as system data representing the current state of the control system and the information vector φ(t) stored in the database 11 is calculated (step S11).

[0042] Specifically, the similarity S(φ - (t), φ - (j)) between the required point φ - (t) and the system data φ - (j) of the j-th information vector stored in the database 11 is defined as follows.

Number

[0043] Note that h i is the bandwidth, and φ - (j) represents the i-th element of the system data in the j-th information vector stored in the database 11. As shown in Equation (37), the similarity S(φ - (t), φ - (j)) can be calculated using the system data φ - (j) of the information vector stored in the database 11.

[0044] Here, the bandwidth h i There are various methods for determining it, but in this embodiment, the following Plug-In Method is used.

Equation

[0045] The standard deviation σ of Equation (38) i is defined as follows using the number of data N.

Equation

[0046] In Equation (37), the similarity S becomes the highest when the requirement point φ - (t) representing the state of the current system is exactly the same as the system data φ - (j). In this case, the similarity S is given by the following equation.

Equation

[0047] Also, when the requirement point φ - (t) and the system data φ - (j) are not similar, the similarity S(φ - (t), φ - (j)) approaches 0. Therefore, the controller 10 selects the information vector φ - (j) that satisfies the following conditional equation based on the similarity S as the neighboring data (step S12).

Equation

[0048] Subsequently, the neighboring data φ - ​Using K(j) included in the information vector as the control parameter corresponding to (j), the PID gains for constructing the local controller are calculated by the Linearly Weighted Average (LWA) method shown below (step S13).

Number

[0049] Also, w i is the weight for the PID gain K(i) included in the selected i-th information vector φ(i) and is given by the following equation.

Number

[0050] The controller 10 performs control of the control target 20 using the control parameter calculated by Equation (42) (step S14). Note that among the system data φ - (j) of the information vectors stored in the database 11, if there is no data similar to the required point φ - (t), that is, if n k = 0, K(t) cannot be calculated. In this case, in this embodiment, the PID gain of the information vector φ with the highest similarity S is adopted.

[0051] Hereinafter, until the control ends, the processes of steps S11 to S14 are repeated at each time step (NO in step S15). When the end conditions such as the end of a predetermined time step or an end instruction by the operator are satisfied (YES in step S15), the control ends.

[0052] (Numerical Example) Hereinafter, a numerical example related to the control system 1 according to this embodiment will be described. In this example, a first-order lag system of the following Equation (44) is considered.

Number

[0053] In this example, T = 80 and K = 1 were set. The controlled object of the above equation (44) was discretized with a sampling time T s = 10 [s] into the following equation (45) to obtain G(z -1 ), which is used as the controlled object. [Equation] In addition, the target value was set as r(t) = 10, and for the parameters related to the reference model G m (z -1 ), σ = 60 and δ = 0 were set.

[0054] Also, the PID gain for obtaining the initial closed-loop data was given by the following equation (46). [Equation] The control results when the above PID gain was applied are shown in Fig. 6. In this example, using the data shown in Fig. 6, the control results when the controlled object undergoes state fluctuations are predicted.

[0055] Applying the method described in the above <Prediction of Closed-Loop Response Considering System Variations>, the closed-loop response assuming the system variation G Δ (z -1 ) is predicted. At this time, the system variation G Δ (z -1 ) is given by the following equation. [Equation] In this numerical example, since the sampling time T s = 10 [s], it is assumed that the state fluctuates at t = 2510 [s].

[0056] As shown in the simulation results of FIG. 7, the output y(t) and the predicted output ŷ(t) are in good agreement, and it can be confirmed that the data prediction method according to the present embodiment makes good predictions during system fluctuations.

[0057] In order to improve the control performance of the control system according to FIG. 7 above, an ideal controller C is designed by the method described in the above <Design of a Controller for Realizing Desired Control Performance>. * FIR (z -1 ) The prediction results at this time are shown in FIG. 8. As shown in FIG. 8, it can be confirmed that the response near t = 2510 [s] is improved compared to the results of FIG. 7.

[0058] Controller C of FIG. 8 * FIR (z -1 ) When used, the order of the controller becomes high and implementation may be difficult. Therefore, the method described in the above <Design of a PID Controller Imitating the Characteristics of Controller C * FIR (z -1 ) is applied to design a PID controller C * FIR (z -1 ) imitating C PID (z -1 ). At this time, since it can be divided into two systems around t = 2510 [s], the PID gains suitable for each section are calculated by the least squares method.

[0059] Subsequently, in accordance with the above-described method, the ^u(t), ^y(t) in FIG. 8 and the PID gains are stored in a database in pairs. Utilizing this database, the control results of applying database-driven PID control and the transition of the PID gains are shown in FIGS. 9 and 10, respectively. Also, for comparison, as a conventional database-driven PID control method, FIGS. 11 and 12 show the results when only the initial input / output data in FIG. 6 is stored in the database without storing ^u(t) and ^y(t). From the results in FIGS. 9 and 11, it can be confirmed that the database-driven PID control system according to the present embodiment quickly returns to the target value when the system fluctuates, and the control method according to the present embodiment is effective.

[0060] In the above numerical examples (FIGS. 7 to 12), the predicted input / output data was calculated assuming that the time when the system fluctuates is t = 2510 [s] in advance. However, in reality, the time when the system fluctuates is often unknown in advance, so FIG. 13 shows the control results of database-driven PID control when t = 1250 [s], which is different from the time assumed for the system fluctuation. For comparison, C * FIR (z -1 ) The control results when adopted are shown in FIG. 14.

[0061] FIG. 13 shows that, according to the algorithm of database-driven control, neighboring data is collected at each sampling time and the PID gains are calculated. Thus, it can be seen that even when the time of system fluctuation is uncertain, good control results can be obtained. On the other hand, in FIG. 14, it can be seen that the control performance deteriorates not only at the original system fluctuation time but also at t = 2510 [s] initially assumed. This is presumably because a FIR-type controller specialized for the system fluctuation assumed in advance is designed. From the above results, it can be understood that by predicting the input / output data in advance by the control system 1 according to the present embodiment and combining it with a database-driven PID controller, a control system with higher control performance can be constructed.

[0062] As described above, according to the control system 1 according to the present embodiment, a control target of a linear time-varying system is simulated as an FIR-type system variation, and input / output data when the system variation occurs is predicted. Further, a controller is designed to improve the control performance deteriorated by the system variation and applied to database-driven control, so that good control results can be obtained even when the system variation time is unknown.

Industrial Applicability

[0063] The present invention is suitable for a control system of a time-varying system in which the characteristics of the system change with time.

Explanation of Signs

[0064] 1 Control system, 10 Controller, 11 Database, 20 Control target

Claims

1. A controlled object having system variations that are characteristic changes over time represented by the following formula, 【Number 1】 Based on the initial target value which is the target value when the control parameter of the controller is set to a predetermined initial parameter, the initial input which is the control input, and the initial output which is the output of the controlled object, a pseudo-reference input of FRIT shown in the following formula is generated. 【Number 2】 Using the pseudo-reference input, an FIR filter that satisfies the following formula is generated. 【Number 3】 Using the FIR filter, the input / output when the control parameter of the controller is different from the initial parameter is predicted by the following formula. 【Number 4】 An input / output prediction method characterized by the above.

2. The controller realizes a reference trajectory represented by the following formula, 【Number 5】 Is of the FIR type represented by the following formula, 【Number 6】 Adjusted by the FRIT method that minimizes the evaluation criterion represented by the following formula, 【Number 7】 Replacing the pseudo-reference input with the following formula, 【Number 8】 Predicting the input / output when the control parameter of the controller is different from the initial parameter. The input / output prediction method according to claim 1, characterized by the above.

3. Using the predicted input / output predicted by the data prediction method of claim 2 and the prediction deviation represented by the following formula, 【Number 9】 The PID gain represented by the following formula, 【Number 10】 Optimized to minimize the evaluation criterion represented by the following formula, 【Number 11】 The optimized PID gain is used as the PID gain of the controller. A method for designing a controller, characterized by the above.

4. Storing in a database an information vector including the PID gain optimized by the design method of claim 3, the predicted input and predicted output corresponding to the optimized PID gain, and a combination with the target value. Calculating a control parameter to be updated based on the information vector stored in the database and the request point representing the current state of the system. Controlling the controlled object by database-driven control based on the calculated control parameter. A control method characterized by the above.

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