Model error suppression compensator

Abstract

To provide a model error suppression compensator that can be easily designed and adjusted.SOLUTION: A model error suppression compensator 1 of the present invention is a model error suppression compensator that adjusts a control input to a controlled object 20 based on a difference between output of a controlled object model 11, which is set in advance as a model representing the response characteristics of the controlled object, and output of the controlled object 20, and is set so as to minimize a variance of a generalized model error estimate that includes the difference between the output of the controlled object model 11 and the output of the controlled object 20 at a specified future time step, and an adjustment term represented by a product of an adjustment value of the control input and an adjustable parameter.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a model error suppression compensator. [Background technology]

[0002] In recent years, the development of advanced control systems using many sensors and actuators has progressed in a wide range of fields, such as industrial machinery and autonomous driving of automobiles. Model-Based Development (MBD) is used as an efficient development method for such complex control systems. In model-based development, a control system is designed for an ideal model constructed from the physical phenomena of the controlled object, and the designed controller is then implemented to obtain the desired control performance. However, in reality, a discrepancy (model error) occurs between the controlled object and the model, and it is believed that this model error affects the control performance.

[0003] As a control system design method for suppressing model errors, a disturbance observer (e.g., Patent Document 1) and a model error compensator (MEC) (e.g., Non-Patent Document 1) have been proposed, which incorporate a model of the controlled object in the control system and utilize the difference between the control output and the model output. By performing such compensation and suppressing the model error, the response characteristics of the controlled object can be made to approach the response characteristics of the model, so that a controller designed for the model can be applied directly to the actual controlled object. The disturbance observer and the model error suppression compensator are control systems specialized in suppressing disturbances and model errors, and have the advantage that they can be used in combination with existing controllers such as PID control that are widely used in industry.

[0004] However, a disturbance observer has the characteristic of requiring an inverse model of the controlled object, and when the controlled object is strictly proper or is a non-minimum phase system with dead time and unstable zeros, it is necessary to design an appropriate filter taking into consideration the suppression performance of proper model error and stability. Also, depending on the characteristics of the controlled object, it may not be possible to obtain the desired control performance. In contrast, a model error suppression compensator does not require an inverse model of the controlled object, and therefore can be applied to a wide range of controlled objects, including non-minimum phase systems with dead time and unstable zeros. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent Publication No. 2021-138335 [Non-patent literature]

[0006] [Non-Patent Document 1] H.Okajima, H.Umei, N.Matsunaga, T.Asai, “A Design Method of Compensator Minimize Model Error”, SICE Journal of Control, Measurement, and System Integration, Vol.6, No.4, pp.267-275, 2013 Summary of the Invention [Problem to be solved by the invention]

[0007] However, since a model error suppression compensator is generally configured to adjust the control input (operating amount) by feeding back the effect of the difference between the output of the controlled object and the output of the model at a high gain, there is a risk that the desired control characteristics cannot be obtained, such as the control system becoming unstable, depending on the characteristics of the controlled object, the model error, etc. Therefore, it is difficult to design and adjust an appropriate model error suppression compensator taking into account the characteristics of the controlled object.

[0008] The present invention has been made in consideration of the above circumstances, and has an object to provide a model error suppression compensator that can be easily designed and adjusted. [Means for solving the problem]

[0009] In order to achieve the above object, a model error suppression compensator according to a first aspect of the present invention comprises: A model error suppression compensator that adjusts a control input input to a controlled object based on a difference between an output of a controlled object model that is preset as a model representing a response characteristic of the controlled object and an output of the controlled object, It is set to minimize the variance of a generalized model error estimate that includes the difference between the output of the controlled object model and the output of the controlled object at a specified future time step, and an adjustment term represented by the product of the adjustment value of the control input and the adjustable parameter.

[0010] Moreover, the above model error suppression compensator is a filter that outputs an adjustment value for a control input based on a difference between an output of a control object model and an output of the control object; a denominator polynomial expressing a transfer characteristic of the filter includes a term of the adjustable parameter; This may also be the case.

[0011] A model error suppression compensator according to a second aspect of the present invention comprises: A model error suppression compensator that adjusts a control input input to a controlled object based on a difference between an output of a controlled object model that is preset as a model representing a response characteristic of the controlled object and an output of the controlled object, The model error suppression compensator comprises: For the control object represented by the following equation,

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[0012] Moreover, the above model error suppression compensator is a filter that outputs an adjustment value for a control input based on a difference between an output of a control object model and an output of the control object; a denominator polynomial expressing a transfer characteristic of the filter includes a term of the adjustable parameter; This may also be the case. Effect of the Invention

[0013] According to the model error suppression compensator of the present invention, the model error suppression compensator can be easily designed and can be easily modified in accordance with the response characteristics of the controlled object. [Brief description of the drawings]

[0014] [Figure 1] 1 is a block diagram showing a configuration of a model error suppression compensator according to an embodiment of the present invention. [Diagram 2] 2 is a block diagram showing a compensation law of a model error suppression compensator according to an embodiment. FIG. [Diagram 3] 11 is a graph showing a simulation result relating to a numerical example in which the dead time L=0 s, where (A) is a graph in the case where a model error suppression compensator is not used, and (B) is a graph in the case where a model error suppression compensator is used. [Figure 4] 10A and 10B are graphs showing simulation results for a numerical example in which the dead time of the controlled object and the dead time of the controlled object model do not match, where (A) is a graph without a model error suppression compensator, (B) is a graph with a model error suppression compensator and a weighting coefficient λ=0, and (C) is a graph with a model error suppression compensator and a weighting coefficient λ=10. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Hereinafter, a model error suppression compensator according to an embodiment of the present invention will be described with reference to the drawings.

[0016] As shown in the block diagram of FIG. 1, the model error suppression compensator 1 according to the present embodiment includes a controlled object model 11 and a filter 12, and outputs y of the controlled object 20 and y of the controlled object model 11. * Based on the difference between this and the control input u input to the control target 20, the control input u is adjusted. As a result, even if the actual control target 20 has a model error, it is possible to obtain control performance close to the desired control performance by using a controller designed based on the control target model 11.

[0017] The model error suppression compensator 1 is configured, for example, using a computer device and is implemented together with a controller of a control system. This embodiment differs from conventional model error suppression compensators in that the filter 12 is designed based on a design method of Generalized Minimum Variance Control (GMVC).

[0018] In the block diagram of Figure 1, P(z -1 ) is the control object 20, P M (z -1 ) indicates the control object model 11, which is a nominal model set in advance as a mathematical model representing the response characteristics of the control object 20. -1 ) is the output y(k) of the control object 20 and the output y *(k) and the compensation input u to suppress the model error. d and filter 12 as a compensation element that feeds back (k).

[0019] Also, u r (k) represents the input from a controller (not shown), and ξ(k) represents the model error of the controlled object 20. By suppressing the influence of the model error of the controlled object 20 using the model error suppression compensator 1, it is possible to bring the response characteristics of the controlled object 20 including the model error suppression compensator 1 closer to the response characteristics of the controlled object model 11. Therefore, it is believed that by incorporating a controller designed by model-based development into an actual controlled object, it is possible to achieve the desired control performance.

[0020] In this embodiment, a model error suppression compensation law is derived by applying a design method used in generalized minimum variance control, which is a control system design method based on minimization of an evaluation criterion, to the design of the model error suppression compensator 1. Generalized minimum variance control is known to be effective for non-minimum phase systems that have dead time and unstable zeros, and is considered to be applicable to a wide range of control targets as a model error suppression compensator. Below, a specific description is given of the model error suppression compensator 1 designed based on the design method of generalized minimum variance control.

[0021] The controlled object 20 according to the present embodiment is a CARIMA (Controlled Auto-Regressive Integrated Moving Average) model described by the following equation: A(z -1 ),B(z -1 ) are of order n and m, respectively.

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[0022] For the control target 20 of the equation (1), a model error suppression and compensation law is derived based on minimization of the evaluation criterion of the following equation.

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[0023] The above formula φ(k+k m +1) is the generalized model error estimate, defined as follows:

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[0024] As described above, the model error suppression compensator 1 according to the present embodiment is m +1) between the output of the controlled object model 11 and the output of the controlled object 20, and the compensation input u d The generalized model error estimate φ(k+k m +1) is set to minimize the variance of

[0025] Here, we introduce the Diophantine equation shown below, E(z -1 ) and F(z -1 ) is calculated. In addition, ΔA(z -1 ) and z-(km+1) From E(z -1 ) and F(z -1 ) is uniquely calculated by E(z -1 ),F(z -1 ) are the degrees of k m ,n.

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[0026] From equations (1), (4), and (5), the generalized model error estimate k at time k is given by m Get a +1 step ahead prediction value.

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[0027] Here, from equation (7), the optimal predicted value at time k is defined as follows:

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[0028] Here, G(z -1 ) is defined as follows, and n g :=m+k m It is.

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[0029] Next, the following equation is obtained from equations (7) and (8).

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[0030] From equations (3) and (10), ^φ(k+k m +1|k) = 0, the model error suppression and compensation law that minimizes the evaluation criterion J shown in the following equation is derived.

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[0031] 2 is a block diagram of a control system including the model error suppression compensator 1 configured by equations (1) and (11). The input / output relationship of the control system shown in FIG.

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[0032] As shown in FIG. 2, the transfer characteristic of the filter 12 can be expressed by the following equation.

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[0033] The designer can adjust the performance of the control system by appropriately setting the weighting coefficient λ for the difference in the compensation input. More specifically, the denominator polynomial of equation (14) expressing the characteristics of the filter 12 includes a term for the weighting coefficient λ, which is an adjustable parameter. Therefore, the designer can adjust the gain of the filter 12 and adjust the control performance by appropriately adjusting the weighting coefficient λ.

[0034] (Numerical example) An example of a computer simulation performed on a control system including the model error suppression compensator 1 according to the present embodiment will be described below. The controlled object in this example is a second-order lag system shown in the following equation. In this example, in order to confirm the effect of the model error suppression compensator 1, the simulation was performed by changing the dead time L [s].

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[0035] The control target shown in equation (15) is discretized to obtain a discrete-time system expressed by the following equation.

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[0036] For the above control object, Gaussian white noise with mean 0 and variance 0.01 is given as the model error ξ(k). The input given to the control object is a step input u r Let (k) = 10.

[0037] FIG. 3 shows the simulation results when the dead time L=0 s is not used (FIG. 3(A)) and when it is used (FIG. 3(B)). The weighting coefficient λ for the difference in the compensation input in the model error suppression compensator 1 is set to λ=0. When the model error suppression compensator 1 is not added to the controlled object 20 (FIG. 3(A)), it can be seen that the output of the controlled object 20 fluctuates irregularly due to the model error and deviates significantly from the output of the controlled object model 11. In contrast, when the model error suppression compensator 1 is provided (FIG. 3(B)), it can be seen that the output of the controlled object 20 can be tracked to match the output of the controlled object model 11 by suppressing the model error by feeding back the compensation input obtained from the difference between the outputs of the controlled object 20 and the controlled object model 11.

[0038] FIG. 4 shows a simulation result when the dead time of the controlled object 20 in the real system does not match the dead time of the controlled object model 11. In this example, the dead time of the controlled object 20 is d=5, the dead time of the controlled object model 11 is d=3, and other conditions are the same as those of the simulation in FIG. 3 described above. FIG. 4(A) shows a simulation result without the model error suppression compensator 1, FIG. 4(B) shows a simulation result with the model error suppression compensator 1 and a weighting factor λ=0, and FIG. 4(C) shows a simulation result with the model error suppression compensator 1 and a weighting factor λ=10. When the weighting factor λ=0, the response of the control system diverges, but when the weighting factor λ=10, the control system is stabilized and tracking of the controlled object model 11 is achieved.

[0039] These results show that the model error suppression compensator 1 according to this embodiment works effectively for a control target having dead time. In addition, since the control characteristics can be adjusted by adjusting only the weighting coefficient λ, which is an adjustable parameter, it is easy to modify the characteristics of the model error suppression compensator 1 and obtain high control performance.

[0040] As described above in detail, the model error suppression compensator according to the present embodiment derives the model error suppression compensation law by applying the method for deriving the control law of the generalized minimum variance control. Specifically, as shown in equations (3) and (4), the model error suppression compensation law is derived so as to minimize the difference between the output of the controlled object and the output of the controlled object model, and the variance of the generalized model error estimate based on the weighting coefficient for this difference. Therefore, for a wide range of controlled objects including non-minimum phase systems having dead time and unstable zeros, the model error suppression compensator can be easily designed based on a clear design method.

[0041] Also, as shown in formula (14), the denominator polynomial expressing the transfer characteristic of the filter 12 includes a weighting coefficient λ. Therefore, the designer can adjust the gain of the filter 12 and adjust the control performance by appropriately adjusting the weighting coefficient λ. This makes it possible to easily suppress excessively high gain of the filter 12 and prevent the control system from becoming unstable. In addition, since the control characteristic can be adjusted by the weighting coefficient λ, even if the response characteristic of the controlled object 20 varies over time, for example, an increase in dead time or a decrease in gain occurs, and the response characteristic of the controlled object 20 deviates from the response characteristic of the controlled object model 11, it is possible to easily make the response characteristic of the controlled object 20 follow the response characteristic of the controlled object model 11. [Industrial Applicability]

[0042] The present invention is suitable for a model error suppression compensator for a controlled object having a model error, and in particular, is suitable for a model error suppression compensator for a controlled object including a non-minimum phase system having a time delay or an unstable zero point. [Explanation of symbols]

[0043] 1 Model error suppression compensator, 11 Controlled object model, 12 Filter, 20 Controlled object

Claims

1. A model error suppression compensator that adjusts a control input input to a controlled object based on a difference between an output of a controlled object model that is preset as a model representing a response characteristic of the controlled object and an output of the controlled object, is set to minimize the variance of a generalized model error estimate including a difference between an output of the controlled plant model and an output of the controlled plant at a predetermined future time step, and an adjustment term represented by a product of an adjustment value of the control input and a tunable parameter; A model error suppression compensator comprising:

2. a filter that outputs an adjustment value for a control input based on a difference between an output of a control object model and an output of the control object; a denominator polynomial expressing a transfer characteristic of the filter includes a term of the adjustable parameter; 2. The model error suppression compensator of claim 1.

3. A model error suppression compensator that adjusts a control input input to a controlled object based on a difference between an output of a controlled object model that is preset as a model representing a response characteristic of the controlled object and an output of the controlled object, The model error suppression compensator is For the control object represented by the following equation, [0010] where the orders of A and B are n and m, y is the output of the control object, u is the input of the control object, ξ is the model error of the control object, z －１ is the delay operator, Δ is the difference operator, k ｍ is the dead time of the controlled plant. The evaluation criterion expressed by the following formula is minimized: [0025] where φ(k+k ｍ +1) is the generalized model error estimate, which is given by: [0030] Here, y ＊ (k+k ｍ +1) is the output of the controlled model, u ｄ (k) is a compensation input for suppressing model error, and λ is an adjustable parameter which is a weighting coefficient for the difference of the compensation input. A model error suppression compensator comprising:

4. a filter that outputs an adjustment value for a control input based on a difference between an output of a control object model and an output of the control object; a denominator polynomial expressing a transfer characteristic of the filter includes a term of the adjustable parameter; 4. The model error suppression compensator of claim 3.

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