JP7724557B2 - Model Error Suppression Compensator - Google Patents

Description

Article 30, paragraph 2 of the Patent Act applies. Publication 1: Posted on the website on August 24, 2022. Proceedings of the 2022 IEEJ Electronics, Information and Systems Division Conference. https://www.bookpark.ne.jp/cm/ieej/detail/IEEJ-BTC2022SS03002-PDF/ Publication 2: Posted on the website on August 31, 2022 at Hiroshima University Higashi-Hiroshima Campus and partially online. 2022 IEEJ Electronics, Information and Systems Division Conference. Publication 3: Posted on the website on February 1, 2023. IEEJ Study Group Research Materials. https://www.bookpark.ne.jp/cm/ieej/detail/IEEJ-BTC2022SS03002-PDF/ jp/cm/ieej/detail/IEEJ-20230205C01201-020-PDF/ Publication 4 February 5, 2023 Ehime University Faculty of Education Large Lecture Room and Online Institute of Electrical Engineers Research Society Control Research Society

The present invention relates to a model error suppression compensator.

In recent years, advanced control systems using numerous sensors and actuators have been developed in a wide range of fields, including industrial machinery and autonomous driving in automobiles. Model-Based Development (MBD) is used as an efficient development method for such complex control systems. In model-based development, control systems are designed for ideal models constructed from the physical phenomena of the controlled object, and the designed controller is then implemented to achieve the desired control performance. However, in reality, discrepancies (model errors) occur between the controlled object and the model, and it is thought that these model errors affect control performance.

Control system design techniques for suppressing model errors include disturbance observers (e.g., Patent Document 1) and model error compensators (MECs) (e.g., Non-Patent Document 1), which incorporate a model of the controlled object into the control system and utilize the difference between the control output and the model output. By performing such compensation and suppressing model errors, the response characteristics of the controlled object can be made to approach those of the model, making it possible to apply a controller designed for the model directly to the actual controlled object. Disturbance observers and model error suppression compensators are control systems specialized for suppressing disturbances and model errors, and have the advantage of being able to be used in conjunction with existing controllers such as PID control, which are widely used in industry.

However, a characteristic of disturbance observers is that they require an inverse model of the controlled object. If the controlled object is strictly proper, or if the controlled object is a non-minimum phase system with dead time or unstable zeros, an appropriate filter must be designed taking into account the performance of suppressing proper model errors and stability. Furthermore, depending on the characteristics of the controlled object, it may not be possible to obtain the desired control performance. In contrast, model error suppression compensators do 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.

Japanese Patent Application Laid-Open No. 2021-138335

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

However, model error suppression compensators are generally configured to adjust the control input (operating variable) 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. Therefore, depending on the characteristics of the controlled object, model errors, etc., there is a risk that the desired control characteristics may not be achieved, such as the control system becoming unstable. Therefore, it is difficult to design and adjust an appropriate model error suppression compensator taking into account the characteristics of the controlled object.

The present invention was made in consideration of the above circumstances, and aims to provide a model error suppression compensator that can be easily designed and adjusted.

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 the generalized model error estimate, which includes the difference between the output of the controlled object model at a predetermined future time step and the output of the controlled object, and an adjustment term represented by the product of the adjustment value of the control input and the adjustable parameter.

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

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 expressed by the following equation,
where the orders of A and B are n and m, y is the output of the controlled object, u is the input of the controlled object, ξ is the model error of the controlled object, z ⁻¹ is the delay operator, Δ is the difference operator, and _km is the dead time of the controlled object.
The evaluation criterion expressed by the following formula is minimized.
where φ(k+k _m +1) is the generalized model error estimate expressed by the following equation:

where y ^* (k+k _m +1) is the output of the controlled object model, u _d (k) is the compensation input for suppressing the model error, and λ is an adjustable parameter that is a weighting coefficient for the difference of the compensation input.

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

The model error suppression compensator of the present invention can be easily designed and easily modified according to the response characteristics of the controlled object.

FIG. 2 is a block diagram showing the configuration of a model error suppression compensator according to an embodiment of the present invention. FIG. 2 is a block diagram showing a compensation law of a model error suppression compensator according to an embodiment. 10A and 10B are graphs showing simulation results for a numerical example in which the dead time L=0 s, where (A) is a graph in the case where there is no model error suppression compensator, and (B) is a graph in the case where there is a model error suppression compensator. 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 for the case without a model error suppression compensator, (B) is a graph for the case with a model error suppression compensator and a weighting factor λ=0, and (C) is a graph for the case with a model error suppression compensator and a weighting factor λ=10.

The following describes a model error suppression compensator according to an embodiment of the present invention, with reference to the accompanying drawings.

1, the model error suppression compensator 1 according to this embodiment includes a controlled object model 11 and a filter 12, and adjusts a control input u input to the controlled object 20 based on the difference between an output y of the controlled object 20 and an output y ^* of the controlled object model 11. As a result, even if the actual controlled object 20 has a model error, it is possible to obtain control performance close to the desired control performance using a controller designed based on the controlled object model 11.

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

In the block diagram of Fig. 1, P(z ^-1 ) denotes the controlled object 20, and P _M (z ^-1 ) denotes the controlled object model 11, which is a pre-set nominal model that serves as a mathematical model representing the response characteristics of the controlled object 20. D(z ^-1 ) denotes a filter 12 as a compensation element that feeds back a compensation input u _d (k) so as to suppress a model error based on the output y(k) of the controlled object 20 and the output y ^* (k) of the controlled object model 11.

Furthermore, 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, the response characteristics of the controlled object 20 including the model error suppression compensator 1 can be made 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, desired control performance can be achieved.

In this embodiment, a model error suppression compensation law is derived by applying a design method used in generalized minimum variance control, a control system design method based on minimizing an evaluation criterion, to the design of the model error suppression compensator 1. Generalized minimum variance control is known to be effective even for non-minimum phase systems that have dead time or unstable zeros, and is thought to be applicable to a wide range of control targets as a model error suppression compensator. Below, we will specifically explain the model error suppression compensator 1 designed based on the generalized minimum variance control design method.

The controlled object 20 according to this embodiment is a CARIMA (Controlled Auto-Regressive Integrated Moving Average) model described by the following equation, where the orders of A(z ⁻¹ ) and B(z ⁻¹ ) are n and m, respectively.
Here, y(k) is the output of the controlled object 20, and u(k) is the input to the controlled object 20. ξ(k) represents the model error added to the controlled object 20, and is assumed to be Gaussian white noise with a mean of 0 and a variance of σ ^2. Furthermore, z ^-1 represents the delay operator, and z ^-1 y(k) = y(k-1). Δ represents the difference operator, and is defined as Δ: = 1 - z ^-1 . Furthermore, _km is the dead time of the controlled object 20. Note that it is assumed that only stochastic model errors occur in the controlled object 20, and the coefficients of the polynomials A(z ^-1 ) and B(z ^-1 ) and the dead time _km are known.

For the controlled object 20 of equation (1), a model error suppression and compensation law is derived based on minimizing the evaluation criterion of the following equation.

In the above equation, φ(k+k _m +1) is the generalized model error estimate, and is defined by the following equation:
Here, y ^* (k+ _km +1) is the model output, _ud (k) is the compensation input for suppressing the model error, and λ is a weighting coefficient for the difference of the compensation input, which is set arbitrarily by the designer.

As described above, the model error suppression compensator 1 according to this embodiment is set so as to minimize the variance of the generalized model error estimate φ(k+ _k +1) which includes the difference between the output of the controlled object model 11 and the output of the controlled object 20 at a predetermined future time step (k+k ₊ 1) and an adjustment term expressed as the product of the compensation input u _d (k), which is an adjustment value of the control input, and the weighting coefficient λ, which is an adjustable parameter.

Here, the Diophantine equation shown below is introduced to find E(z ^-1 ) and F(z ^-1 ). Note that the orders of E(z ^-1 ) and F(z ^{-1 ) are km and n,} respectively, so that E(z ^-1 ) and F(z ^-1 ) can be uniquely calculated from ΔA(z ^-1 ) and z -( _km +1).

From equations (1), (4), and (5), the _km +1 step ahead predicted value of the generalized model error estimate at time k is obtained as shown in the following equation.

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

Here, G(z ⁻¹ ) is defined by the following equation, where n _g :=m+k _m .

Next, the following equation is obtained from equations (7) and (8):

From equations (3) and (10), by setting φ(k+ _km +1|k)=0, the model error suppression and compensation rule that minimizes the evaluation criterion J shown in the following equation is derived.

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

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

Designers 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 in equation (14), which represents the characteristics of filter 12, includes a term for the weighting coefficient λ, which is an adjustable parameter. Therefore, by appropriately adjusting the weighting coefficient λ, designers can adjust the gain of filter 12 and thereby adjust the control performance.

(Numerical example)
An example of a computer simulation performed on a control system equipped with the model error suppression compensator 1 according to this 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].

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

Gaussian white noise with a mean of 0 and a variance of 0.01 is given as the model error ξ(k) to the above control object. The input given to the control object is a step input u _r (k)=10.

Figure 3 shows simulation results for a dead time L = 0 s when there is no model error suppression compensator 1 (Figure 3(A)) and when there is one (Figure 3(B)). The weighting coefficient λ for the difference in 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 (Figure 3(A)), it can be seen that the output of the controlled object 20 fluctuates irregularly due to model error and deviates significantly from the output of the controlled object model 11. In contrast, when the model error suppression compensator 1 is included (Figure 3(B)), the compensation input obtained from the difference in output between the controlled object 20 and the controlled object model 11 is fed back to suppress the model error, enabling the output of the controlled object 20 to track and match the output of the controlled object model 11.

Figure 4 shows the simulation results when the dead time of the controlled object 20 in the actual 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 in the simulation of Figure 3 described above. Figure 4(A) shows the simulation results without the model error suppression compensator 1, Figure 4(B) shows the simulation results with the model error suppression compensator 1 and a weighting coefficient λ = 0, and Figure 4(C) shows the simulation results with the model error suppression compensator 1 and a weighting coefficient λ = 10. When the weighting coefficient λ = 0, the response of the control system diverges, but when the weighting coefficient λ = 10, the control system is stabilized and tracking of the controlled object model 11 is achieved.

These results show that the model error suppression compensator 1 according to this embodiment works effectively for controlled objects with dead time. Furthermore, because the control characteristics can be adjusted by adjusting only the adjustable parameter, the weighting coefficient λ, it is clear that the characteristics of the model error suppression compensator 1 can be easily modified and high control performance can be obtained.

As explained in detail above, the model error suppression compensator according to this embodiment derives the model error suppression compensation law by applying the method for deriving the control law of 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, a model error suppression compensator can be easily designed based on a clear design method for a wide range of controlled objects, including non-minimum phase systems with dead time and unstable zeros.

Furthermore, as shown in equation (14), the denominator polynomial representing the transfer characteristics of filter 12 includes a weighting coefficient λ. Therefore, by appropriately adjusting weighting coefficient λ, the designer can adjust the gain of filter 12 and thereby adjust the control performance. This makes it easy to prevent filter 12 from becoming excessively high in gain and prevent the control system from becoming unstable. Furthermore, because the control characteristics can be adjusted using weighting coefficient λ, even if the response characteristics of the controlled object 20 fluctuate over time, such as an increase in dead time or a decrease in gain, causing the response characteristics of the controlled object 20 to deviate from those of the controlled object model 11, it is possible to easily make the response characteristics of the controlled object 20 track those of the controlled object model 11.

The present invention is suitable for model error suppression compensators for controlled objects that have model errors. In particular, it is suitable for model error suppression compensators for controlled objects that include non-minimum phase systems with dead time or unstable zeros.

1. Model error suppression compensator, 11. Controlled object model, 12. Filter, 20. Controlled object

Claims (4)

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 object model and an output of the controlled object at a predetermined future time step, and an adjustment term represented by the product of an adjustment value of the control input and an adjustable parameter;
A model error suppression compensator comprising: a filter that outputs an adjustment value for the control input based on a difference between an output of the controlled object model and an output of the controlled object;
a denominator polynomial representing the transfer characteristic of the filter includes a term for the adjustable parameter;
2. The model error suppression compensator of claim 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,
The model error suppression compensator comprises:
For the control object expressed by the following equation,
where the orders of A and B are n and m, y is the output of the controlled object, u is the input of the controlled object, ξ is the model error of the controlled object, z ⁻¹ is the delay operator, Δ is the difference operator, and _km is the dead time of the controlled object.
Minimize the evaluation criteria expressed by the following formula:
where φ(k+k _m +1) is the generalized model error estimate expressed by the following equation:

where y ^* (k+k _m +1) is the output of the controlled object model, u _d (k) is the compensation input for suppressing the model error, and λ is an adjustable parameter that is a weighting coefficient for the difference of the compensation input.
A model error suppression compensator comprising: a filter that outputs an adjustment value for the control input based on a difference between an output of the controlled object model and an output of the controlled object;
a denominator polynomial representing the transfer characteristic of the filter includes a term for the adjustable parameter;
4. The model error suppression compensator of claim 3.