JPH0677211B2 - Plant modeling equipment - Google Patents

Description

Description: TECHNICAL FIELD The present invention is an apparatus for estimating a transfer function necessary for designing a control system from a response waveform of a control target whose dynamic characteristics are unknown, and is a device for designing a plant control system. , A plant modeling device suitable for testing and monitoring.

[Technical background of the invention and its problems]

A model representing the dynamic characteristics of the plant, such as a transfer function, is required for designing the control system of the plant, numerical testing, monitoring of the control system, and the like. Conventionally, a number of methods have been proposed for obtaining the transfer function of a plant whose dynamic characteristics are unknown from the data related to the response waveform. For example, the parameters of the transfer function are estimated from various constants related to the shape of the step response waveform, or the response It was possible to estimate the pulse transfer function from the sampled values of the waveform. However, each method is an estimation method based on the assumption of the transfer function order in advance, and the optimum order has to be determined by trial and error. Also, it is convenient to handle the data related to the response waveform as sample values when using a digital computer, but the corresponding transfer function should be obtained in the form of a continuous system, considering the design of the control system. Is preferred. However, there is no method to estimate the transfer function of a continuous system directly from the sampled values of the response waveform.

[Object of the Invention]

The present invention, in order to solve the above problems, a function of estimating an optimum model order at a time from a sample value of a response waveform of a plant to be controlled, and a function of directly estimating a continuous-time transfer function. It is an object of the present invention to provide a plant modelling device having excellent estimation accuracy by including the above.

[Outline of Invention]

According to the present invention, as a first step, data is corrected by removing noise or a dead time component that adversely affects the estimation from the sample value of the response waveform of the plant to be controlled, and then as a second step, the plant is adjusted. The impulse response sequence of is calculated, and the optimal order is determined from the size of the singular value of the Hankel matrix generated by it, and at the same time, the state-space model in the discrete time domain is realized. By converting to a continuous-time domain state-space model in which the responses match at points and estimating the transfer function corresponding to it, we obtain a model with the continuous-time transfer function of the optimal order, and also the response waveform of that model. Is a plant modeling apparatus capable of determining the model goodness of fit by comparing with the original data.

〔The invention's effect〕

 The effects of the present invention are as follows.

(1) Since only a finite number of sample values of the response waveform are used as the data to be the basis of the estimation, it is easy to collect the data in the actual plant and suitable for the processing by the digital computer.

(2) Since the order of the model is determined while simultaneously observing the sizes of the individual modes included in the dynamic characteristics of the plant, it is possible to save the trouble of searching for the optimum order by trial and error.

(3) Since the transfer function in the continuous time domain can be obtained, it is convenient for designing a continuous time control system.

(4) If the data that is the basis of the estimation includes noise or a time delay component, it is difficult to approximate it with a finite-dimensional model, which may adversely affect the estimation result. By performing data correction in advance, it is possible to eliminate such an influence and improve the estimation accuracy.

(5) The accuracy of the model can be evaluated and confirmed by determining the degree of conformity of the obtained model to the original data.

Example of Invention

Embodiments of the present invention will be described in detail. Fig. 1 shows the plant
The structure of a modeling apparatus is shown. This is to obtain a transfer function G (s) as a model from the sample data of the response waveform. The response waveform data acquisition unit 1, the data correction unit
2, impulse response unit 3, discrete-time minimum realization model estimation unit 4,
Order determination unit 5, graphic terminal 6, console 7, model conversion unit 8, transfer function calculation unit 9, transfer function display recording unit 10, and
It comprises a model evaluation unit 11. The operator performs all operations of this apparatus through the graphic terminal 6 and the console 7.

In the present embodiment, as shown in FIG. 2, estimation is performed using a step response waveform 12 as shown in FIG. 3 when a stepped input signal is applied to the operating end as a response waveform. To do. Further, here, the target is a plant with one input and one output, but it is also applicable to a plant with multiple inputs and multiple outputs.

First, as shown in FIG. 3 from the step response waveform 12, a finite number of sample value data {x ₀ , x ₁ , ..., X _N } are measured at every sampling period τ, and the response waveform data acquisition unit 1
After being taken into the modeling system, the data correction unit 2 performs the following processing.

(1) As shown in FIG. 4, when it is determined that the dead time obviously exists in the initial stage of the response waveform 13, the dead time is determined.
The data of the portion 14 is deleted to obtain the step response waveform 14 as shown in FIG.

(2) As shown in FIG. 6, when the response waveform 16 is disturbed by noise such as observation noise, the entire data is smoothed to obtain the step response waveform 17 as shown in FIG.

(3) The remaining part is deleted by specifying the data length (the number of sample values) used for estimation.

These data corrections are performed according to the above (1) and (2).
The processing of can improve the accuracy of estimation,
Also, by the processing of (3) above, it is possible to select modeling of only the excessive portion of the response waveform, modeling including the steady characteristics, and the like.

Next, the impulse response sequence estimation unit 3 of FIG. 1 obtains the impulse response sequence {h ₀ , h ₁ , ..., H _n } of the plant according to the following equation.

In discrete time minimal realization model estimator 4 implements a discrete-time state-space model as follows based on the impulse response example {h _i}.

Where x _k is the (n-dimensional) plant state vector, u
_k and y _k are scalar quantities representing the input and output of the plant, A is an n × n matrix, B and C are n-dimensional vectors, and D is a scalar. The order of x _k (that is, the order of the model (2) expression) n
Can be checked by the rank of the following Hankel matrix.

In order to check the rank, the order determination unit 6 has the following two functions.

(1) The matrix H ₁ is decomposed into singular values as shown in Expression (4), and the singular values σ _i are displayed on the graphic terminal 6 as a curve 18 on a logarithmic scale as shown in FIG. Urge.

(2) Similarly, the singular value is obtained, and the order considered to be the most appropriate is determined by comparing the rate of change and the magnitude of the observation noise included in the original data. As an evaluation for judgment, an evaluation function of the following form is introduced here, and the order n that minimizes it is obtained.

J (n) =-f ([sigma] _{n- [} sigma] _{n + 1} ) + g ([sigma] _{n- [} sigma]
_noise ) + h (n) (5) Here, σ _n means a singular value represented by the equation (4), and f, g, h are the following functions.

(I) f (σ _n −σ _{n + 1} ): rate of change of singular value (σ _n −
Depending on the size of the sigma _{n + 1),} a function whose value becomes larger _{(ii) g (σ n -σ} noise): the magnitude relation of magnitude sigma _noise of the observation noise included in the singular value sigma _n and data, (Iii) h (n): a function that monotonically increases with an increase in the order n, where n is the order of the model selected as described above.
The discrete-time model (2) is calculated by the procedure shown in the following expressions (6) to (10).

However, And

Is a submatrix in the singular value decomposition expression of H _{1 in} the equation (4), and each has a size of i × n, n × (N−i).

Next, the model conversion unit 8 obtains a continuous system state space model (11) such that the response matches the model response of the equation (2) at each sample point.

(However, the dimension of each variable in the equation (11) corresponds to the equation (2).) In this embodiment, the following method is used.

First, the matrix A of the equation (2) is diagonalized by an appropriate conversion matrix T.

Next, A _c , B _c , C _c , and D _c are obtained by the following procedure.

A _c = ding {η ₁ , η ₂ , ..., η _n } (15) where Then, the transfer function calculation unit 9 obtains the transfer function, that is, the estimated model G (s) of the plant from the continuous time model (11) obtained in the previous stage based on the equation (19).

(In means a unit matrix of size n × n.) The result is displayed on the terminal, written in the disk memory, etc. by the transfer function display / recording unit 10.

Finally, in the model evaluation unit 11, the obtained transfer function (19)
Based on the equation, the response waveform is calculated and displayed together with the actual data on the graphic display. Also, the degree of conformity to the actual data that is the basis of the estimation of the calculated response waveform is (20)
Calculated from the formula and displayed as an evaluation of the estimated model to prompt the operator to make a decision.

Here, x _i is real data, x _i is a value at each sample point of the response waveform calculated from the estimation model, N is the number of data, and α _i (i = 1 to N) is a weighting coefficient.

The smaller the evaluation value J _Model is, the better the fitness of the estimation model is.

FIG. 9 shows a step response sample value {x ₀ , x of the actual data 19
₂ , ... x _N } and the transfer function estimated based on it From that, the calculated response waveform (step response) 20 is shown. It can be seen that the step response waveform (solid line) based on the estimated transfer function almost coincides with the actual data (point) that is the basis of the estimation.

[Brief description of drawings]

FIG. 1 is a schematic configuration diagram of a plant modeling apparatus of the present invention, FIG. 2 is a circuit diagram showing a method of acquiring a sample value for each sampling period τ from a step response of a plant, and FIG. 3 is a step response waveform. FIG. 4 is an explanatory waveform diagram showing a procedure for deleting data for waste time from the step response waveform, FIG. 5 is a curve diagram of the deleted step response waveform, and FIG. 6 shows noise. FIG. 7 is a curve diagram showing the disturbed data, FIG. 7 is a curve diagram showing the step response waveform obtained by smoothing the data by fihtering, and FIG. 8 is displayed as an index for determining the order of the model ( A curve diagram showing the state of the singular value of the equation (5), FIG. 9 shows the transfer function estimated from the actual data according to the present method,
It is the waveform curve figure which displayed the response waveform with data. 1 ... Response waveform data acquisition unit 2 ... Data correction unit 3 ... Impulse response sequence calculation unit 4 ... Discrete time model estimation unit 5 ... Order determination unit 6 ... Graphic terminal 7 ... Console 8 ... Model conversion Part 9 …… Transfer function calculation unit 10 …… Transfer function display and recording unit 11 …… Model evaluation unit

 ─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP-A-57-23117 (JP, A) JP-A-56-60914 (JP, A) JP-A-59-69813 (JP, A) JP-A-58- 208812 (JP, A) JP 58-172714 (JP, A) JP 57-146314 (JP, A) JP 51-94075 (JP, A)

Claims (1)

[Claims] 1. A data acquisition means for taking in a finite number of sample value data of a response waveform to a known operation signal of a plant to be controlled, a data correction means for performing partial deletion of data, interpolation and filtering, and the data correction means. A means for determining the order of the transfer function from the information of the data, a discrete time model estimating means for estimating a state space model in the discrete time domain corresponding to the order, and an estimation model estimated by the discrete time model estimating means Model conversion means for converting into a state space model in the continuous time domain such that the responses match at each sample point, and transfer function calculation for obtaining the transfer function in the continuous time domain from the continuous time state space model converted by this model conversion means Means and a transfer function for outputting the transfer function obtained by the transfer function calculating means to a display device and recording the transfer function in an external storage device. Plant modeling system that includes a Display recording means.