JP3342948B2 - H infinity norm measuring device and control system stability monitoring device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an H-infinity norm measuring device for measuring H-infinity norm which is a characteristic of a control system of each industrial plant, and a control system stability monitoring device for monitoring the stability of the control system. About.

[0002]

2. Description of the Related Art Various types of control devices (controllers) are used in various plants in the industrial world, such as steel, petrochemical, and power plants, in order to operate the plants optimally. To design a stable controller, it is necessary to optimally determine the parameters (control constants) of the controller according to the dynamic characteristics of the control target. However, even if the control is performed using the optimal control constant once determined, the performance of the plant fluctuates during operation, and the control performance is reduced,
May lose stability. Since the influence of such a case appears on the output of the plant, the operator constantly monitors the output of the plant, and when the characteristics of the plant change as described above, the operator has readjusted the control constants.

[0003]

In such a plant where the characteristic changes drastically, the operator must constantly monitor the state of the control system, which is a factor that increases the load on the operator.

Further, in order to automatically monitor the stability of the controlled object with respect to dynamic characteristic fluctuation, ie, robust stability, in order to reduce the load on the operator, it is necessary to estimate the degree of the dynamic characteristic fluctuation of the controlled object online. For this purpose, it is necessary to perform a large amount of arithmetic processing using input / output response data to be controlled. Performing a large amount of arithmetic processing in a conventional controller in real time has a problem in that the load on the processing device increases.

The present invention has been made in view of the above circumstances, and a first object of the present invention is to provide an H infinity norm measuring device capable of measuring in real time the H infinity norm which is a dynamic characteristic of a controlled object. It is to provide.

A second object of the present invention is to provide a control system stability monitoring device capable of automatically monitoring the robust stability of a control target without imposing a load on an operator and a processing device of a controller body. It is.

[0007]

A first aspect of the H-infinity norm measuring apparatus according to the first invention is to output n (≧ 1) output signals based on m (≧ 1) input signals. Means for identifying the average value and the range of variation of the parameters of the time series model of the system using the set membership identification method based on the time series data of the input signal and the output signal, and the identification means Estimating means for estimating the frequency response of the time-series model based on the average value and the fluctuation range of the identified time-series model parameters, and forming a frequency response matrix from the frequency responses estimated by the estimating means, Computing means for computing the maximum value of the maximum singular value of the frequency response matrix, wherein the maximum value computed by the computing means is defined as H infinity norm. That.

A second aspect of the H-infinity norm measuring apparatus according to the first invention is directed to a system for outputting n (≧ 2) output signals based on m (≧ 2) input signals. Means for configuring a matrix U for an input signal sequence and a matrix Y for an output signal sequence based on time-series data of an input signal and time-series data of an output signal;
It sought product matrix U ^-1 Y of the inverse matrix and the matrix Y of characterized by a maximum singular value to the H-infinity norm and a calculation means for calculating a maximum singular value of the product matrix.

A third aspect of the H-infinity norm measuring apparatus according to the first invention is a system for outputting one output signal based on one input signal. Fourier transform means for performing a discrete-time Fourier transform on the time-series data of the output signal to obtain a Fourier transform of the input signal and a Fourier transform of the output signal at each frequency, and, for all frequencies, an output signal for the Fourier transform of the input signal. Calculating means for calculating the maximum value of the Fourier transform ratio, wherein the maximum value is H infinity norm.

A first aspect of the control system stability monitoring apparatus according to the second invention is a control object having m manipulated variables and p controlled variables, a set value of the controlled variable, and feedback control. In a feedback control system including a controller that outputs an operation amount based on the amount, an observation unit that sequentially observes the operation amount and the control amount, and a control amount based on the observed value of the operation amount based on a linear model of the control target. A model response calculating means for sequentially calculating a predicted value, a model error response calculating means for sequentially calculating a signal sequence of a model error which is a difference between a predicted value of the control amount and an observed value, and a transfer function of a linear model to be controlled as P , when the transfer function of the controller C, a unit matrix I, T = (I + CP ) has a transfer function T represented by ^-1 C, the transfer function of the signal sequence of the model error as the input signal A filter means for calculating an output signal when the input signal is input to the input device; an H infinity norm measuring device for measuring an H infinity norm for a system in which an observed value of the manipulated variable is an input signal and an output of the filter means is an output signal; The feedback control system is characterized in that the feedback control system includes robustness stable when the H-infinity norm is smaller than 1, and determines that it is not robust stable when the H-infinity norm is 1 or more.

According to a second aspect of the control system stability monitoring apparatus according to the second aspect of the present invention, in the first aspect of the second aspect of the present invention, the operation amount of the controlled object and the p. e. Determining means for determining the reproducibility of the H-infinity norm signal and the reproducibility of the H-infinity norm signal, and determining the reliability of the stability determination result from the determination result. Is lower than the threshold value, or when an external command is received, p. e. Test signal generating means for generating a test signal that satisfies the characteristics and superimposing the test signal on the set value of the manipulated variable of the controlled object or the controlled variable.

[0012]

According to the H infinity norm measuring apparatus according to the first aspect of the present invention, the H infinity norm can be measured in real time from input / output data of the target system. Since the measurement of the H infinity norm can be performed independently of the controller to be controlled, no load is applied to the processing device of the controller body.

According to the stability monitoring apparatus according to the second aspect of the present invention, since the transfer function T of the filter means is T = (I + CP) ^-1 C, the operation amount of the controlled object is observed. If the H-infinity norm for the transfer function (system) from the value to the signal sequence of the output of the filter means is measured, the measured H-infinity norm is an index of the stability of the feedback control system. Thus, the stability of the feedback control system can be automatically and sequentially monitored by successively measuring the H infinity norm, and no load is applied to the operator. Further, since the above-described measurement is performed independently of the processing device of the controller main body, no load is applied to the processing device of the controller main body.

[0014]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the H infinity norm measuring apparatus according to the first invention will be described with reference to FIGS. H infinity norm measuring apparatus 10 of this embodiment, m (≧ 1), as shown in FIG. 2 pieces of manipulated variables u _1, ... p (≧ based on u _m
1) number of controlled variables y _1, and outputs a ... y _p, the transfer function G
H infinity norm of the control object system 70 is | G | _∞
And the operation amount u _1, ... u _m and the controlled variable y _1, and requests based on ... y _p. The H infinity norm measuring apparatus 10 of this embodiment has analog data input terminals 11 ₁ ,... 11 _m and 12 ₁ ,.
_p , A / D converters 13a and 13b, clock timer 14, digital data input terminal 15, buffer memories 16a and 16b, parameter setting terminal 17, data bus 18, program area 19a and data area 19b. , A CPU 20, and D
/ A converter 21, digital data output terminal 22,
And an analog data output terminal 23.

Next, the configuration and operation of the H infinity norm measuring apparatus 10 of this embodiment will be described. The manipulated variable u _i input via the analog data input terminal 11 _i (i = 1,... M) is sent to the A / D converter 13a, and is input to the analog data input terminal 12 _h (h = 1,. controlled variable y _h inputted via is sent to the a / D converter 13b. Then, these manipulated variables u _1, ... u _m and the control amount y _1, ...
y _p is based on the output signal of the clock timer 14 A / D
The data is digitized at regular intervals in the converters 13a and 13b and sent to the buffer memories 16a and 16b, respectively. Note that these manipulated variables u _1, ... u _m and the control amount y _1, ... y _p can also be entered directly into the buffer memory 16a and 16b via the digital input terminal 15 if the digitized. Buffer memory 1
Inside 6a and 16b, the latest signal data is input every data observation cycle, and the data input N (≧ 2) cycles before is deleted. For example, as shown in FIG. 4, the buffer memory 16a stores m data u
₁ (k-N), ... to erase the memory of the stored address of u _m (k-N), and inputs the latest m data u ₁ to the address _{(k), ... u m (} k) . In the next cycle, the address of interest is moved to the next address, and the same processing is continued. As a result, the buffer memory 16a always stores Nm data from the present to N-1 steps before. Similarly, N is stored in the buffer memory 16b.
-P data will be stored. Figure 1 again
Returning to the description, the buffer memories 16a, 16b,
The memory 19 and the CPU 20 are connected to the data bus 18. The CPU 20 extracts data from the buffer memories 16a and 16b according to the program written in the program area 19a of the memory 19, and
The calculation of the H infinity norm is performed on the data area 19b of No. 9. The result is sequentially output from the analog data output terminal 23 via the digital data output terminal 22 or the D / A converter 21. Further, parameters such as calculation conditions can be set and changed via the parameter setting terminal 17. In addition, H infinity norm | G | _∞ Figure 3
Is defined as the upper limit value of the gain frequency characteristic of the transfer function G of the controlled system.

[0016] Next, H infinity norm | G | the first operation of _∞
A specific example will be described. Now, the system of interest m input signal (the operation amount) u _1, ... p number of output signals based on the u _m (controlled variable) y _1, ... be one that outputs y _p, the pulse Transfer function (discrete time transfer function) matrix G
But

[0017]

(Equation 1) However

[0018]

(Equation 2) It is assumed that The current time is set to k + N. At this time

[0019]

(Equation 3) The input signal sequence u _h (k + i), (h = 1,
.. M, i = 0,... N) and the output signal sequence y _h (k +
i), (h = 1, ... p, i = 0, ... N from the observation data of the transfer function G) H infinity norm | G | _∞ is calculated by the following equation (4).

| G | _∞ = σ _max (U ⁻¹ Y) (4) where σ _max (A) is the maximum singular value of the matrix A (the product of the conjugate transpose matrix A ^* of the matrix A and the matrix A The square root of the largest eigenvalue of the matrix A ^* A), and the number of data N is N for a certain integer n.
+ 1 = m (n + 1), and the matrix U for the input signal sequence and the matrix Y for the output signal sequence are

[0021]

(Equation 4) It is expressed as That is, the matrix U is (N + 1) × (m (n
+1)) matrix, and the matrix Y is (N + 1) × (p (n +
1)) It is a matrix.

The reason why the H infinity norm (approximate value) is calculated by the above equation (4) will be described below.

First, at time k + N, input / output data u ₁ (k)... U _m (k),... U ₁ (k + N),.
_{m (k + N) y 1} (k) ... y p (k), ... y 1 (k + N), ... y
Consider applying the following nth-order impulse response model (also referred to as a moving average model) to _p (k + N).

[0024]

(Equation 5) Here, g _ih (z ⁻¹ ) = g _ih1 z ⁻¹ + g _ih2 z ⁻² +... + G _ihn z ⁻ⁿ (8).

At this time, the following equation (9) is established between the observation data and the model parameters according to the definition of the impulse response model.

Y = UG (9) where G is

[0027]

(Equation 6) , G ^T (i) (i = 1,... N) is a transpose of the matrix G (i), and the matrix G (i) is

[0028]

(Equation 7) It is. Thereby, G = U ^-1 Y (12) is established. When the pulse transfer function (1) and (2) is the impulse response of up to n-order systems of formula (7) and (8) represented by the formula, its H infinity norm | G | is _∞ (10 It is known that it must be equal to or greater than the maximum singular value of the matrix G in equation (1). Therefore, if the order n of the impulse response model is sufficiently large, σ _max (G) = σ _max (U ⁻¹ Y) becomes H
Infinity norm | G | would give a good approximation of _∞.

The number of input signals m = 1 and the number of output signals p =
The calculation method of the H infinity norm of the controlled system that is 1 is
“Time domain identi” by Tong Zhou and Hideki Kimura
fication for robust control ”, System & Control L
etlers 20 (1993) pp. 167-178. That is, the time series data u (i) (i = 0,...) Of the input signal u
N) and time series data y (i) (i = 0,...) Of the output signal y.
N), the matrices U and Y are converted into the following equations (13) and (14).

[0030]

(Equation 8) _│G│∞ = σ _max (U ^-1 Y)... (15) based on these matrices.

Next, a second specific example of the calculation of the H infinity norm will be described. First, an order n (<N) of time series data between input and output data is set. Here, n indicates the number of time-series data of the same type extracted from the buffer memory. Then, a finite-dimensional time-series model G (z ^-1 ) = G (1) z ^-1 + G (2) z ^-2 + ... + G (n) z ^-n (16) and its frequency response are estimated. Where G (k),
(K = 1,..., N) is a p × m matrix having elements g _ij (k). The above estimation is performed in the following procedure. Step 1: From the buffer memory, input data u _h , (h
= 1,... M) and output data y _i , (i = 1,.
N data u _h (k) and y _i (k), (k
= 0,... N-1). Procedure 2: The following steps 1 to 6 are repeated for i = 1,.

[0032] a) Step 1: i = 1, ... to P, the data _{y i (1), ... y} i ( amplitude A _i of the noise is assumed to be included in N) (1), ... A i ( Set n).

B) Step 2: First, k = nθ (n) = [g _i1 (1)... G _i1 (n)... G _im (1).
_im (n)] ^T = [0 ...... O] ^{T φ} (n) = _{[u 1 (n-1) ...} u 1 (0) ... u m (n-1) ... u m (0) ] ^T P (N) = γI is set. Here, I is a unit matrix having a size of nm × nm × nm, and γ is a large positive value.

[0034] c) Step 3: a k = k + 1, φ ( k) = _{[u 1 (k-1) ...} u 1 (k-n) ... u m (k-1) ... u m (k-n) ] ^{T g (k) = φ (} k) T P (k-1) φ (k) ε (k) = y i (k) -φ (k) T θ (k-1) c 0 = (n- 1) A _i ² (k) g ² (k) c ₁ = ｛(2n−1) A _i ² (k) −g (k) + ε
² (k)｝ g (k) c ₂ = n (A _i ² (k) −ε ² (k)) − g (k) is calculated. Then, if c ₂ <0, a positive solution of the quadratic equation c ₀ ρ ² (k) + c ₁ ρ (k) + c ₂ = 0, that is,

[0035]

(Equation 9) Is determined, and if c ₂ ≧ 0, ρ (k) = 0.

D) Step 4: The estimated parameter vector θ is updated by the following update equation.

[0037]

(Equation 10) e) Step 5: Repeat steps 3 and 4 until k equals N.

When the repetition for the variable k is completed,
Based on the information that the observation signal contains an unknown disturbance of the amplitude A _i (k), the average value θ (N) and the variation width of the parameter θ of the time series model represented by the equation (16) of the target system are observed. It can be determined from the data. This parameter θ (θ-θ (N) ) T P -1 (N) (θ-θ (N)) a set of ellipsoid satisfying ≦ 1, that is, the center is the average value theta (N)
And is represented as a set of ellipsoids whose diameter is the reciprocal of the square root of the eigenvalue of the matrix P ^-1 (N). As a result, there are advantages in that the model parameters can be estimated including the fluctuation range of the target system, and that an infinite-dimensional system can be modeled including an error caused by approximation with a finite-dimensional model such as Expression (16).

Obtaining the average value and the fluctuation range of the parameter θ as described above is called a set membership identification method and is known. For example, E.Fogel and YFHuang: On
theValue of Information in System Identification
: Bounded Noise Case, Automatica, Vol.18, pp229 〜23
8 (1982).

F) Step 6: Estimate the frequency response of the model obtained as described above. Assuming that j is an imaginary unit, the frequency response G (jω) of the target system at a certain frequency ω (0 ≦ ω ≦ π) is as follows: Ψ (jω) = [exp (−jω) exp (−2jω). mjω)] ^T , the average value in the frequency domain is G _ihN (jω) = Ψ ^T (jω) θ _h (N). Here, θ _h (N) is (h−1) · m of θ (N).
This is a vector obtained by extracting and reconstructing m elements from the + 1st to the hmth. Also, the matrix P (N) has (h−1) · m + 1-th to hm-th and (h−1) · m +
_Assuming that an m × m matrix obtained by extracting and reconstructing the 1st to _hmth columns is P _ih (N), and the conversion of this matrix P _ih (N) into the frequency domain is Φ _ih (jω), Φ _ih (jω) is

[0041]

[Equation 11] It is expressed as Where Re (A) and Im (A) are the matrix A
Shows the matrix of the real part and the matrix of the imaginary part. That is, A = R
e (A) + j · (Im (A)).

Now, the frequency response G (jω) of the target system
_Let the component of the i-th row and the h-th column be G _ih (jω), and let X _ih (jω) = G _ihn (jω) −G _ih (jω) denote a variation range from the average value G _ihN (jω). , The variation width X _ih (jω) of the i-th row and h-th column component G _ih (jω) of the frequency response G (jω) is given by the following inequality:

[0043]

(Equation 12) Meet.

Ω = 0, 2π / N,... 2π
(N-1) / N is obtained. Step 3: Frequency response G obtained as described above
_{From ih} (jω), i = 1,... p, h = 1,... m, a frequency response matrix G (jω) = {G _ih (jω)} (ω = 0, 2π / N,. / N). And G (jω) among all frequencies ω
Let the maximum value of the maximum singular value of be H infinity norm.

Next, a third specific example of the calculation of the H infinity norm will be described. In the third specific example, the H infinity norm of a system that outputs one output signal y based on one input signal u is calculated. Hereinafter, the calculation procedure will be described.

Procedure 1: The past n data u (i), y (i), (i) from the buffer memories 16a, 16b, respectively.
= 0,... N-1).

Step 2: A discrete time Fourier transform is applied to each data series.

[0048]

(Equation 13) Step 3: Use the following formula to calculate the maximum value of the gain.

[0049]

[Equation 14] , And this maximum value is defined as H infinity norm.

As described above, according to the H-infinity norm measuring apparatus of this embodiment, input / output response data u _i (i = 1,... M), y _h (h = 1,. ) Is stored in the buffer memories 16a and 16b, and the H infinity norm can be measured from a finite number of data. Since the measurement of the H infinity norm is performed using a dedicated device, the H infinity norm to be controlled can be measured in real time without applying a load to the processing device of the controller body.

FIG. 5 shows the configuration of a first embodiment of the control system stability monitoring apparatus 1 according to the second invention. The stability monitoring device 1 of this embodiment includes a model response calculating means 4, a model error response calculating means 5, a filter 6, a H infinity norm measuring device 10, and a judging means 30. The stability monitoring device 1 includes a control parameter adjusting unit 50.
Parameters and set values r ₁ ,.
Output y ₁ of _p and the plant 70, ... the operation amount u ₁ controller 60 to the plant 70 based on the y _p, ... u _m
And the control quantities y ₁ ,.
_It is used in a feedback control system that controls _p to be the above set values r ₁ ,... rp.

The configuration of the stability monitoring apparatus of this embodiment will be described below together with the operation. Note the operation amount u _1, ... u _m and the control amount y _1, ... y _p is the time-series data thereof per an observation period is assumed to be input to the stability monitoring device 1 of the present embodiment. A preset transfer function model P of the plant 70 and an operation amount u which is an output of the controller 60
₁ (k),... U _m (k)

[0053]

(Equation 15) Controlled variable y ₁ (k) using, ... model response eta ₁ is the predicted value of _{y p (k) (k)} , ... η p (k) is calculated.
Here, P _ih (i = 1,... P, h = 1,... M) is represented by a discrete-time transfer function.

Next, the model response _{η 1 (k), ... η} p
(K) and the actual control quantity _{y 1 (k), ... y} p (k) model error response epsilon ₁ based on (k), ... epsilon _p (k) is epsilon _i (k) = y _i (k) −η _i (k) (i = 1,
.. P) are sequentially calculated in the model error response calculation means 5.

Next, in the filter 6, based on a filter transfer function F = (I + CP) ^-1 C composed of a transfer function model P to be controlled and a transfer function C of the controller 60 at that time, a model error response ε ₁ ( k),... ε _p (k)

[0056]

(Equation 16) Filter operation output e ₁ (k) using, ... Request e _m (k). Here, F _ih (i = 1,..., M = 1,..., P) are each element of the filter transfer function F and are represented by a discrete-time transfer function.

[0057] then observed the operation amount _{u 1 (k), ... u} m
(K) and the filter operation output e ₁ (k), ... based on e _m (k), the operation amount u ₁ (k), ... and input signal u _m (k), the filter operation output e ₁ (k) , ... a system for the output signal e _m (k), i.e. the plant 70, model response operating means 4, a system of model error response operating means 5 and the filter 6 and G, the H infinity norm | a _∞ | G Determined by the H infinity norm measuring device 10. This H infinity norm | G | _} can be obtained by the procedure described in the first invention.

Then, the measured H infinity norm | G
| _∞ are successively sent to the judging means 30, and this judging means 3
At 0, at each time | G | _∞ <1, then the present control system is determined to be robust stability, | G | _∞ ≧ 1 if the current control system is determined not to be robust stability,
This determination result is sequentially sent to the operator terminal 40 and displayed.

G | | [0059] Next H-infinity norm was measured as described above _∞ will be described determines why the control system smaller than 1 is robust stability. Now, FIG.
A system 81 having a transfer function Δ and a transfer function T shown in FIG.
Consider a closed loop system consisting of a system 82 with
Sufficient condition for the closed-loop system is stable | TΔ | given by _∞ <1 ...... (17). This means that when the signal goes around the closed loop system shown in FIG. 6, the gain becomes 1 or less, so that the energy of the signal is surely attenuated. As a result, the above-described closed loop system is bounded by any disturbance. Means that the signal of the closed loop system is bounded and stable even if it is disturbed by. Based on this, the stability of the feedback control system shown in FIG. 7 will be considered. In FIG. 7, C
Denotes a transfer function of the controller 83, P denotes a transfer function of the model 84 to be controlled, and Δ denotes a transfer function of the system 81 for calculating an error between the actual control target and the model 84. In the control system shown in FIG. 7, the fact that stability is maintained even when a model error exists is called robust stability. When the feedback control system shown in FIG. 7 is converted into a closed loop system shown in FIG. 6 as viewed from the system 81, T = (I + CP) ^-1 C (18) Here, I indicates a unit matrix.

Substituting this into the sufficient condition for stability described above results in | (I + CP) ⁻¹ CΔ | _∞ <1 (19), and this equation (19) is a robust value of the feedback control system shown in FIG. This is a condition for stability.

[0061] Returning to FIG. 5 again, now, the plant 70, model response operating means 4 and consisting of model errors response operating means 5 system, i.e., the operation amount _{u 1 (k), ... u} m
(K) as an input signal, the model error response ε ₁ (k),.
Assuming that the transfer function of a system that uses ε _p (k) as an output signal is Δ, the H infinity norm | G | of the system G including the plant 70, the model response operation unit 4, the model error response operation unit 5, and the filter 6 _∞ is expressed as | G | _∞ = | (I + CP) ⁻¹ CΔ | _∞ (20) Therefore, the H infinity norm measuring device 1
The H infinity norm | G | _{求 め} is obtained by 0, and (19),
When | G | _} is smaller than 1 according to the equation (20), it can be determined that the control system that performs the feedback control of the plant 70 by the controller 60 is robustly stable.

As described above, in the stability monitoring device 1,
An operation amount and a control amount of a plant to be controlled are sequentially input, and a determination result signal regarding robust stability and an H infinity norm signal | G |
_∞ is output sequentially. These signals are sent to the operator terminal 4
0 is always displayed. If it is determined that the robustness is not stable, the operator terminal receiving the signal makes an alarm sound and displays an alarm message on the screen to notify the operator of the abnormality of the plant control system. The operator can determine the degree of the robust stability by seeing how small the H infinity norm signal | G | _} is, or how much exceeds it. FIG. 8 shows an example of a screen configuration of the operator terminal for displaying them. FIG. 8A shows a case where robust stability is achieved, and the plant flow 91 displayed on the screen is displayed.
If you specify the desired control system, the state for that the control system is displayed in the message window © 92, robust stability display meter 93 | G | value of _∞ is displayed. on the other hand,
FIG. 8B shows a case where the robust stability is not obtained. An alarm sounds, the alarm sign 94 blinks, and a control loop that does not satisfy the robust stability in the plant flow 91 blinks. Also, a message is displayed to the message window © 92, the robust stability display meter 93 | G | value of _∞ indicates that exceeds 1.

The judgment result signal, the H-infinity norm signal, and the like output from the stability monitoring device 1 are also input to the control parameter adjusting means 50. When the controller 60 is in the automatic adjustment mode, the robust stability is obtained by the following procedure. The control parameters are adjusted to be optimal.

[0064] Step 1: H infinity norm signal | G | capture _∞. Step 2: If | G | _∞ <η, control gain _Kp is slightly increased. _Kp ← _Kp × 1.1 If | G | _∞ > η, the control gain _Kp is slightly reduced. K _p ← K _p ÷ 1.1 if | G | _∞ = η if control gain is to remain status quo. Step 3: Set the control gain _Kp in the controller 60 and return to step 1. Here, η (0 <η <1) is a parameter for designating a preferable robust stability of the control system, and is set from the operator terminal 40.

As described above, according to the stability monitoring apparatus of this embodiment, the control system H is obtained from the observation data of the operation amount u and the control amount y of the control system without imposing a load on the processing device of the controller body. Measure the infinity norm in real time,
Based on the magnitude of the H infinity norm, it is determined whether the control system is robustly stable. Then, the operator is notified of the determination result, and when the robust stability is not satisfied, an alarm is issued, and a countermeasure such as adjusting a gain of the controller can be taken.As a result, a load of the operator monitoring the control system can be reduced. Can be reduced and the safety of Plato operation can be increased.

Next, FIG. 9 shows the configuration of a second embodiment of the stability monitoring apparatus 1 according to the second invention. The stability monitoring device 1 of this embodiment is different from the stability monitoring device 1 of the first embodiment shown in FIG.
Are newly provided. The certainty determination means 2 is the first
And second monitoring means. The first monitoring condition is p. e (peristentl
The second monitoring means monitors the reproducibility of the H infinity norm, i.e., monitoring whether or not the input / output signal contains a sufficiently large number of frequency components.

In the first monitoring means, first, an input / output signal to be controlled, that is, a control amount y _i (i = 1,... P),
The manipulated variable u _h (h = 1,..., M) is observed in real time at a time k for each predetermined cycle, and the following vector φ _i (k) = [y _i (k−1) ),... Y _i (kn), u
_{1 (k-1), ...} u 1 (k-n), ..., u m (k-
_{1), ... u m (k} -n) ] a ^{T i (i = 1, ...} m) obtained for each.

Next, at each time k, the covariance matrix Γ (k) is updated according to the following equation.

Γ _i (k) = λ _i Γ _i (k−1) + φ
^{_{i (k) φ T i (}} k) _{where, 1 ≧ λ i> 0,} Γ (0) is a positive definite matrix.
And p. e. The sex measure pe (k) is expressed by the following equation:

[0070]

[Equation 17] Calculate using Where σ _max (A) and σ
_min (A) means the maximum singular value and the minimum singular value of the matrix A, respectively. Pe (k) in equation (21) means the reciprocal of the condition number of the covariance matrix for the input / output signal vector φ (k) to be controlled. If this value is small, the dynamic characteristic model of the control target is obtained from the input / output signal. Means that it is difficult to estimate.

[0071] In the second monitoring means, which is the output of the H infinity norm measuring device H infinity norm estimation result signal | G | a _∞ observed at each time k, the mean for the results of the past N steps The value AH (k) and the variance BH (k) are given by the following equations:

[0072]

(Equation 18) Is determined in real time using. The reciprocal re (k) = (BH (k) / AH (k)) ⁻¹ of the signal obtained by normalizing the variance BH (k) is used as a measure of the reproducibility of the H infinity norm. When the output signal of the H infinity norm measuring apparatus 10 fluctuates due to disturbance or observation noise received by the control target, the variance BH (k) of the result of Expression (22) increases and the signal re (k) decreases. . Therefore, the magnitude of re (k) is a measure of the reproducibility of the H infinity norm of the model error estimated by the stability monitoring device 1.

The p.o. of the input / output signal of the control object estimated by the above procedure e. The measure of sex pe (k) or the measure of reproducibility of the model error H-infinity norm re (k) is output as a measure of the certainty of the judgment result in the stability monitoring device 1. This result is first displayed on the operator terminal 40 to inform the plant operator of the reliability of the stability monitoring function. Second, it is sent to the control parameter adjusting means 50, and when the certainty factor is lower than a certain threshold value, the automatic adjustment of the control parameters is suppressed even if it is determined that the robust stability is poor. Thus, it is possible to prevent the control system from being adversely affected by forcibly adjusting the control parameters when the stability of the control system is erroneously determined.

Next, in the test signal generating means 3, p. e.
Sex determination means (determination means 1) to p. e. Sex measure signal or a certainty signal from the certainty determination means 2 and when it falls below a certain threshold, or when the plant operator confirms the certainty and determines that it is necessary. Only when a command is input, p. e. Satisfying test signal δ _1, ... δ _m or d _1, ... operation amount _{u i (i = 1, ...} m) of the control system of d _p or setpoint signal r _i
(I = 1,... P). As the test signal, an arbitrary signal is examined from among a pulse signal, a rectangular wave signal, an M-sequence signal, and a pseudo white signal. An example of these signals is shown in FIG.
(A), (b), (c), and (d) show.

In the embodiment of the H infinity norm measuring apparatus according to the first invention and the first embodiment of the stability monitoring apparatus according to the second invention, the estimation of the H infinity norm of the model error and the feedback control system are performed. Are all based on the manipulated variable of the controlled object and the observed value of the controlled variable. However, when the set value is constant for a long time, both the operation amount and the control amount become constant values, and it becomes difficult to obtain significant information regarding the model error and the stability from those signals. Further, when the control system receives a large disturbance or observation noise, the model error and the stability judgment result estimated from the observation data have low reliability. Therefore, the pe property and the reproducibility of the H infinity norm are monitored as in the second embodiment described above,
If necessary, the reliability of the stability monitoring can be improved more than in the first embodiment by automatically adjusting the control parameters or superimposing the test signal on the setting signal or the operation amount.

[0076]

According to the H-infinity norm measuring device of the first invention, the H-infinity norm can be measured in real time based on the input signal and the output signal of the controlled system. Since this measurement can be performed independently of the controller to be controlled, no load is applied to the processing device of the controller body.

Further, according to the stability monitoring apparatus of the second invention, it is possible to automatically determine, in real time, the robust stability with respect to the dynamic characteristic change of the controlled object, and to reduce the load on the plant monitoring work of the plant operator. Reduction can be achieved. Further, by adjusting the control system according to the result, the reliability of the control system can be improved.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of an H-infinity norm measuring apparatus according to a first invention.

FIG. 2 is a block diagram illustrating a relationship between an H-infinity norm measuring device and a control target.

FIG. 3 is a graph illustrating the meaning of an H infinity norm.

FIG. 4 is a schematic diagram illustrating the structure of a buffer memory according to the embodiment shown in FIG. 1;

FIG. 5 is a block diagram showing a configuration of a first embodiment of a stability monitoring apparatus according to the second invention.

FIG. 6 is a block diagram illustrating the stability of a closed loop system.

FIG. 7 is a block diagram illustrating robust stability of a feedback control system.

8 is a schematic diagram showing an example of a display screen on the operator terminal of the embodiment shown in FIG.

FIG. 9 is a block diagram showing a configuration of a second embodiment of the stability monitoring apparatus according to the second invention.

FIG. 10 is a waveform chart showing a waveform of a test signal generated by the test signal generating means according to the embodiment shown in FIG. 9;

[Explanation of symbols]

REFERENCE SIGNS LIST 1 stability monitoring device 2 certainty determination means 3 test signal generation means 4 model response calculation means 5 model error response calculation means 6 filter 10 H infinity norm measurement device 11 _i (i = 1,... M) analog data input terminal 12 _i (i = 1,... p) Analog data input terminal 13a, 13b A / D converter 14 Clock timer 15 Digital data input terminal 16a, 16b Buffer memory 17 Parameter setting terminal 18 Data bus 19 Memory 19a Program area 19b Data area 20 CPU 21 D / A converter 22 Digital data output terminal 23 Analog data output terminal

Continuation of front page (56) References JP-A-6-26895 (JP, A) JP-A-6-19511 (JP, A) JP-A-5-313706 (JP, A) JP-A-5-35309 (JP) , A) (58) Field surveyed (Int. Cl. ⁷ , DB name) G05B 13/02

Claims (6)

(57) [Claims] 1. The method according to claim 1, wherein n (≧ 1) is based on m (≧ 1) input signals.
1) For a system that outputs a number of output signals, an average value and a variation range of a parameter of a time series model of the system based on the time series data of the input signal and the output signal using a set membership identification method. Identification means for identifying; estimating means for estimating a frequency response of the time-series model based on an average value and a variation range of parameters of the time-series model identified by the identification means; and frequency response estimated by the estimating means And a calculating means for calculating the maximum value of the maximum singular value of the frequency response matrix among all the frequencies, wherein the maximum value calculated by the calculating means is H infinity norm. H infinity norm measuring apparatus, characterized in that: 2. The method according to claim 1, wherein n (≥2) based on m (≥2) input signals.
2) for a system that outputs a number of output signals, a configuration unit configured to form a matrix U for an input signal sequence and a matrix Y for an output signal sequence based on the time-series data of the input signal and the time-series data of the output signal; Calculating means for calculating a product matrix U ^-1 Y of an inverse matrix of the matrix U and the matrix Y, and calculating a maximum singular value of the product matrix, wherein the maximum singular value is an H infinity norm. An H-infinity norm measuring apparatus, characterized in that: 3. A system for outputting one output signal based on one input signal by performing a discrete-time Fourier transform on the time-series data of the input signal and the time-series data of the output signal. Fourier transform means for obtaining a Fourier transform of an input signal and a Fourier transform of an output signal at each frequency; And an H infinity norm measuring apparatus, wherein the maximum value is an H infinity norm. 4. A controlled object having m (≧ 1) manipulated variables and p (≧ 1) controlled variables, and outputs a manipulated variable based on a set value of the controlled variable and the controlled variable fed back. A feedback control system comprising: a controller that sequentially observes the operation amount and the control amount; and sequentially calculates a predicted value of the control amount from the observation value of the operation amount based on a linear model of the control target. Model response calculating means for calculating; a model error response calculating means for sequentially calculating a signal sequence of a model error which is a difference between the predicted value of the control amount and the observed value; and P, a transfer function of the linear model to be controlled. When the transfer function of the controller is C and I are unit matrices, the transfer function has a transfer function T represented by T = (I + CP) ^-1 C, and the signal function of the model error is an input signal and the transfer function is A filter means for calculating an output signal when input to T; an H infinity norm measuring device for measuring an H infinity norm for a system in which the observed value of the manipulated variable is used as an input signal and the output of the filter means is used as an output signal And determining means for determining that the feedback control system is robustly stable when the H-infinity norm is smaller than 1, and determining that it is not robustly stable when the value is 1 or more. Control system stability monitoring device. 5. The stability monitoring device according to claim 4, wherein the operation amount of the controlled object and the p. e. Determining the reliability (sustained excitability, persistent excitingness) and the reproducibility of the H-infinity norm signal, and determining the reliability of the stability determination result from the determination result; When the value is lower than a predetermined threshold value or when an external command is received, p. e. And a test signal generating means for generating a test signal satisfying the characteristic and superimposing the test signal on the manipulated variable of the controlled object or the set value of the control variable. 6. The stability of a control system according to claim 4, wherein the H-infinity norm measuring device is the H-infinity norm measuring device according to any one of claims 1 to 3. Monitoring device.