RU2429518C1 - Method of fault finding in continuous system dynamic unit - Google Patents

Abstract

FIELD: physics. ^ SUBSTANCE: known good system response at check intervals in check points is registered. Integral estimates of system output signals are defined and registered. Integral transforms of model dynamic characteristics are defined for each check point. Said output signal integral estimates are defined to determine deformations of model signal integral estimates. Normalised deformation of model signal integral estimates are defined. System with rated characteristics is replaced by controlled system. Integral estimates of controlled system signals are defined for control points. Deviation of controlled system signal integral estimates are defined. Normalised deviation of controlled system signal integral estimates is defined to calculate magnitudes of diagnostic indications. ^ EFFECT: expanded operating performances. ^ 1 dwg

Description

The invention relates to the field of monitoring and diagnosing automatic control systems and their elements.

A known method for diagnosing dynamic links of control systems (RF Patent No. 2110828, MKI ⁶ G05B 23/02, 1998), based on the integration of the output signal of the block with a weight e- ^αt , where α is a real constant.

The disadvantage of this method is that it is applicable only to control the parameters of the aperiodic link of the first order.

The closest technical solution (prototype) is a device for monitoring the parameters of the links of control systems (RF Patent No. 2173873, MKI ⁶ G05B 23/02, 2001).

The disadvantage of this method and device is that they are applicable only for the diagnosis of aperiodic first order, aperiodic second order and vibrational links.

The technical problem to which this invention is directed is to expand the functionality of the method for troubleshooting in the form of deviations of the transfer function parameters of blocks of arbitrary structure in a dynamic system with an arbitrary connection of blocks.

путем подачи на первые входы k блоков перемножения сигналов системы управления, на вторые входы блоков перемножения подают экспоненциальный сигнал e^-αt, выходные сигналы k блоков перемножения подают на входы k блоков интегрирования, интегрирование завершают в момент времени T_K, полученные в результате интегрирования оценки выходных сигналов F_{j ном}(α), j=1,…,k регистрируют, определяют интегральные преобразования динамических характеристик модели для каждой из k контрольных точек, полученные в результате пробных отклонений m параметров всех блоков, для чего поочередно в каждый параметр передаточной функции блоков динамической системы вводят пробное отклонение и находят интегральные оценки выходных сигналов системы для параметра интегрирования α и тестового сигнала x(t), полученные в результате интегрирования оценки выходных сигналов для каждой из k контрольных точек и каждого из m пробных отклонений P_ji(α), j=1,…,k, i=1,…,m регистрируют, определяют деформации интегральных оценок сигналов модели, полученные в результате пробных отклонений соответствующих параметров структурных блоков ΔP_ji(α)=P_ji(α)-F_{j ном}(α), j=1,…,k; i=1,…,m, определяют нормированные значения деформаций интегральных оценок сигналов модели, полученные в результате пробных отклонений соответствующих параметров блоков из соотношенияThe problem is achieved by pre-registering the reaction of a known-good system f _{j nom} (t), j = 1, 2, ..., k on the interval t∈ [0, T _K ] at k control points and determine the integral estimates of the output signals F _{j nom} (α), j = 1, ..., k of the system, for which, at the time the test signal is input to the input of the system with nominal characteristics, the signals of the control system are simultaneously integrated at each of the k control points with weights e ^-αt , where

by applying the control system signals to the first inputs k of the multiplication blocks, the exponential signal e ^{-t is} supplied to the second inputs of the multiplying blocks, the output signals of the multiplying blocks are fed to the inputs of the integration blocks k, the integration is completed at time T _K , obtained by integrating the output estimates signals F _{j prefecture} (α), j = 1, ..., k register define integral transform dynamic characteristics model for each of the control points k resulting test parameter deviations of all m blocks, for which a test deviation is introduced into each parameter of the transfer function of the blocks of the dynamic system and integral estimates of the system output signals are found for the integration parameter α and test signal x (t) obtained by integrating the output signal estimate for each of the k control points and each m deviations of test P _ji (α), j = 1, ..., k, i = 1, ..., m is recorded, is determined deformation signal integrated model estimates resulting test deviations of the corresponding parameters are structural blocks _{ΔP ji (α) = P ji} (α) -F j _prefecture (α), j = 1, ..., k; i = 1, ..., m, determine the normalized strain values of the integral estimates of the model signals obtained as a result of trial deviations of the corresponding block parameters from the relation

replace the system with the nominal characteristics of the controlled one, a similar test signal x (t) is supplied to the input of the system, determine the integral estimates of the signals of the controlled system for k control points F _j (α), j = 1, ..., k for the integration parameter α, determine the deviations of the integral estimates of signals of the controlled system for k control points from the nominal values ΔF _j (α) = F _j (α) -F _{j nom} (α), j = 1, ..., k, determine the normalized values of the deviations of the integrated estimates of the signals of the controlled system from the relation

determine diagnostic signs from the ratio

at a minimum, the values of the diagnostic symptom determine the faulty parameter.

The essence of the proposed method is as follows. The method is based on the use of trial deviations of the model parameters of a continuous dynamic system. To obtain diagnostic signs of dynamic elements, Laplace transforms of time functions are used:

in the range of real values of the Laplace variable p = α in the interval 0≤α≤∞. Using the Laplace transform allows you to switch from processing time functions to analyzing the numerical values of their functionals.

Integral transformations are found on the time interval T _k at k control points:

Using a vector interpretation of expression (3), we write it in the following form:

и нормированным вектором (единичной длины) отклонений интегральных оценок сигналов модели

, полученных в результате пробного отклонения i-го параметра.where φ _i (α) is the angle between the normalized vector (unit length vector) of the deviations of the integral estimates of the object signals

and the normalized vector (unit length) of the deviations of the integral estimates of the model signals

obtained as a result of a trial deviation of the i-th parameter.

Thus, the normalized diagnostic sign (3) is the value of the square of the sine of the angle formed in the k-dimensional space (where k is the number of control points) by the normalized vectors of test deviations of the integral estimates of the model signals and the real deformation of the integral estimates of the signals of the diagnostic object.

A test deviation of the parameter, minimizing the value of the diagnostic sign (3), indicates the presence of a defect in this parameter. The range of possible values of a diagnostic feature lies in the interval [0, 1].

Thus, the proposed troubleshooting method is reduced to the following operations.

1. As a dynamic system, consider a system consisting of arbitrarily connected dynamic elements, the transfer functions of which contain m parameters.

2. Pre-determine the control time T _To ≥T _PP , where T _PP - the transition process of the system. The transient time is estimated for the nominal values of the parameters of the dynamic system.

.3. Determine the parameter of the integral signal conversion from the ratio

.

4. Fix the number of control points k.

деформаций интегральных оценок сигналов модели, полученные в результате пробных отклонений i-го параметра каждого из m параметров блоков для номинальных значений параметров передаточных функций блоков и определенного выше параметра α, для чего выполняют пункты 6-10.5. Predefined normalized vectors

deformations of the integral estimates of the model signals obtained as a result of test deviations of the i-th parameter of each of the m block parameters for the nominal values of the parameters of the transfer functions of the blocks and the parameter α defined above, for which points 6-10 are performed.

6. The test signal x (t) (unit step, linearly increasing, rectangular pulse, etc.) is supplied to the input of the control system with nominal characteristics. The proposed method does not provide fundamental restrictions on the type of input test exposure.

, для чего сигналы системы управления подают на первые входы k блоков перемножения, на вторые входы блоков перемножения подают экспоненциальный сигнал e^-αt, выходные сигналы k блоков перемножения подают на входы k блоков интегрирования, интегрирование завершают в момент времени Т_к, полученные в результате интегрирования оценки выходных сигналов F_{j ном}(α), j=1,…,k регистрируют.7. The response of the system f _{j nom} (t), j = 1, 2, ..., k on the interval t∈ [0, T _K ] at k control points is recorded and the integral estimates of the output signals F _{j nom} (α), j = 1, ..., k of the system. To do this, at the time of supplying a test signal to the input of the control system with nominal characteristics, the integration of the control system signals at each of k control points with weights e ^{-αt starts simultaneously}

why the control system signals are fed to the first inputs of the multiplication blocks, the exponential signal e ^{-αt is} supplied to the second inputs of the multiplication blocks, the output signals of the multiplication blocks are fed to the inputs of the integration blocks k, the integration is completed at time T _to , obtained as a result of integration estimates of the output signals F _{j nom} (α), j = 1, ..., k are recorded.

8. Determine the integral estimates of the model signals for each of the k control points obtained as a result of the test deviations of each of the m block parameters, for which, for each parameter of the dynamic system block, a test deviation of this parameter of the transfer function is introduced and steps 6 and 7 are performed for one and the same test signal x (t). Estimates of the output signals obtained as a result of integration for each of k control points and each of m test deviations P _ji (α), j = 1, ..., k; i = 1, ..., m are recorded.

9. The deformations of the integral estimates of the model signals obtained as a result of test deviations of the parameters of the corresponding blocks ΔP _ji (α) = P _ji (α) -F _{j nom} (α), j = 1, ..., k; i = 1, ..., m.

10. Determine the normalized strain values of the integral estimates of the model signals obtained as a result of trial deviations of the corresponding parameters of the blocks by the formula

.

.

11. Replace the system with the rated characteristics controlled. A similar test signal x (t) is supplied to the system input.

12. Determine the integral estimates of the signals of the controlled system for k control points F _j (α), j = 1, ..., k, performing the operations described in paragraphs 6 and 7 with respect to the controlled system.

13. The deviations of the integral estimates of the signals of the controlled system for k control points from the nominal values ΔF _j (α) = F _j (α) -F _{j nom} (α), j = 1, ..., k are determined.

14. The normalized values of the deviations of the integrated estimates of the signals of the controlled system are calculated by the formula

15. Calculate the diagnostic signs of a faulty parameter by the formula (3).

16. At a minimum, the values of the diagnostic symptom determine the defective parameter.

Since diagnostic signs (3) have a range of possible values limited by the interval [0, 1], the difference between the closest to the minimum sign and the minimum sign (which indicates a defective parameter) quantitatively characterizes the distinguishability of this defect, taking into account the location of the block parameter on the structural diagram, the type and parameters of the transfer functions of the blocks and all the diagnostic conditions under which these values of the diagnostic signs are obtained (type of test signal, parameter value α, number and size the position of the control points, the value of the interval T _to ). The best distinguishability is when the indicated difference is equal to unity (in terms of vector interpretation, the normalized strain vectors of integral signal estimates corresponding to these parameters for test deviations are orthogonal). The worst distinguishability is when the indicated difference is zero (in terms of vector interpretation, the normalized strain vectors of the integral signal estimates corresponding to these parameters for test deviations are collinear). Therefore, the use of normalized diagnostic features allows you to compare the diagnostic results to select the optimal defect search modes.

Consider the implementation of the proposed method for finding a single defect for a system whose structural diagram is shown in the drawing (see drawing. Structural diagram of the diagnostic object).

Transfer functions of blocks:

;

;

,

;

;

,

nominal values of parameters: T ₁ '= 5 s (J ₁ ); b1 = 1 (J ₂ ); T ₁ ″ = 1 s (J ₃ ); K ₂ = 1 (J ₄ ); T ₂ = 1 s (J ₅ ); b2 = 1 (J ₆ ); K ₃ = 1 (J ₇ ); T ₃ = 5 s (J ₈ ) and b3 = 1 (J ₉ ). When searching for a single defect in the form of a deviation of the time constant T ₁ = 4 (defect No. 1) s in the first link by supplying a step test input signal of unit amplitude and integral signal estimation for parameter α = 0.5 and T _to = 10 s, the values of diagnostic signs were obtained by formula (3) when using three control points located at the outputs of the blocks. The defect found by obtaining test deviations of 10% and calculations by the formula (3), gives the following values of diagnostic signs: J ₁ = 2.28e-008; J ₂ = 1.421e-007; J ₃ = 5.444e-008; J ₄ = 0.7841; J ₅ = 0.7822; J ₆ = 0.7849; J ₇ = 0.07426; J ₈ = 0.07403; J ₉ = 0.07481. An analysis of the values of diagnostic features shows that the distinguishability of parametric defects located in different blocks is much better than the distinguishability of parametric defects located in one block. It should be noted that the method is workable even with large values of the test deviations of the parameters (10-40%). A limitation on the value of the test deviation is the need to maintain the stability of the model with a test deviation.

The search for a parametric malfunction according to the proposed method as applied to the diagnostic object shown in the drawing is reduced to the following operations:

1. Fix the number of parameters of dynamic elements m = 9.

2. By analyzing the graphs of the nominal transient characteristics, the time of the transition process of the system is determined. For this example, the transient time is T _PP = 8 s. The monitoring time T _k ≥T _{PP is} fixed. For this example, T _k = 10 s.

. Для данного примера α=0.5.3. Determine the signal integration parameter

. For this example, α = 0.5.

4. Fix the control points at the outputs of the blocks: k = 3.

5. Preliminarily find the elements of the vectors ΔP ₁ (α), ΔP ₂ (α), ΔP ₃ (α) of strains of the integral estimates of the model signals obtained as a result of trial deviations of the corresponding parameters. The value of the test deviations is chosen equal to 10%:

деформаций интегральных оценок сигналов модели, полученные в результате пробных отклонений соответствующих параметров:6. Find normalized vectors

deformations of the integral estimates of the model signals obtained as a result of trial deviations of the corresponding parameters:

7. Replace the system with the nominal characteristics of the controlled, in which the deviation of the parameter T _{1 of the} first block from the nominal by 20% is introduced. At the input of the system we apply a similar test signal x (t).

8. The deviations of the integral estimates of the signals of the controlled system for three control points from the nominal values ΔF _j (α) = F _j (α) -F _{j nom} (α), j = 1, 2, 3 are determined

ΔF ₁ (α) = 0.4002, ΔF ₂ (α) = 0.2667, ΔF ₃ (α) = 0.07619.

9. Calculate the normalized values of the deviations of the integral transforms of the dynamic characteristics of the controlled system

,

,

.

,

,

.

10. Calculate the diagnostic signs of a faulty unit by the formula (3): J ₁ = 2.28e-008; J ₂ = 1.421e-007; J ₃ = 5.444e-008; J ₄ = 0.7841; J ₅ = 0.7822; J ₆ = 0.7849; J ₇ = 0.07426; J ₈ = 0.07403; J ₉ = 0.07481.

11. At the minimum, the values of the diagnostic sign determine the defective parameter (in this case, No. 1).

Modeling the processes of searching for parametric defects in the second and third blocks for a given diagnostic object with the same SS integration parameter and with a single step input signal gives the following values of diagnostic signs.

If there is a defect in block No. 2 (in the form of a decrease in the parameter T ₂ by 20%, defect No. 5): J ₁ = 0.7821; J ₂ = 0.7819; J ₃ = 0.7822; J ₄ = 6.319e-006; J ₅ = 4.41e-008; J ₆ = 1.23e-005; J ₇ = 0.7448; J ₈ = 0.7455; J ₉ = 0.743.

If there is a defect in block No. 3 (in the form of a decrease in the parameter T ₃ by 20%, defect No. 8): J ₁ = 0.07407; J ₂ = 0.07384; J ₃ = 0.07406; J ₄ = 0.7476; J ₅ = 0.7457; J ₆ = 0.7485; J ₇ = 7.831e-007; J ₈ = 1.531e-010; J ₉ = 9.831e-006.

The minimum value of a diagnostic sign in both cases correctly indicates a defective parameter.

An analysis of the values of diagnostic features also shows that the distinguishability of parametric defects located in different blocks is much better than the distinguishability of parametric defects located in one block.

Claims (1)

A method for troubleshooting a dynamic unit in a continuous system, based on the fact that the number m of parameters included in the system is fixed, the monitoring time T _K ≥T _PP is determined, the signal integration parameter is determined from the relation

, use the test signal in the interval t∈ [0, T _K ], calculate the integral signal estimates obtained for real values of the integration parameter α, fix the number k of control points of the system, record the response of the system and models, determine the diagnostic sign, determine the minimum diagnostic sign faulty parameter, characterized in that the reaction of a known-good system f _{j nom} (t), j = 1, 2, ..., k on the interval t∈ [0, T _K ] at k control points is recorded, integral estimates of the output signals F _{j are} determined _nom (α), j = 1, ..., k of the system, for which, at the time of feeding a test signal to the input of a system with nominal characteristics, they simultaneously begin integrating the system signals at each of k control points with weights e ^-αt , by applying k multiplying blocks of the system signals to the first inputs the second inputs of the multiplication units supply an exponential signal e ^-t , the output signals of the multiplying units are fed to the inputs of the integration units k, the integration is completed at time T _K , obtained by integrating the estimates of the output signals F _{j nom} (α), j = 1, ..., k are recorded, integral estimates of the model signals for each of the k control points are determined, obtained as a result of test deviations of each of the m parameters, for which, for each parameter of the dynamic block of the system, a test deviation of its parameter is introduced transfer function and find the integrated estimates of the system output signals for the integration parameter α and the test signal x (t) obtained by integrating the estimates of the output signals for each of k control points and each of m test deviations P _ji (α), j = 1, ..., k, i = 1, ..., m is recorded, is determined deformation integral model estimations of signals resulting test deviations of the corresponding parameters _{ΔP ji (α) = P ji} (α) - F _{j nom} (α), j = 1, ..., k; i = 1, ..., m, determine the normalized strain values of the integral estimates of the model signals obtained as a result of trial deviations of the corresponding parameters from the relation

replace the system with the nominal characteristics of the controlled system, the analogous test signal x (t) is fed to the input of the controlled system, the integral estimates of the signals of the controlled system are determined for k control points F _j (α), j = 1, ..., k for the integration parameter α, the deviations are determined integral estimates of the signals of the controlled system for k control points from the nominal values ΔF _j (α) = F _j (α) -F _{j nom} (α), j = 1, ..., k, determine the normalized deviations of the integral estimates of the signals of the controlled system from the relation

determine diagnostic signs from the ratio

at the minimum of a diagnostic symptom, a faulty parameter is determined.