RU2486569C1 - Method to search for faulty block in discrete dynamic system - Google Patents

Abstract

FIELD: information technologies.SUBSTANCE: previously a reaction of a knowingly good time-discrete system is registered for discrete beats of diagnostics with discrete permanent pitch in the observation interval at reference points, and integral estimates of output signals of the discrete system are determined repeatedly (simultaneously) for the values of the discrete integration parameter. For this purpose at the moment of test signal supply to the inlet of the discrete system with rated characteristics, simultaneously discrete integration of control system signals is started with the pitch in seconds for integration parameters in each of the reference points with weights with the pitch in seconds, by supplying of control system signals to the first inlets of the multiplication blocks. Discrete exponential signals are supplied to the second inputs of the multiplication blocks with the pitch in seconds for discrete integration blocks, output signals of the multiplication blocks are supplied to the inputs of the discrete integration blocks with the pitch in seconds. Integration is stopped at the moment of time, estimates of output signals produced as a result of discrete integration are registered. The number of considered single defects of blocks is fixed, integral estimates of model signals are determined for each of the reference points and parameters of discrete integration, produced as a result of test deviations of parameters of each block. For this purpose in turns for each block of the discrete dynamic system they introduce test deviation of the parameter of its discrete transfer function, and integral estimates of output signals of the system are found for parameters of discrete integral conversions and the test signal. Estimates of output signals produced as a result of discrete integration for each of the reference points, every test deviation and every parameter of discrete integration are registered. Deviations of integral estimates of discrete model signals are determined, being produced as a result of test deviations of parameters of appropriate structural blocks, the rated values of deviations of integral estimates of discrete model signals are determined, being produced as a result of test deviations of parameters of appropriate blocks for parameters of discrete integration. The system with rated characteristics is replaced with a controlled one, an identical test signal is supplied to the inlet of the system, integral estimates are determined for signals of the controlled discrete system for reference points and for parameters of the discrete integration. Deviations of integral estimates of controlled discrete system signals are determined for reference points and parameters of discrete integration from rated values. Rated values of deviations of integral estimates of controlled discrete system signals are determined for parameters of discrete integration, diagnostic criteria are determined with parameters of discrete integration, by the minimum value of the diagnostic criterion, a faulty block is determined.EFFECT: improved noise immunity of the method for diagnostics of discrete systems of automatic control by improvement of defects observability.1 dwg

Description

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

, где α_l - вещественная константа, l - количество констант.A known method of finding a faulty unit in a dynamic system (Patent for the invention No. 2439648 dated 01/10/2012 according to the application No. 201042159/08 (060530), MKI ⁶ G05B 23/02, 2012), based on the multiple integration of the output signal of the block with the scales $$e^{-{\alpha }_{l}t}$$

, where α _l is a real constant, l is the number of constants.

The disadvantage of this method is that it provides defect detection only in a continuous dynamic system.

The closest technical solution (prototype) is a method for finding a faulty unit in a discrete dynamic system (Patent for the invention No. 2444774 dated 03/10/2012 by application No. 20111101271/08 (001575), MKI ⁶ G05B 23/02, 2012).

The disadvantage of this method is that it provides the identification of defects with low distinguishability, that is, it has a low noise immunity.

The technical problem to which this invention is directed is to improve the noise immunity of the method for diagnosing discrete automatic control systems by improving the distinguishability of defects. This is achieved by repeatedly calculating the integral estimates of the dynamic characteristics for several different values of the integration parameter α ₁ , α ₂ ... α _n .

, j=1, …, k, l=1, …, n дискретной системы для n значений параметра дискретного интегрирования α_l, для чего в момент подачи тестового сигнала на вход дискретной системы с номинальными характеристиками одновременно начинают дискретное интегрирование сигналов системы управления с шагом Ts секунд для n параметров интегрирования в каждой из k контрольных точек с весами $$e^{-{\alpha }_{l}t{T}_S}$$

с шагом Ts секунд, путем подачи на первые входы k·n блоков перемножения сигналов системы управления, на вторые входы блоков перемножения подают дискретные экспоненциальные сигналы $$e^{-{\alpha }_{l}t{T}_S}$$

с шагом Ts секунд для n блоков дискретного интегрирования, выходные сигналы k·n блоков перемножения подают на входы k·n блоков дискретного интегрирования с шагом Ts секунд, интегрирование завершают в момент времени Т_к, полученные в результате дискретного интегрирования оценки выходных сигналов $$F_{jном}\left({\alpha }_l\right)$$

, j=1, …, k; l=1, …, n регистрируют, фиксируют число m рассматриваемых одиночных дефектов блоков, определяют интегральные оценки сигналов модели для каждой из k контрольных точек и n параметров дискретного интегрирования, полученные в результате пробных отклонений параметров каждого из m блоков, для чего поочередно для каждого блока дискретной динамической системы вводят пробное отклонение параметра его дискретной передаточной функции и находят интегральные оценки выходных сигналов системы для n параметров дискретных интегральных преобразований α_l и тестового сигнала x(t), полученные в результате дискретного интегрирования оценки выходных сигналов для каждой из k контрольных точек, каждого из m пробных отклонений и каждого из n параметров дискретного интегрирования $$P_{ji}\left({\alpha }_l\right)={\displaystyle \sum _{t=1}^N{P}_{ji}\left(t\right)\cdot e^{-{\alpha }_l\cdot t\cdot T_S}}$$

, j=1, …, k; i=1, …, m; l=1, …, n регистрируют, определяют отклонения интегральных оценок сигналов дискретной модели, полученных в результате пробных отклонений параметров соответствующих структурных блоков $$\Delta P_{ji}\left({\alpha }_l\right)=P_{ji}\left({\alpha }_l\right)-F_{jном}\left({\alpha }_l\right)$$

, j=1, …, k; i=1, …, m; l=1, …, n определяют нормированные значения отклонений интегральных оценок сигналов дискретной модели, полученных в результате пробных отклонений параметров соответствующих блоков для n параметров дискретного интегрирования из соотношенияThe problem is achieved by pre-registering the reaction of a known-good discrete in time system f_jnom(t), j = 1, 2 ..., k for N discrete diagnostic clock cycles t∈ [1, N] with a discrete constant step Ts on the observation interval [0, T_k] (where T_k= T_s· N) at k control points, and the integral estimates of the output signals are repeatedly determined (simultaneously) $$F_{jn\mathrm{about}m}\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{f}_{jn\mathrm{about}m}\left(t\right)\cdot e^{-{\alpha }_l\cdot t\cdot T_S}}$$

, j = 1, ..., k, l = 1, ..., n of the discrete system for n values of the parameter of discrete integration α_lwhy, at the time of supplying a test signal to the input of a discrete system with nominal characteristics, discrete integration of the control system signals with a step of Ts seconds for n integration parameters at each of k control points with weights $$e^{-{\alpha }_{l}t{T}_S}$$

 with a step Ts of seconds, by applying to the first inputs k · n blocks of multiplication of signals of the control system, discrete exponential signals are fed to the second inputs of the blocks of multiplication $$e^{-{\alpha }_{l}t{T}_S}$$

with a step of Ts seconds for n discrete integration blocks, the output signals k · n of multiplication blocks are fed to the inputs k · n of discrete integration blocks with a step of Ts seconds, the integration is completed at time T_toobtained as a result of discrete integration of the output signal estimate $$F_{jn\mathrm{about}m}\left({\alpha }_l\right)$$

, j = 1, ..., k; l = 1,. of a block of a discrete dynamic system, a test deviation of the parameter of its discrete transfer function is introduced and integral estimates of the system output signals are found for n parameters of discrete integral transformations α_l and test signal x (t) obtained as a result of discrete integration of the output signal estimate for each of k control points, each of m test deviations, and each of n discrete integration parameters $$P_{ji}\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{P}_{ji}\left(t\right)\cdot e^{-{\alpha }_l\cdot t\cdot T_S}}$$

, j = 1, ..., k; i = 1, ..., m; l = 1, ..., n register, determine the deviation of the integrated estimates of the signals of the discrete model obtained as a result of trial deviations of the parameters of the corresponding structural blocks $$\Delta P_{ji}\left({\alpha }_l\right)=P_{ji}\left({\alpha }_l\right)-F_{jn\mathrm{about}m}\left({\alpha }_l\right)$$

, j = 1, ..., k; i = 1, ..., m; l = 1, ..., n determine the normalized values of the deviations of the integrated estimates of the signals of the discrete model obtained as a result of trial deviations of the parameters of the corresponding blocks for n parameters of discrete integration from the relation

$$\Delta {\widehat{P}}_{ji}\left({\alpha }_l\right)=\frac{\Delta P_{ji}\left({\alpha }_l\right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta P_{ri}^2\left({\alpha }_l\right)}}},\left(\mathrm{one}\right)$$

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 discrete system for k control points and for n discrete integration parameters α_l: F_j(α_l), j = 1, ..., k; l = 1, ..., n determine the deviations of the integral estimates of the signals of the controlled discrete system for k control points and n parameters of discrete integration from the nominal values ΔF_j(α_l) = F_j(α_l) -F_{j nom}(α_l), j = 1, ..., k; l = 1, ..., n, determine the normalized values of the deviations of the integral estimates of the discrete system for n parameters of discrete integration from the relation

$$\Delta {\widehat{F}}_j\left({\alpha }_l\right)=\frac{\Delta F_j\left({\alpha }_l\right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta F_r^2\left({\alpha }_l\right)}}},\text{(2)}$$

determine diagnostic features with n parameters of discrete integration from the relation

$$J_i=\frac{\mathrm{one}}{n}{\displaystyle \sum _{l=\mathrm{one}}^n\left\{\mathrm{one}-{\left[{\displaystyle \sum _{j=\mathrm{one}}^k\Delta {\widehat{P}}_{ji}\left({\alpha }_l\right)\cdot \Delta {\widehat{F}}_j\left({\alpha }_l\right)}\right]}^2\right\}},i=\mathrm{one}...,m,(3)$$

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

Thus, the proposed method for finding a faulty unit is reduced to performing the following operations:

1. As a discrete dynamic system, consider a system, for example, with discrete interpolation of zero order, with a sampling step Ts, consisting of randomly connected dynamic blocks, with the number of single block defects considered m.

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

3. Determine n parameters that are multiples of 5 / T _k multiple signal integration.

4. Fix the number of control points k.

интегральных оценок отклонений сигналов дискретной модели, полученные в результате пробных отклонений параметров i-го блока каждого из m блоков и номинальных значений параметров передаточных функций остальных блоков и n определенных выше параметров α_l, для чего выполняют пункты 6-10.5. Predefined normalized vectors $$\Delta {\widehat{P}}_{ji}\left({\alpha }_l\right)$$

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

6. Apply a test signal (single step, linearly increasing, rectangular pulse, etc.) 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.

, j=1, …, k; l=1, …, n дискретной системы. Для этого в момент подачи тестового сигнала на вход системы управления с номинальными характеристиками одновременно начинают дискретное интегрирование сигналов системы управления с шагом Ts секунд в каждой из k контрольных точек и n параметрах α_l с дискретными весами $${\text{e}}^{\text{-}{\alpha }_{\text{l}}{\text{tT}}_{\text{S}}}$$

, для чего сигналы системы управления подают на первые входы k·n блоков перемножения, на вторые входы блоков перемножения подают дискретные экспоненциальные сигналы $${\text{e}}^{\text{-}{\alpha }_{\text{l}}{\text{tT}}_{\text{S}}}$$

с шагом Ts секунд, выходные сигналы k·n блоков перемножения подают на входы k·n блоков дискретного интегрирования с шагом Ts секунд, дискретное интегрирование завершают в момент времени Т_к, полученные в результате дискретного интегрирования оценки выходных сигналов F_jном(α_l), j=1, …, k; l=1, …, n регистрируют.7. The reaction of the system f _jnom (t), j = 1, 2, ..., k on the interval t∈ [1, N] with a discrete step Ts seconds on the observation interval [0, T _k ] (where T _k = T _s · N) at k control points and determine the discrete integral estimates of the output signals $$F_{j\text{nom}}\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{f}_{\text{j nom}}\left(t\right)\cdot {\text{e}}^{\text{-}{\alpha }_{\text{l}}\cdot \text{t}\cdot {\text{T}}_{\text{S}}}}$$

, j = 1, ..., k; l = 1, ..., n of the discrete system. For this, at the moment of supplying a test signal to the input of the control system with nominal characteristics, discrete integration of the control system signals with a step of Ts seconds at each of k control points and n parameters α _l with discrete weights $${\text{e}}^{\text{-}{\alpha }_{\text{l}}{\text{tT}}_{\text{S}}}$$

why the control system signals are fed to the first inputs of k · n multiplication blocks, discrete exponential signals are fed to the second inputs of the multiplication blocks $${\text{e}}^{\text{-}{\alpha }_{\text{l}}{\text{tT}}_{\text{S}}}$$

with a step of Ts seconds, the output signals k · n of the multiplication units are fed to the inputs of k · n of discrete integration blocks with a step of Ts seconds, the discrete integration is completed at time T _k , obtained as a result of discrete integration of the output signal estimate F _jн (α _l ), j = 1, ..., k; l = 1, ..., n is recorded.

, j=1, …, k; i=1, …, l=1, …, n регистрируют.8. Determine the integral estimates of the signals of the discrete model for each of k control points and each of n values of the parameter of discrete integration α _l , obtained as a result of test deviations of the parameters of each of m blocks, for which the test deviation of the parameter of discrete transfer function and perform step 7 for the same test signal. Estimates of the output signals obtained as a result of discrete integration for each of k control points, each of m test deviations, and each of n discrete integration parameters $$P_{ji}\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{P}_{ji}\left(t\right)\cdot }{\text{e}}^{\text{-}{\alpha }_l\cdot t\cdot T_S}$$

, j = 1, ..., k; i = 1, ..., l = 1, ..., n are recorded.

9. The deviations of the integrated estimates of the signals of the discrete model are determined, obtained as a result of trial deviations of the parameters of the corresponding blocks ΔP _ji (α _l ) = P _ji (α _l ) -F _jn (α _l ), j = 1, ..., k; i = 1, ..., m; l = 1, ..., n.

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

, j=1, …, k; i=1, …, m; l=1, …, n. $$\Delta {\widehat{P}}_{ji}\left({\alpha }_l\right)=\frac{\Delta P_{ji}\left({\alpha }_l\right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta P_{ri}^2\left({\alpha }_l\right)}}}$$

, j = 1, ..., k; i = 1, ..., m; l = 1, ..., n.

11. Replace the system with the rated characteristics controlled. A similar test signal is applied to the input of the system.

, j=1, …, k; l=1, …, n, осуществляя операции, описанные в пунктах 6 и 7 применительно к контролируемой системе.12. Determine the integral estimates of the signals of the controlled discrete system for k control points and n integration parameters $$F_j\left({\alpha }_l\right)={\displaystyle \sum _{r=\mathrm{one}}^N{f}_j\left(t\right)\cdot {\text{e}}^{\text{-}{\alpha }_{\text{l}}\cdot \text{t}\cdot {\text{T}}_{\text{S}}}}$$

, j = 1, ..., k; l = 1, ..., n, performing the operations described in paragraphs 6 and 7 in relation to the controlled system.

13. The deviations of the integral estimates of the signals of the controlled discrete system for k control points and n integration parameters from the nominal values ΔF _j (α _l ) = F _j (α _l ) -F _jnom (α _l ), j = 1, ..., k; l = 1, ..., n.

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

, j=1, …, k; l=1, …, n. $$\Delta {\widehat{F}}_j\left({\alpha }_l\right)=\frac{\Delta F_j\left({\alpha }_l\right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta F_r^2\left({\alpha }_l\right)}}}$$

, j = 1, ..., k; l = 1, ..., n.

15. Calculate the diagnostic signs of the presence of a faulty unit (with n integration parameters) according to the formula (3).

16. At the minimum, the values of the diagnostic sign determine the defective block.

Consider the implementation of the proposed method for finding a defect for a discrete system, the structural diagram of which is shown in the figure (see. Fig. The structural diagram of the diagnostic object).

Discrete transfer functions of blocks:

; $$H_2\left(z\right)=\frac{k_2}{z-Q_2}$$

; $$H_3\left(z\right)=\frac{k_3}{z-Q_3}$$

, $$H_{\mathrm{one}}\left(z\right)=\frac{k_{\mathrm{one}}\left(z-Z_{\mathrm{one}}\right)}{z-Q_{\mathrm{one}}}$$

; $$H_2\left(z\right)=\frac{k_2}{z-Q_2}$$

; $$H_3\left(z\right)=\frac{k_3}{z-Q_3}$$

,

nominal values of the parameters: K ₁ = 5; Z ₁ = 0.98; K ₂ = 0.09516; Q ₂ = 0.9048; K ₃ = 0.0198; Q ₃ = 0.9802. When searching for a single structural defect in the form of a deviation of the gain by 20% (k ₁ = 4) in the first link, when applying a step test input signal of unit amplitude and integral signal estimates for the parameters α ₁ = 0.5, α ₂ = 0.1, α ₃ = 2.5 and T _k = 10 s, using three control points located at the outputs of the blocks, using test deviations of 10%, the values of diagnostic signs were obtained by the formula (3): J ₁ = 0.2511; J ₂ = 0.9382; J ₃ = 0.5738. The analysis of the values of diagnostic signs shows that the defect in the first block of the monitored system is located correctly. 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 trial deviation is the need to maintain the stability of models with trial deviations.

Simulation of defects search processes in the first block (in the form of a decrease in the parameter k ₁ by 20%) leads to the calculation of diagnostic features for three integration parameters (α ₁ = 0.5, α ₂ = 0.1 and α ₃ = 2.5) according to formula (3): J ₁ = 0, J ₂ = 0.8254, J ₃ = 0.0898. Distinguishability of the defect: ΔJ = J ₃ -J ₁ = 0.0898.

For comparison, we present the diagnostic signs of the presence of a faulty unit (in the form of a decrease in the parameter k ₁ by 20%) with one integration parameter α = 0.5: J ₁ = 0; J ₂ = 0.7843; J ₃ = 0.0717. Distinguishability of the defect ΔJ = J ₃ -J ₁ = 0.0717.

The above results show that the actual distinguishability of finding defects by this method is higher, therefore, the noise immunity of the method will also be higher.

The simulation of defects search processes in the second and third blocks for a given diagnostic object, with the same integration parameters α and with a single step input signal, gives the following values of diagnostic signs:

Simulation of the defect search processes in the second block (in the form of a decrease in the parameter k ₂ by 20%) leads to the calculation of diagnostic features with three integration parameters (α ₁ = 0.5, α ₂ = 0.1 and α ₃ = 2.5) according to formula (3): J ₁ = 0.8387; J ₂ = 0; J ₃ = 0.7703. Distinctness of the defect: ΔJ = J ₃ -J ₁ = 0.7703.

For comparison, we present the diagnostic signs of the presence of a faulty unit (in the form of a decrease in the parameter k ₂ by 20%) with one integration parameter α = 0.5: J ₁ = 0.7845; J ₂ = 0; J ₃ = 0.7481. Distinguishability of the defect ΔJ = J ₃ -J ₁ = 0.7481.

Simulation of defects search processes in the third block (in the form of a decrease in the parameter k ₃ by 20%) leads to the calculation of diagnostic features with three integration parameters (α ₁ = 0.5, α ₂ = 0.1 and α ₃ = 2.5) according to formula (3): J ₁ = 0.09889; J ₂ = 0.7714; J ₃ = 0. Distinguishability of the defect: ΔJ = J ₃ -J ₁ = 0.09889.

For comparison, we present the diagnostic signs of a faulty unit (in the form of a decrease in the parameter k ₃ by 20%) with one integration parameter α = 0.5: J ₁ = 0.07173; J ₂ = 0.7481; J ₃ = 0. Distinctness of the defect ΔJ = J ₃ -J- = 0.07173.

The minimum value of the diagnostic sign in all cases correctly indicates a defective block.

Thus, all three defects are better when using the proposed method.

Claims (1)

A method for finding a faulty block in a discrete dynamic system, based on the fact that the number m of blocks included in the system is fixed, the monitoring time T_TO≥T_PP, determine the parameter of the integral signal conversion from the ratio $$\alpha =\frac{5}{T_{\mathrm{TO}}}$$

use a test signal on the interval [0, T_TO], as the dynamic characteristics of the system, use the integral estimates obtained for the real values of the α Laplace variable, fix the number k of control points of the system, pre-register the reaction of a known-good discrete in time system f_jnom(t), j = 1, 2, ..., k for N discrete diagnostic clock cycles t∈ [1, N] with a discrete constant step Ts on the observation interval [0, T_k] (where T_k= T_s· N) at k control points, determine the integral estimates of the output signals F_jnom(α), j = 1, ..., k of a discrete system, for which, at the moment of supplying a test signal to the input of a discrete system with nominal characteristics, discrete integration of the control system signals with a step of Ts seconds at each of k control points with discrete weights $$e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

 in steps of Ts seconds, where $$\alpha =\frac{5}{T_{\mathrm{to}}}$$

, by applying to the first inputs of k blocks of multiplication of signals of the control system, a discrete exponential signal is supplied to the second inputs of blocks of multiplication $$e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

 with a step Ts of seconds, the output signals of k blocks of multiplication are fed to the inputs of k blocks of discrete integration with a step of Ts seconds, discrete integration is completed at time T_toobtained as a result of integrating the estimates of the output signals $$F_{j\text{nom}}\left(\alpha \right)={\displaystyle \sum _{t=\mathrm{one}}^N{f}_{j\text{nom}}}\left(t\right)\cdot e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

, j = 1, ..., k register, determine the integral estimates of the model signals for each of k control points obtained as a result of test deviations for m single block defects, for which a test deviation of the parameter of the discrete transfer function is introduced into each block of the discrete dynamic system and integral estimates of the system output signals are found for the parameter discrete integral transform α and test signal x (t) obtained as a result of discrete integration of the output signal estimate for each of k control points and each of m test deviations $$P_{j\text{i}}\left(\alpha \right)={\displaystyle \sum _{t=\mathrm{one}}^N{P}_{ji}}\left(t\right)\cdot e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

, j = 1, ...,k; i = 1, ..., m register, determine the deviation of the integrated estimates of the signals of the discrete model obtained as a result of trial deviations of the parameters of the corresponding blocks ΔP_ji(α) = P_ji(α) -F_jnom(α), j = 1, ...,k; i = 1,..., m, determine the normalized values of the deviations of the integrated estimates of the signals of the discrete model obtained as a result of trial deviations of the parameters of the corresponding blocks by the formula $$\Delta {\widehat{P}}_{ji}\left(\alpha \right)=\frac{\Delta P_{ji}\left(\alpha \right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta P_{ri}^2\left(\alpha \right)}}}$$

, j = 1, ..., k; i = 1, ..., m, replace the system with nominal characteristics of the controlled, a similar test signal is fed to the input of the system, the integrated estimates of the signals of the controlled discrete system for k control points are determined $$F_{\text{j}}\left(\alpha \right)={\displaystyle \sum _{t=\mathrm{one}}^N{f}_j}\left(t\right)\cdot e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

, j = 1, ..., k, performing the operations described earlier in relation to the controlled system, determine the deviations of the integrated estimates of the signals of the controlled discrete system for k control points from the nominal values ΔF_j(α) = F_j(α) -F_jnom(α), j = 1, ..., k, normalized deviations of the integral estimates of the signals of the controlled discrete system are calculated by the formula $$\Delta {\widehat{F}}_j\left(\alpha \right)=\frac{\Delta F_j\left(\alpha \right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta F_r^2\left(\alpha \right)}}}$$

, j = 1, ..., k, diagnostic signs are determined, at the minimum of the diagnostic sign, a defect is determined, characterized in that n parameters of signal integration are multiples of $$\frac{5}{T_{\mathrm{TO}}}$$

, as the dynamic characteristics of the system use integral estimates obtained for n real values of α_l, and determine the integral estimates of the output signals F_jnom(α_l), j = 1, ..., k; l = 1, ..., n of the system, for which, at the time of supplying a test signal to the input of the system with nominal characteristics, the integration of control system signals at each of k control points for n integration parameters with weights $$e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

, l = 1, ..., n, by applying to the first inputs k · n blocks of multiplication of signals of the control system, exponential signals are fed to the second inputs of the blocks of multiplication $$e^{-{\alpha }_{\mathrm{one}}\cdot t\cdot T_S}$$

, l = 1, ..., n output signals k · n blocks of multiplication are fed to the inputs of k · n blocks of integration, integration is completed at time T_toobtained as a result of integrating the estimates of the output signals $$F_{j\text{nom}}\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{f}_{jn\mathrm{about}m}}\left(t\right)\cdot e^{-{\alpha }_l\cdot t\cdot T_S}$$

, j = 1, ..., k; l = 1, ..., n are recorded, integral estimates of the model signals for each of the k control points and n integration parameters are determined, obtained as a result of trial deviations of the parameters of each of the m blocks, for which a trial deviation of its transfer parameter is introduced for each block of the dynamic model functions and find integral estimates of the model output signals for n parameters α_l and test signal x (t) obtained by integrating the estimates of the output signals for each of k control points, each of m test deviations, and each of n integration parameters $$P_{j\text{i}}\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{P}_{ji}}\left(t\right)\cdot e^{-{\alpha }_l\cdot t\cdot T_S}$$

, j = 1, ...,k; i = 1, ..., m; l = 1, ..., n are recorded, the deviations of the integral estimates of the model signals obtained as a result of the test deviations of the parameters of the corresponding blocks ΔP are determined_ji(α_l) = P_ji(α_l) -F_jnom(α_l), j = 1, ..., k; i = 1, ..., m; l = 1, ..., n, determine the normalized deviation values of the integral estimates of the model signals obtained as a result of trial deviations of the parameters of the corresponding blocks from the relation $$\Delta {\widehat{P}}_{ji}\left({\alpha }_l\right)=\frac{\Delta P_{ji}\left({\alpha }_l\right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta P_{ri}^2\left({\alpha }_l\right)}}}$$

, determine the integral estimates of the signals of the controlled system for k control points and n integration parameters $$F_j\left({\alpha }_l\right)={\displaystyle \sum _{t=\mathrm{one}}^N{f}_j}\left(t\right)\cdot e^{-{\alpha }_l\cdot t\cdot T_S}$$

, j = 1, ..., k; l = 1, ..., n, determine the deviations of the integrated estimates of the signals of the controlled system for k control points and n integration parameters from the nominal values ΔF_j(α_l) = F_j(α_l) -F_jnom(α_l), j = 1, ..., k; l = 1, ..., n, determine the normalized values of the deviations of the integral estimates of the signals of the controlled system from the relation $$\Delta {\widehat{F}}_j\left({\alpha }_l\right)=\frac{\Delta F_j\left({\alpha }_l\right)}{\sqrt{{\displaystyle \sum _{r=\mathrm{one}}^k\Delta F_r^2\left({\alpha }_l\right)}}}$$

, determine the diagnostic signs from the ratio $$J_i=\frac{\mathrm{one}}{n}{\displaystyle \sum _{l=\mathrm{one}}^n\left\{\mathrm{one}-{\left[{\displaystyle \sum _{j=\mathrm{one}}^k\Delta {\widehat{P}}_{ji}\left({\alpha }_l\right)\cdot \Delta \widehat{F}\left({\alpha }_l\right)}\right]}^2\right\}}$$

, i = 1, ..., m, at the minimum of a diagnostic sign, the faulty block is determined.

Images