# Method to search for faulty block in discrete dynamic system

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.

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

There is a method of finding a defective block in the dynamic system (Patent for invention №2439648 from 10.01.2012 to application number 2010142159/08(060530), MKI^{6}G05B 23/02, 2012), based on the multiple integration of the output signal of the block with weights_{l}- material constant, l is the number of constants.

The disadvantage of this method is that it enables the detection of defects only in a continuous dynamic system.

The closest technical solution (prototype) is a way of finding a defective block in the discrete dynamical system (Patent for invention №2444774 from 10.03.2012 on application No. 2011101271/08(001575), MKI^{6}G05B 23/02, 2012).

The disadvantage of this method is that it enables the detection of defects with low visibility, that is, has low noise immunity.

Technical problem on which this invention is directed, is to improve the noise immunity of the method of diagnosis of discrete automatic control systems by improving the distinctiveness of defects. This is achieved by applying many the times of calculation of integral estimates of the dynamic characteristics for several different values of the parameter of integration α_{
1}α_{2}...α_{n}.

This object is achieved in that pre-register response known good discrete-time system f_{j}(t), j=1, 2..., k for N discrete quanta diagnosis t∈[1,N] with discrete constant step Ts to the observation interval [0,T_{k}] (where T_{k}=T_{s}·N) in the k control points, and repeatedly define (simultaneously) integral evaluation of the output signals_{l}, which at the time of the test signal to the input of a discrete system with a nominal characteristics simultaneously begin the discrete integration of the control signals in increments of Ts seconds for n parameters of integration in each of the k control points with weights^{}increments of Ts seconds for n discrete blocks of integration, the output signals k·n blocks multiplication served on inputs k·n blocks of discrete integration step Ts seconds, the integration is completed at time T_{to}obtained by discrete integration of the evaluation of the output signals_{
l}and the test signal x(t), the resulting discrete integration of the evaluation of the output signals for each of the k control points, each of the m test variance and each of the n parameters of the discrete integration

replace the system with a nominal characteristics controlled at the input of the system serves a similar test signal x(t), define the integral evaluation of the signals controlled discrete system for the k control points and n parameters of the discrete integration α_{l}:_{}F_{j}(α_{l}), j=1, ..., k; l=1, ..., n define the deviation of the integral estimates of the signals controlled discrete system for the k control points and n parameters of the discrete integration of the nominal values of ∆ F_{j}(α_{l})=F_{j}(α_{l})-F_{l}), j=1, ..., k; l=1, ..., n, define the normalized Delta values of the integral estimates of the discrete system for the n parameters of the discrete integration of the ratio

determine diagnostic characteristics for n parameters of the discrete integration of the ratio

the minimum values of the diagnostic characteristic to determine a defective unit.

Thus, the proposed method of finding the defective block is to perform the following operations:

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

2. Pre-determine the testing time T_{To}≥T_{PP}where T_{PP}the time transition of the discrete system. Transition time estimate for the nominal values of the parameters of the dynamic system.

3. Define n parameters that are multiples of 5/T_{k}multiple signal integration.

4. Record the number of control points k.

5. Pre-determine the normalized vector_{l}what do paragraphs 6-10.

6. Serves the test signal (a single step, linearly increasing, rectangular pulse and so on) to the input of the control system with a nominal characteristics. Fundamental limitations on the type of input test the impact of proposed method does not.

7. Record the response of the system f_{j}(t), j=1, 2, ..., k on the interval t∈[1,N] with a discrete step Ts seconds, the observation interval [0,T_{k}] (where T_{k}=T_{s}·N) in the k control points define discrete integral evaluation of the output signals_{l}with discrete weights_{to}obtained by discrete integration of the evaluation of the output signals F_{j}(α_{l}), j=1, ..., k; l=1, ..., n register.

8. Define the integral evaluation of the signals of the discrete model for each of the k control points and each of the n values of the discrete integration α_{l}obtained in the course of the trial deviations couples who metres of each of the m blocks,
why alternately for each block in the discrete-time dynamical system is administered trial deviation parameter of the discrete transfer function and perform item 7 for the same test signal. The resulting discrete integration of the evaluation of the output signals for each of the k control points, each of the m test variance and each of the n parameters of the discrete integration

9. Determine the deviation of the integral of the estimated signals of the discrete model, the resulting trial deviations of the respective blocks ΔP_{ji}(α_{l})=P_{ji}(α_{l})-F_{j}(α_{l}), j=1, ..., k; i=1, ..., m; l=1, ..., n.

10. Define the normalized Delta values of the integral estimates of signals discrete model, the resulting trial deviations of the respective units according to the formula:

11. Replace the system with a nominal characteristics controlled. At the input of the system serves a similar test signal.

12. Define the integral evaluation of the signals controlled discrete system for the k control points and n parameters integration

13. Determine the deviation of the integral estimates of the signals controlled discrete system for the k control points and n parameters of integration from the nominal values ∆ F_{j}(α_{l})=F_{j}(α_{l})-F_{j}(α_{l}), j=1, ..., k; l=1, ..., n.

14. Calculate the normalized values of the variance of the integral estimates of the signals controlled discrete system according to the formula:

15. Calculate the diagnostic signs of a defective block (with n parameters of integration) by the formula (3).

16. The minimum values of the diagnostic sign determine the defective block.

Consider the implementation of the proposed method of finding the defect for discrete-time systems, block diagram of which is presented on the figure (see Fig. Block diagram of the diagnostic object).

Discrete transfer function block:/p>

rated: K_{1}=5; Z_{1}=0.98; K_{2}=0.09516; Q_{2}=0.9048;_{3}=0.0198; Q_{3}=0.9802. When you search for a single structural defect in the form of deviation of the gain by 20% (k_{1}=4) in the first link, when the flow speed of the test input signal of unit amplitude and the integral of the estimated signals for parameters α_{1}=0.5, α_{2}=0.1, α_{3}=2.5 and T_{to}=10, using three control points located at the outputs of blocks using a trial deviation to a value of 10%, the obtained values of diagnostic signs by the formula (3): J_{1}=0.2511; J_{2}=0.9382; J_{3}=0.5738. Analysis of the values of the diagnostic signs shows
what the defect is in the first block of the controlled system is correct. It should be noted that the method is operable at larger values of the test deviations (10-40%). The limitation on the amount of trial deviation is the need to preserve the stability of models with a trial deviations.

Modeling of finding defects in the first block (in the form of reducing the parameter k_{1}20%) leads to the calculation of diagnostic features in three dimensions of integration (α_{1}=0.5, α_{2}=0.1 and α_{3}=2.5) according to the formula (3): J_{1}=0, J_{2}=0.8254, J_{3}=0.0898. The appearance of the defect: ΔJ=J_{3}-J_{1}=0.0898.

For comparison, see diagnostic signs of a defective block (in the form of reducing the parameter k_{1}20%) with one parameter of integration α=0.5: J_{1}=0; J_{2}=0.7843; J_{3}=0.0717. The appearance of the defect ΔJ=J_{3}-J_{1}=0.0717.

The results show that the actual appearance of finding defects by this method above, therefore, will be higher and the robustness of the method.

Modeling of finding defects in the second and third blocks for the object of diagnosis, with the same parameters α and integration with unit step input signal gives the following values of diagnostic features:

The model is the formation process of finding defects in the second block (in the form of reducing the parameter k_{
2}20%) leads to the calculation of diagnostic features in three dimensions of integration (α_{1}=0.5, α_{2}=0.1 and α_{3}=2.5) according to the formula (3): J_{1}=0.8387; J_{2}=0; J_{3}=0.7703. The appearance of the defect: ΔJ=J_{3}-J_{1}=0.7703.

For comparison, see diagnostic signs of a defective block (in the form of reducing the parameter k_{2}20%) with one parameter of integration α=0.5: J_{1}=0.7845; J_{2}=0; J_{3}=0.7481. The appearance of the defect ΔJ=J_{3}-J_{1}=0.7481.

Modeling of finding defects in the third block (in the form of reducing the parameter k_{3}20%) leads to the calculation of diagnostic features in three dimensions of integration (α_{1}=0.5, α_{2}=0.1 and α_{3}=2.5) according to the formula (3): J_{1}=0.09889; J_{2}=0,7714; J_{3}=0. The appearance of the defect: ΔJ=J_{3}-J_{1}=0.09889.

For comparison, see diagnostic signs of a defective block (in the form of reducing the parameter k_{3}20%) with one parameter of integration α=0.5: J_{1}=0.07173; J_{2}=0.7481; J_{3}=0. The appearance of the defect ΔJ=J_{3}-J-=0.07173.

The minimum value of the diagnostic sign in all cases correctly points to the defective block.

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

The way of finding a bad block in a discrete dynamicsystems,
based on the fact that record the number m of blocks included in a system, determine the testing time T_{To}≥T_{PP}determine the parameter integral transforms of the signals from the relation_{To}]as the dynamic characteristics of the system using integral estimates for real values of α Laplace variable, fixed number k of control points system, pre-register response known good discrete-time system f_{j}(t), j=1, 2, ..., k for N discrete quanta diagnosis t∈[1,N] with discrete constant step Ts to the observation interval [0,T_{k}] (where T_{k}=T_{s}·N) in the k control points that define the integral evaluation of the output signals F_{j}(α), j=1, ..., k of the discrete system, which at the time of the test signal to the input of a discrete system with a nominal characteristics simultaneously begin the discrete integration of the control signals in increments of Ts seconds in each of the k control points with discrete weights_{to}obtained by integrating the evaluation of the output signals**,**k; i=1, ..., m register determine the deviation of the integral of the estimated signals of the discrete model, the resulting trial deviations of the respective blocks ΔP_{ji}(α)=P_{ji}(α)-F_{j}(α), j=1, ...**,**k; i=1**,**..., m, define the normalized Delta values of the integral estimates of signals discrete model, the resulting trial deviations of the respective units according to the formula_{j}(α)=F_{j}(α)-F_{j}(α), j=1, ..., k, compute the normalized values of otklonenie the integral estimates of the signals controlled discrete system according to the formula_{l}determine the integral evaluation of the output signals F_{j}(α_{l}), j=1, ..., k; l=1, ..., n of the system, which at the time of the test signal at the input of the system with nominal characteristics simultaneously begin the integration of the control signals in each of the k control points for n parameters integration with weights_{to}obtained by integrating the evaluation of the output signals_{
l}and the test signal x(t), obtained by integrating the evaluation of the output signals for each of the k control points, each of the m test variance and each of the n parameters of integration**,**k; i=1, ..., m; l=1, ..., n register determine the deviation of the integral of the estimated signal model, the resulting trial deviations of the respective blocks ΔP_{ji}(α_{l})=P_{ji}(α_{l})-F_{j}(α_{l}), j=1, ..., k; i=1, ..., m; l=1, ..., n, define the normalized variance of the integral of the estimated signal model, the resulting trial variance parameters of the corresponding blocks of the ratio of

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