# Method of searching for faulty module in dynamic system

FIELD: information technology.

SUBSTANCE: number of dynamic modules of a controlled system is determined, the reaction of a good system is recorded at an interval at control points and integral estimates of output signals of the system are determined. System signals are transmitted to the first inputs of multiplier units; an arithmetic mean value of moduli of signal time derivatives is transmitted to second inputs of the multiplier units; output signals of the multiplier units are transmitted to inputs of integration units; integration is completed at a certain moment in time; output signal estimates obtained from integration are recorded; simultaneously, integral estimates of signals of models are determined for each of the control points, obtained as a result of test deviations of parameters of each of the modules, for which a corresponding test deviation of parameters is introduced into each model for the dynamic system module. Deviations of integral estimates of signals of the model, obtained as a result of test deviations of parameters of corresponding modules, are determined. Standardised values of deviations of integral estimates of signals of the model are determined. Standardised values of deviations of integral estimates of signals are determined. Diagnostic features are determined and a faulty module is determined from the minimum value of the diagnostic feature.

EFFECT: increased noise-immunity of diagnosing continuous automatic control systems.

1 dwg

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

The known method of dynamic control block the system control (Patent RF №2136033, MKI^{6}G05B 23/02, 1999), based on the integration of the output and input signals of the block with a weight of e^{-αt}where α is a real constant.

The disadvantage of this method is that its application for control of multiple units of a control system of an arbitrary structure leads to the necessity of integration of input and output signals of each of the controlled block.

The closest technical solution (prototype) is a way of finding a bad block in a dynamic system (a Positive decision from 12.07.2010, for a patent on the invention under the application №2009123999/08(033242), MKI^{6}G05 23/02, 2010).

The disadvantage of this method is that it involves the integration of special test signals using exponential weighting function and enables the detection of defects with low visibility, that is, has low noise immunity.

Technical problem on which this invention is directed, is to expand the functionality of the method by applying the working diagnosis (without using testoval the impact), increasing the noise immunity of the method of diagnosing a continuous automatic control systems by improving the distinctiveness of defects and reduction of hardware costs for the calculation of the weighting function. This is achieved by replacing the exponential weight function, which is the arithmetic mean of modules derived time signal system with the nominal characteristics of the controlled system and models with pilot deviations.

This object is achieved in that a fixed number m dynamic blocks of the controlled system, record the reaction of a known good system f_{j}(t), j=1, 2,..., k on the intervalin the k control points, and define the integral evaluation of the output signals F_{j}(d), j=1,...,k system, which at the time of submitting a test or working input system with a nominal characteristics simultaneously begin the integration of the signal for each of the k control points with weight function equal to the average value of modules derived its signals at the test points, where the averaging is done according to the number of control points. For this purpose, the first inputs of the k blocks the multiplication signal system, on the second input units of the multiplication serves the arithmetic mean value m is a module derived time signal,
the output signals of the k blocks multiplication served on inputs k blocks of integration, integration completed at time T_{to}obtained by integrating the evaluation of the output signals F_{j}(d), j=1,...,k register, simultaneously determine the integral evaluation of the signals m models for each of the k control points obtained in the course of the trial deviations of each of the m blocks, each i-th model enter the appropriate trial deviation for the i-th block of the dynamic system and are integral evaluation of the output signals of the systems trial variance when the same test or operating signal x(t), obtained by integrating the evaluation of the output signals for each of the k control points, each of the m test deviations P_{ji}(d), j=1,...,k; i=1,...,m register, simultaneously to the input of the controlled system serves a test or working signal x(t), define the integral evaluation of the signals of the controlled system for the k control points F_{j}(d), j=1,...,k, the obtained register values, determine the deviation of the integral of the estimated signal model, the resulting trial deviations of the respective blocks

Δ_{ji}(d)=R_{ji}(d)-(F_{j}(d), j=1,...,k; i=1,...,m, define the normalized Delta values of the integral estimates of the signal is s models,
the resulting trial deviations of the respective blocks

determine the deviation of the integral of the estimated signals of the controlled system for the k control points ∆ F_{j}(d)=F_{j}(d)-(F_{j}(d), j=1,...,k, define the normalized Delta values of the integral estimates of the signals of the controlled system

determine diagnostic characteristics:

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

The essence of the method consists in the following.

The method is based on the use of pilot deviations of the model parameters of a continuous dynamical system. To obtain diagnostic features dynamic elements are integral evaluation on the time interval T_{k}in the k control points

The weight function in equation (4) in the average value of the modules derived signals at the test points carries information about the importance of time from the point of view of the rate of change of the signals in all the control points. More than the average rate of change of the signals, the more weight is integrated output signal. Using the vector interpretation of expression (3), we write it in the next view of the

where φ_{i}(d) the angle between the normalized vector (a vector of unit length) of the variance of the integral estimates of the signals of the objectand the normalized vector (unit length) of the variance of the integral of the estimated signal modelobtained in the course of the trial deviation parameter of the i-th block.

Thus, the normalized diagnostic feature (3) represents the value of the square of the sine of an angle formed in the k-dimensional space (where k is the number of control points) normalized vectors trial variance of the integral of the estimated signal model and the real deformation of the integral estimates of the signals of the diagnostic object.

Trial deviation of the parameter block that minimizes the value of the diagnostic sign (3), indicates the presence of a defect in this unit. The region of possible values of the diagnostic characteristic lies in the interval [0,1].

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

1. As dynamic systems consider a system consisting of randomly connected m dynamic elements.

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

3. Record the number of control points k.

4. At the same time serves the test signal x(t) (unit step) or work input control system with nominal parameters, the input of the controlled system, the inputs of the m models with nominal parameters, each of which introduced a trial deviations of one block so that the i-th system introduced trial deviation in the i-th block.

5. At the same time record the response of the system with the nominal characteristics of the f_{j}(t), the response of the controlled system f_{j}(t), reaction models with a trial variance in the i-th block of p_{ji}(t) in k control points j=1, 2,..., k on the interval.

6. At the same time define the integral evaluation of the output signals F_{j}(d), j=1,...,k system with nominal characteristics of the controlled system F_{j}(d), j=1,...,k, models with a trial variance in the i-th block of P_{ji}(d), j=1,..., k; i=1,...,m (formula 4). To this effect, when the input signal is simultaneously begin the integration of the signals in each of the k control points in the system with the nominal characteristics of the controlled system, models with a trial deviations blocks with weight function equal to the average of arithmetices the mu value of modules derived signals at the test points,
where the averaging is done according to the number of control points, to which output signals of each system serves to first inputs of the k blocks multiplication on the second input units of the multiplication serves an average of modules derived signals at the test points, where the averaging is done according to the number of control points of the output signals, the output signals of the k blocks multiplication served on inputs k blocks of integration, integration completed at time T_{to}obtained by integrating the evaluation of the output signals F_{j}(d), j=1,...,k, F_{j}(d), j=1,...,k, and P_{ji}(d), j=1,...,k; i=1,...,m register.

7. Determine the deviation of the integral of the estimated signal model, the resulting trial deviations of the respective blocks

ΔP_{ji}(d)=P_{ji}(d)-(F_{j}(d), j=1,...,k; i=1,...,m.

8. Define the normalized variance of the integral of the estimated signal model, the resulting trial deviations of the respective units according to the formula:

.

9. Determine the deviation of the integral of the estimated signals of the controlled system for the k control points from the nominal values ∆ F_{j}(d)=F_{j}(d)-(F_{j}(d), j=1,...,k.

10. Calculate the normalized values of the variance of the integral estimates of signals to the control system by the formula:

.

11. Calculate the diagnostic signs of a defective block by the formula (3).

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

Because diagnostic criteria (3) have a range of possible values bounded by the interval [0,1], then the difference between the closest to the minimum characteristic and minimal sign (which indicates that the defective block) quantifies the appearance of the defect with respect to the location of the block on the block diagram, type and parameters of the transfer functions of the blocks and all of the terms of diagnosis, in which these values are diagnostic features (number and location of control points, the value of the interval T_{to}). The best appearance of defects is provided when the difference is equal to (in terms of the vector interpretation of the normalized vectors of deformation of integral transformations of the dynamic characteristics of these blocks for trial orthogonal deviations). The worst visibility - when the difference is equal to zero (in terms of the vector interpretation of the normalized vectors of deformation of integral transformations of the dynamic characteristics of these units to test deviations collinear).

Consider the implementation of the FPIC of the BA search single defect system, structural diagram of which is presented on the figure (see drawing).

Transfer function block:

;;,

where the nominal parameter values: T_{1}=5; K_{1}=1; K_{2}=1; T_{2}=1; K_{3}=1; T_{3}=5 C.

When modeling as an input signal we use a pseudo-random signal (when modeling were used unit Band-Limited White Noise in Matlab). The time control will choose T_{to}equal to 10 C.

The value trial deviations of the model parameters chosen equal to 10%.

Modeling of finding defects in the first block (in the form of reduction of the parameter T_{1}20%) leads to the calculation of diagnostic signs by the formula (3): J_{1}=0, J_{2}=0.2067, J_{3}=0.2266. The appearance of the defect: ΔJ=J_{3}-J_{1}=0.2067.

For comparison, see diagnostic signs of a defective block with exponential weight one option of integration α=0.5 (a Positive decision from 12.07.2010, for a patent on the invention under the application №2009123999/08(033242), MKI^{6}G05 23/02, 2010): J_{1}=0, J_{2}=0.7828, J_{3}=0.07399. The appearance of the defect ΔJ=J_{3}-J_{1}=0.07399.

The results show that the actual appearance of finding defects by this method is higher, therefore, you who have and robustness of the method.

Modeling of finding defects in the second block (in the form of reduction of the parameter T_{2}20%) of the diagnostic object using the differential weight and with the same input gives the following values of diagnostic features:

J_{1}=0.2752, J_{2}=0.006981, J_{3}=0.7004.

The appearance of the defect ΔJ=J_{3}-J_{2}=0.2682.

For comparison, see diagnostic signs of a defective block with exponential weight one option of integration α=0.5: J_{1}=0.7828, J_{2}=0, J_{3}=0.7462. The appearance of the defect: ΔJ=J_{3}-J_{2}=0.7462.

Modeling of finding defects in the third block (in the form of reduction of the parameter T_{3}20%) of the diagnostic object under the same conditions gives the following values:

J_{1}=0.1824, J_{2}=0.5691, J_{3}=0.003594.

The appearance of the defect: ΔJ=J_{1}-J_{3}=0.1788.

For comparison, see diagnostic signs of a defective block with one parameter of integration α=0.5:

J_{1}=0.07403, J_{2}=0.7463, J_{3}=0.

The appearance of the defect ΔJ=J_{1}-J_{3}=0.07403.

The minimum value of the diagnostic sign in all cases correctly points to the defective block, and this method in two cases out of three improves the actual appearance of defects, followed the Sabbath.) increases the immunity of the diagnosis.

In addition, the inventive method allows the diagnosis of the real functioning of the diagnostic object (working diagnosis).

The way of finding a bad block in a dynamic system, based on the fact that a fixed number m of dynamic elements included in the system, determine the testing time T_{To}≥T_{PP}use the input signal x(t) on the interval t∈[0, T_{K}]fix a number k control points in the system, record the response of the controlled system f_{j}(t), j=1, 2, ..., k, record the response of the system with the nominal characteristics of the f_{j}(t), j=1, ..., k, in the interval t∈[0, T_{K}] k control points that define the integral evaluation of the output signals of the system, which at the time of filing of the signal at the input of the system with nominal characteristics simultaneously begin the integration of the signals in each of the k control points by submitting to the first inputs of the k blocks multiplying output signals of the system, on a second input units of the multiplication serves weighting function, the output signals of the k blocks multiplication served on inputs k blocks of integration, integration completed at time T_{to}obtained by integrating the evaluation of the output signals of the register definition is given in the integral evaluation of the output signals of the model for each of the k control points,
the resulting trial deviations of each of the m blocks, and for each block of a dynamic system is administered trial deviation parameter transfer function and find the integral evaluation of the output signals of the model for the weighting function and the input signal x(t), obtained by integrating the evaluation of the output signals for each of the k control points and each of the m test register deviations, determine the deviation of the integral of the estimated signal model, the resulting trial deviations of the respective blocks ΔP_{ji}(d)=P_{ji}(d)-(F_{j}(d), j=1, ..., k; i=1, ..., m, define the normalized variance of the integral of the estimated signal model, the resulting trial variance parameters of the corresponding blocks from the relation:

define the integral evaluation of the signals of the controlled system for the k control points F_{j}(d), j=1, ..., k, define the deviation of the integral of the estimated signals of the controlled system for the k control points from the nominal values ∆ F_{j}(d)=F_{i}(d)-(F_{j}(d), j=1, ..., k, define the normalized Delta values of the integral estimates of the signals of the controlled system from the relation:

determine diagnostic characteristics from the ratio of the texts:

the minimum diagnostic characteristic to determine a defective unit, characterized in that simultaneously serves the test or working signal x(t) at the input of the system with nominal characteristics to the input of the controlled system, the inputs of the m models with nominal characteristics, each of which introduced a trial deviations of one block so that the i-th system introduced trial deviation in the i-th block, as the dynamic characteristics of the system using integral estimates for the weighting function equal to the average of the modules derived from output signals of the system at various control points, ratio

evaluation of the output signals F_{j}(d), j=1, ..., k system with nominal characteristics, which at the time of filing of the input signal at the input of the system with nominal characteristics simultaneously begin the integration of the signals in each of the k control points for the weighting function, by submitting to the first inputs of the k blocks the multiplication of the signals on the second input units of the multiplication serves an average of modules derived from output signals of the system with the nominal characteristics of the output signals k blocks multiplication served on the inputs of the k blocks in which agrilevante,
the integration is completed at time T_{to}obtained by integrating the evaluation of the output signals F_{j}(d), j=1, ..., k, register, similarly define the integral evaluation of the signals m models for each of the k control points obtained in the course of the trial deviations of each of the m blocks obtained as a result of integrated assessment of output signals for each of the k control points of each of the m test of variance P_{ji}(d), j=1, ..., k; i=1, ..., m, are used for calculation of diagnostic features.

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