Method for identification of linearized dynamic object
 Device for measuring two-dimensional distributions of random processes / 2253892Device has ADC, address multiplexer, adder, AND element, OR element, two memory blocks, quality control block, division block, indication block, count number counter, reverse counter, control block, quality control block. |
 Device for determining characteristics of a random process / 2253147Device has buffer memory register, pulse generator, switches, register, commutators, pulse counter, inversions number counter, comparison circuit, AND elements group, subtraction elements group, scale amplifiers group, adders group, delay elements groups, delay elements, cycles counter, OR elements group, reverse value computation blocks group, square-ware generators group. |
 Device for measuring distributions of random processes / 2249851Device has ADC, address multiplexer, memory block, combination adder, division block, counts number counter, control block, quality control block, indication block. |
 Method for identification of linearized dynamic object / 2256950On basis of discontinuous measurements of input x(t) and output y(t) signals of object with discretization step Δt ranges are determined according to formula: [x(nΔt)-εx,x(nΔt)+εx],[y(nΔt)-εy,y(Δt)+εy], where n=0, 1, 2,..., and εx, εy - values of limit allowed errors of used measurement means, interval values of input and output signals are sent to continuous division identifier, on which continuous division is produced with several interval coefficients, on basis of which interval discontinuous transfer function is restored and also predicting model, and interval model values of output object signal are determined. |
 Imitation equipment for testing of receiving equipment of communication lines with frequency, time and code division of channels / 2277308Imitation equipment comprises serially connected noise-resistant (NR) coder, modulator, summator, converter, attenuator, and also noise generator and generator of pseudorandom sequence, outputs of which are connected to the second and third inputs of summator accordingly, personal computer, which comprises module of buffer accumulation with input-output high-speed device (IOHSD) and block of software. IOHSD output is connected to input of NR coder, and outputs of NR coder, modulator, summator and attenuator via controlled article are connected to the second inputs of IOHSD by the third inputs of IOHSD, which are inputs of outer signal from other devices, including actual signal. |
 On-line calibration method / 2280270Proposed method includes process data acquisition, processing of acquired data with aid of mathematical model to obtain quality prediction, processing of this prediction by means of independent dynamic transfer function to generate two intermediate signals, saving of these signals as function of time, extraction of two intermediate signals from former minimal and maximal values during real and verified quality measurements within time interval, calculation of deviation as difference between actual confident measurement and zone enclosed between probable maximal and minimal predictions, and repetition of these stages in case absolute value of deviation obtained equals zero or in case absolute value of deviation is higher than zero. |
 Method for monitoring and controlling a technological process / 2289837Method contains following operations: independent values being observed {G1(t),...Gp(t)} are measured; by means of prediction model M or a line of models, input variables of which contain independent values being observed, estimate Res(t)=M(G1(t),...Gp(t)) of result R(t) is performed; by means of application of control rule L, input variable of which is estimate result Res(t), new given values {C1(t+1),... Cn(t+1)}=(Res(t)), are computed, useable up to moment t+1; and values {C1(t),... Cn(t)} are replaced with values {C1(t+1),... Cn(t+1)}, while prediction model is a statistic correcting model. |
 Device and method for controlling technical plant, which contains a set of systems, in particular, electric power plant / 2313815In the method corresponding to invention, and also in corresponding device for controlling technical plant, improvement of dynamic model is provided for at least one system of technical plant during operation of system by means of algorithm based on artificial intelligence. |
 Generation of sequence of operations by complex analysis on basis of single well predictive mode-modular dynamic tester (swpm-mdt) / 2336567Invention is related to computer system, which is based on software of single well predictive model (SWPM). The first specific sequence of operations is automatically created, which consists of the first multitude program modules, in response to the first set of user tasks, and the first specific sequence of operations is automatically executed in response to the first set of input data for creation of the first target product, and the second specific sequence of operations is automatically created, which consists of the second multitude program modules, in response to the second set of user tasks, and the second specific sequence of operations is automatically executed in response to the second set of input data for creation of the second target product, in which target product is three-dimensional model of collector response. |
 Model forecasting control of processes of regulating air pollution / 2379736Invention relates to control of technological processors. A controller of operation of a system for regulating air pollution, which controls emission of pollutants, has several technological parametres (MPP). One or more MPP are a controlled technological parametre (CTPP), and one of the MPP is volume of pollutant (AOP) emitted by the system. The given value of AOP (AOPV) is a target function or the limit for the actual value (AV) of the emitted AOP. The controller includes either a process model based on a neural network or a process model based on a non-neural network, which is the relationship between each CTPP and the emitted AOP. The control processor can have logic for forecasting based on the model of how change in the current value of each CTPP affects the future AV of the emitted AOP, selecting one change in one CTPP based on the forecast effect of that change on AOPV, and direct control of one CTPP in accordance with the selected change for that CTPP. |
 Device to model procedure of complex dynamic object recognition in time interval / 2427873Principles of the stated invention consist in modelling recognition procedure and are reduced down to implementation of the principle of non-final decision making by assessment of expected action by calculation of number of switches in a subunit of faults detection on a time interval. The device is realised by coupling of a multi-channel device of matrix structure with feedback and a device for monitoring and linearisation of transfer ratios of multi-channel converters. |
 Simulator complex for nc machines / 2438156Existing simulator complex for numerically controlled (NC) machines additionally includes: a loading mode unit, an operational unit for generating elastic deformation forces, a numerically controlled machine for recording elastic deformation forces, an operational unit for generating elastic deformation simulating forces, a cutting force component switch, operational units for generating the actual size of the component on each coordinate. |
 Control and/or regulation method of industrial process / 2444042Method involves the stages at which: physical mathematical model of industrial process is formed, by means of which there calculated are control parameters for control or regulation of industrial process; at manufacture or processing of a product there determined is some number (M) of measured values (TF-TH); model is corrected with some number (M) of primary correcting coefficients (k1); at that, number (M) of primary correcting coefficients (k1) is equal to number (M) of measured values (TF-TH); at that, model is corrected with some number (N-M) of secondary correcting coefficients (k2). |
|
Device for measuring distributions of random processes / 2249851 Device has ADC, address multiplexer, memory block, combination adder, division block, counts number counter, control block, quality control block, indication block. |
|
Device for determining characteristics of a random process / 2253147 Device has buffer memory register, pulse generator, switches, register, commutators, pulse counter, inversions number counter, comparison circuit, AND elements group, subtraction elements group, scale amplifiers group, adders group, delay elements groups, delay elements, cycles counter, OR elements group, reverse value computation blocks group, square-ware generators group. |
|
Device for measuring two-dimensional distributions of random processes / 2253892 Device has ADC, address multiplexer, adder, AND element, OR element, two memory blocks, quality control block, division block, indication block, count number counter, reverse counter, control block, quality control block. |
|
Method for identification of linearized dynamic object / 2256950 On basis of discontinuous measurements of input x(t) and output y(t) signals of object with discretization step Δt ranges are determined according to formula: [x(nΔt)-εx,x(nΔt)+εx],[y(nΔt)-εy,y(Δt)+εy], where n=0, 1, 2,..., and εx, εy - values of limit allowed errors of used measurement means, interval values of input and output signals are sent to continuous division identifier, on which continuous division is produced with several interval coefficients, on basis of which interval discontinuous transfer function is restored and also predicting model, and interval model values of output object signal are determined. |
 Method for separating trend using method of sliding trend estimates multiplication of its single source realization and device for realization of said method / 2257610Device has physical value measurements results storage block, delay block, averaging-out block, control block, clock pulse generation block, block for approximation using method of least squares, block for storing trend estimates. |
 Statistical analyzer of quality and recording of electric power flow / 2260842Device has current input clamp and mating input clamp, current counter with inbuilt pulse sensor, converter of alternating voltage to direct voltage, analog=digital converter, register, digital memory block, pulse counter, selection pulse generator, second and first D-triggers, first, second and third and fourth AND elements, SR-trigger, OR element, clock pulse generator, pulse distributor. |
 Device for classification of digital signals order / 2268485Device has analog-digital converter, two memory block, n comparators, decoder, n counters. |
 Probability device / 2276402Probability device contains indicator of random series 1, block for forming non-integer indicator values 2, correction block 3, block for forming values of matrix 4, control block 5, threshold devices block 6, block for forming indicator values 7, clock pulses generator 8, DENY element 9, AND elements block 10, memory block 11, decoder 12, time setting block 13, OR element 14, block 15 for increasing trustworthiness. Device makes it possible to model controllable semi-markov circuits with high trustworthiness with consideration of controlling effects, and dynamically changes threshold values of states, set both numerically and qualitatively, and untrustworthily, due to serial comparison of source data, received as binary code; taking of decision is possible about their mathematical nature and also transformation of source data in block 15, given in incorrect manner, to form, useable for parametric modeling procedure realization. |
FIELD: cybernetics.
SUBSTANCE: on basis of discontinuous measurements of input x(t) and output y(t) signals of object with discretization step Δt ranges are determined according to formula: [x(nΔt)-εx,x(nΔt)+εx],[y(nΔt)-εy,y(Δt)+εy], where n=0, 1, 2,..., and εx, εy - values of limit allowed errors of used measurement means, interval values of input and output signals are sent to continuous division identifier, on which continuous division is produced with several interval coefficients, on basis of which interval discontinuous transfer function is restored and also predicting model, and interval model values of output object signal are determined.
EFFECT: higher efficiency, higher precision, higher trustworthiness, broader functional capabilities.
4 dwg
The invention relates to the technical Cybernetics and is intended for use in the method of the current object identification in real time, aimed at increasing the degree of automation of the process.
Known equivalent means of identification (Bochkov A.F., Nguyen Viet dung. Identification of nonlinear dynamic objects on interval of the experimental data / Coll. scientific papers №2 “Devices and device automation, computing, electronics and optoelectronics”. / Smolensk, 1992. - p.44-54), which is the dimension of input-output values of the object, then select the model order based on the known a priori estimation of the time-memory object and the step size of the discretization, the approximation of the object is truncated near Volterra or orthogonal system of functions Laguerre, issued a linear equation of the output object.
The disadvantages of this method of identification:
- not considered instrumental measurement errors, rounding errors, quantization errors in the presence of ADC errors due to the finite word length of the computer, etc.;
- the need for a priori estimation of the time of memory identified object, i.e. a preliminary choice of the model order;
- Robin test models;
- the use of the method of the search for parameter values is istemi Laguerre filters;
- drafting tables with values of the equation coefficients output in relation to the chosen structure and parameters of model building, selection of the most reliable values of the coefficients of the equation.
- the role of modeling errors associated with the model view, Taylor series, using the Laguerre filter system;
- the coefficients of the model are point values.
Closest to the proposed method is a method of identifying a linear feature (patent RF №2146063, IPC G 05 In 17/02, published 27.02.2000), the essence of which consists in the following: the results of measurements of input and output signals at evenly spaced intervals with a sampling increment Δ t served on the ID of the continuous fraction, then compute the discrete transfer function of the object as the ratio of the Z-transforms of the output and input signals of the object according to the formula:
To obtain the discrete transfer function (1) apply the modified algorithm Vuelveme, which allows you to use continued fractions to automatically determine the structure and unknown parameters of the model, and also to eliminate the procedure of Robin test models. To do this, use sequential processing of input and output signals of the object is of the formula:
prior to the execution of the rules stop, where α0n=x(nΔ t) is a sequence of discrete samples of the input object, α1n=y(nΔ t) is a sequence of samples of the output of the object, m=2, 3, 4,... , n=0, 1, 2,... .
Having a discrete transfer function in the form of a continuous shot and turning it into fractional-rational function
where aibjthe parameters of the model object
moving from this expression for the predictive model in the form of differential equations
where x(kΔ t) is the signal value at the input of the object in the k-th step; y(kΔ t) is the signal value at the output of the object in the k-th cycle.
The equation (4) allows to recover the values of the model signal y(kΔ t) at the output of the model.
A significant drawback of this method is that when you build a discrete model of the object does not account for the errors inherent in a single source the measured values, the input-output signals. Measuring discrete input-output signals are produced, starting with a single rounded to the original values, and the linear spacing between the discrete values of the signals perform in a single curve. Measurement errors, modeling, rounding contribute most significant distortion in the values of input-output the data values, and, therefore, the use of the described method can lead to incorrect estimates of the model parameters and substitution of (distorted) structure prediction of the model object. Thus, the authentication method does not take into account the accuracy of the measuring equipment.
The invention seeks structurally-parametric identification of linear object in a certain way specified value of the measured input-output signals of the object to automatically determine the structure and unknown parameters of the mathematical model of the object, improving the quality and reliability of simulation results of the control object, and on that basis to determine the development processes of the object during its operation.
The problem is solved by a new method for the identification of linearized object that includes the definition of the discrete experimental values of the input x(t) and output y(t) signals of the object with discretization step Δ t and consistently supply the ID of continuous fractions with subsequent restoration of the discrete transfer function and the prediction model of the dynamic object and the definition of the model values of the output signal of the object, which offers after determining the values of the input and output signals of the object to perform posttrainintervalnom their values according to the dependencies:
[x(nΔ t)-εxx(nΔ t)+εx],
[u(nΔ t)-εyat(nΔ t)+εy],
n=0, 1,... ,
where εxand εy- the maximum permissible error applicable measuring input and output signals,
the ID of continuous fractions to obtain continuous fraction with interval coefficients, to restore the interval of the discrete transfer function and the prediction model of the object on the interval coefficients, determination of model values of the output signal of the object to produce in the interval values that are limited to the two prediction functions with real coefficients, defined by the limit values, permissible error of measuring.
The implementation of the method is illustrated in the block diagram (figure 1), which contains:
unit 1 identification object;
unit 2 measurement and generation interval data input;
unit 3 measurement and generation interval data output;
unit 4 ID interval continuous fractions;
unit 5 recovery interval discrete transfer function;
unit 6 recovery interval prediction model;
unit 7 the selection boundary differential equations.
Fixed input signal x(nΔ t)is fed to the input of block 1 of the identification object and the input unit 2 measurement and generation interval data of the input signal. The output signal y(nΔ t) is fed to the input unit 3 measurement and generation interval data on the output signal. Formed on the basis of discrete point measurement interval of values of the input and output signals to the input unit 4 ID interval continuous fractions. Unit 4 converts an interval of values of the input and output signals in an identity matrix and forms a continuous fraction with interval coefficients. The coefficients of the continuous fraction is fed to the input of block 5 of the recovery interval of the discrete transfer function. Next, the parameters of the resulting model is fed to the input of block 6 recovery interval prediction model, which defines the interval model values of the output signal of the identification object. The parameters of interval models come next to the input unit 7 allocation boundary differential equations in which there are two prediction functions with real coefficients, limiting the received interval set. The predicted values of the output signal of the object are limited to these two functions multiple values.
The proposed method is as follows. According to the results of measurements of the input and output of signals from multiple source in is deasie time sampling increment Δ t build the intervals [x(nΔ t)-εxx(nΔ t)+εx] and [y(nΔ t)-εy, y(nΔ t)+εy], n=0, 1,... where εxthat εy- the maximum permissible error of measuring input and output signals are determined from experimental data. Then apply the interval modified method Vuelveme for approximation of continuous fractions model transfer function object with interval coefficients. For this calculation is determined by identifying the matrix:
in which 0 is the string contains the intervals measured input values: a0n=x(nΔ t)-εxb0n=x(nΔ t)+εx; 1-row contains the interval of output values: a1n=y(nΔ t)-εyb1n=y(nΔ t)+εyn=0, 1,... , and the elements [amnbmn] consistently determined by relations analogous to (2)that in the interval case have the form:
where the boundaries of the intervals [amnbmn] are defined as follows:
m=2, 3, 4,... , n=0, 1, 2,...
Rule of stopping the calculation of the matrix elements (5) is the appearance lines, the intervals which contain num is 0.
The zero elements of column identifies the matrix (5) generate private numerators correct-fractions with interval coefficients:
where z is a variable consistent Z-transformation z=esΔt. The line number, all intervals which contain the number 0, allows to identify the function.
If some of the k-th row of the matrix (5) a nite number g of the first interval contains 0, then is a left shift of all elements of this string in r positions until in the zero column interval not containing 0, and then continues the calculation of the matrix elements according to the relations (7)-(8) to account for the shift. When restoring the correct S-fraction (9) the corresponding k-th row, the numerator is multiplied by z-(r+1)instead of the z-1.
Received continuous fraction is converted to an interval of the discrete transfer function of the object:
where,
;
,
After receiving interval of the discrete transfer function of the object and interpreting z-1as the operator of the inverse of the time difference, go to a prediction model in the form of a differential equation with interval coefficients, which allows the t to restore the interval values of the model output models:
where y(n)=y(nΔ t) and y(n-j)=y([n-j]Δ t) is the model prediction values of the function at the points of withdrawal of discrete samples nΔ t, n=0, 1, 2,... , x(n-i)=x([n-i]Δ t) - values are discrete samples of the input signal. Can be used as built earlier interval and point discrete values of the input signal, for example, the average sample value of the sample x(0Δ t), x(1Δ t), x(2Δ t),... , x((k-1)Δ t), where k is the number of measured values of the input signal.
The obtained differential equation can be further introduce two boundary differential equations with real coecients ymin(n) and ymax(n)forming intervals of the form:
The obtained interval model is interpreted as follows: all measured and expected values of output variables lie within the generated intervals (12). If the actual values of the output variable outside built by the first measurement intervals, we can say that the object changed its behavior and properties.
The degree of inaccuracy interval model (11), which is the width of the resulting interval (12)depends on the selected sampling Δ t and the values of maximum permissible errors εxand εyused measurement tools. Paul is an increase of more accurate prediction interval of the model (11) is possible when changing the sampling step Δ t and choosing a more accurate means of measuring the input and output signals of the identified object. The interval of values for the variables x(nΔ t) leads to the extension of the intervals [ymin(n), ymax(n)], n=0, 1, 2,... than using point estimates of input values x(nΔ t).
Example 1.
Let the object identification - steam power plant, the transfer function is described by an aperiodic link 2-th order:
To the input of the object will provide a pulse signal:
Then the output object, a signal is generated
y(t)=0.666667e-0.454545t-0.666667e-1.428571t.
Consider the case of precisely measured values of input and output signals. Make the dimension of the input x(t) and output y(t) with sampling interval Δ t=0.8 C. Let the maximum permissible errors of measurement tools known: εx=0.1% and εy=0.05% of the upper limit of measurements: εx=0.001 and ε y=0.000127.
Applicable interval modified method Vuelveme for the approximation of the continuous fraction model interval transfer function. For this we define an identity matrix (5):
All elements in the fifth row of the matrix contain the number 0, therefore, calculated the e following matrix rows on this line stops. 1-th line is the left-shift by 1 the element that caused the initial value u(0)=0. On the basis of zero elements of matrix column approximate the continuous shot interval of the discrete transfer function of the object. Since u(0)=0, then the first private numerator of the fraction is the multiplier z-1:
Thus, the interval of the discrete transfer function of the fractional-rational expressions. Turning to the time domain, the received discrete interval prediction model:
y(n)=[0.250447, 0.251203]× (n-1)+[0.966286, 1.063411]y(n-1)+[-0.265650, -0.179497]y(n-2),
n=0, 1, 2,...
Highlighting the boundary functions, we obtain:
ymin(n)=0.250447x(n-1)+0.966286y(n-1)-0.265650y(n-2),
ymax(n)=0.251203x(n-1)+1.063411y(n-1)-0.179497y(n-2),
n=0, 1, 2,...
Figure 2 shows the measured values of the output signal and the boundary values of functions. In building the model was used only a few discrete samples of the input and output signals, and they, as well as the expected future values of the output signal y(nΔ t)lie in the interval [ymin(n), ymax(n)].
Example 2.
Object identification is a correcting device AC passopisciaro type specified by the transfer function of the form:
Input object is served a single step signal:
Perform the measurement of noisy input and output variable of the object with discretization step Δ t=7 C. Imagine the measured values of the input variable in the form:
x(nΔ t)=1(nΔ t)+a(nΔ t),
where a(t) is white noise with mean 0 and standard deviation 0.1, and the value of the output signal measured at the reference points in the form:
y(nΔ t)=3-1 .8e-0.2t+b(nΔ t),
where b(t) is white noise with mean 0 and standard deviation 0.2. Consider maximum permissible error of measurement of input values εx=1% of the upper limit of the measurement, the measurement error of the output values set equal to εy=0.1% of the upper limit of the measurement.
Expect an identity matrix:
The calculation of matrix elements is terminated on the fourth line. Since u(0)≠ 0, then the first row of the matrix there is no shift elements, as in the first private numerator continuous fraction no additional multiplier z-1. The zero elements of the column determines the interval of the discrete transfer function
Discrete prediction model takes the form of the next interval differential equations:
y(n)=[1.138322, 1.173593]x(n)+[1.248957, 1.442291]x(n-1)+[0.05321, 0.285863]y(n-1),
n=0, 1, 2,...
Allocated boundary prediction functions:
ymin(n)=1.138322x(n)+1.248957x(n-1)+0.085321y(n-1),
ymax(n)=1.173593x(n)+1.442291x(n-1)+0.285863y(n-1),
n=0, 1, 2,...
Figure 3 and figure 4 shows the measured values of the output signal y(0Δ t), y(1Δ t),... , y(19Δ t), participated in the construction of interval models, boundary functions ymin(n) and ymax(n), and future values of the output signal y(20Δ t), y(21Δ t),... , y(35Δ t). When calculating the values of the prediction functions ymin(n) and ymax(n) the values x(n) used average sample of 20 of the first measured values of the input signal. Figure 3 and 4 shows also the exact values of the output signal y(t) and the model obtained normal, not modified interval method Viskovatov. Figure 3 and 4 shows that when using the method Viskovatov happened distortion model: graph prediction function does not display the actual values of the output signal and does not allow a more reliable estimate of the position of the future values of the output signal of the object. Obviously, the expected value of y(20Δ t), y(21Δ t),... are obtained in the intervals [ymin(n), ymax(n)]. That is, the obtained interval model builds credible intervals for future values of the output signal y(nΔ t), allowing you to more effectively control the path and to diagnose the state of the object.
1. The method of identification of the linearized dynamic object that includes the definition of discrete values of the input x(t) and output y(t) signals of the object with discretization step Δt and consistently supply the ID of continuous fractions with subsequent restoration of the discrete transfer function and the prediction model of the dynamic object and the definition of the model values of the output signal of the object, characterized in that the determination of an experimental discrete values of input and output signals of the object is performed, starting from several initial values of the signal within the limits defined by the expression
[x(nΔt)-εxx(nΔt)+εx];
[u(nΔt)-εyat(nΔt)+εy];
n=0, 1,...,
where εxand εy- the maximum permissible error applicable measuring input and output signals,
the ID of the continuous fraction receive continuous fraction with multiple interval coefficients, the recovery interval of the discrete transfer function and the prediction of the model object produced by interval coefficients, determination of model values of the output signal of the object is produced in the interval values that are limited to the two prediction is functions with real coefficients, set the limits of permissible errors of measurement.