SU802922A1 - Method of adaptive control of systems in uncertainty conditions - Google Patents

Description

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The invention relates to self-reactive systems and may find application in the design of control systems for multi-parameter objects under conditions of uncertainty.

A known method of adaptive control in which, over a given period of time, a signal is selected that corresponds to a change in the parameter of the process being monitored, and is used to influence the process 1 itself.

However, this method does not provide high quality control, since the adaptation occurs by comparing the parameter of the monitored process with the previous value and is not suitable for controlling non-stationary processes.

The closest in technical essence to the invention is a method of adaptive control of multiparameter objects in conditions of uncertainty, based on measurement for each system, its output signals, disturbance signals and signals corresponding to the parameters of the object and the parameters of the controls.

forming the state of the system by measuring the signals of the first multidimensional signal, generating limit control signals, measuring the control signals, generating for each parameter of the output signal of each system a statistical reference output signal, generating signals

O mismatch between the output signals of the systems and the statistical ethical output signals and use them to correct the control signals 2.

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In this method, in order to reduce the uncertainty in the current state of A. fi, the object's prehistory is used, determined by its L. conditions on the ".- 1 preceding control lines and the observed Xjt-- data associated with these H-states managers of operations in

Uncertainty arises because of incomplete knowledge of the structure of the characteristics of the control object, and, accordingly, ignorance of the a priori distribution of the P (L (X, V, V)) state and the statistical dependence of the data

observations of Hz from the states of the control object A, f and, as a result, the likelihood function Rc (Xk (i.

In the course of the operation of an object over time, the uncertainty of these characteristics is eliminated in an adaptive manner and, thus, improves the quality of control.

The disadvantage of this method is that it is designed to operate under conditions of stationary external influences and object parameters. In practice, in most cases, disturbing influences and parameters of objects are non-stationary in time. The imposition of limitations on the stationarity of controlled processes makes this method unacceptable for most of the tasks to be solved, especially for controlling large systems.

The problem of adaptive control of non-stationary processes under uncertainty conditions is not solved by known methods.

In addition, the known method does not provide quality control as it has a narrow scope, low speed and accuracy. The method is not very effective, since the adaptation of the control action is carried out without taking into account the type of disturbing effects, which does not allow efficient use of the available resource of actions. In addition, long-term accumulation of a significant history of the object is required for entering the regime, and in many cases the history should contain data for several years.

The purpose of the invention is to improve the accuracy and speed of operation, expanding the field of application, reducing the time to start-up mode when managing each system.

This is achieved by generating the multidimensional generalized signal by the first multidimensional signals of the system states and decomposing it in terms of statistically uniform signals for each output signal parameter, generating for each system signals corresponding to the parameters of the object and the parameters of control positions, signals perturbations and limit orders of the second multidimensional controls; the signal of the state is system, for which for each statistically homogeneous signal of each parameter of the output signal of the multidimensional generalized signal is formed. signal of threshold levels, compare them with the second multidimensional signals of the state of the systems, form the group of the first multidimensional signals, from which groups of signals corresponding to the object parameters and output signal parameters of the systems are determined, the first statistical reference signals are determined by them, scaled according to the signal levels corresponding to the parameters of the objects, and for each system, the second statistical reference signals are normalized by the parameters of the system’s output signal; they are compared with the output and the input signals of the system and Forray respective first and second correcting statistical Sig mismatch; for each system, the first correction statistical error signal is compared with the threshold error signal, the received signal adjusts the system control signals, measures the increments of the control signals and the signals corresponding to the measured signals of the system control increments, and the first multidimensional error signal is formed: the first multidimensional correction signal system state signal, for each system when the first corrective statistical signal is equal to zero mismatch. According to the control signals and parameter values of the output signal of systems of the same group, a second multidimensional correction signal of the FJ system state is formed.

As a rule, each large system is unique. However, this uniqueness is determined by the uniqueness of the group of heterogeneous heterogeneous objects in the lower level of the hierarchy, although these objects themselves are not unique, which makes it possible in the proposed method to simultaneously adapt a large number of systems of the same type that are part of various large systems.

We will consider each autonomous system adapted by the proposed method as a subsystem of the general adaptation system. Each tl.- subsystem has a set of acceptable values of the control action

Woo

- The disturbing effects F, which can be represented as the sum of the global ROL and local components, act on the control object and the governing body of each subsystem.

FM in + f,

where - represents the mathematical expectation of controlled and uncontrolled disturbances.

fyi- CFtJ + fFHfcnJ /

where F | cft, is a randomly controlled component of the disturbing action, variable in time with respect to the objects of the group; FHK is a randomly uncontrollable component of the disturbance; I / C - expectation

F / M-AF fAFH / f -tuFfTj,

) is the noise component of the disturbance, which may be represented by white noise.

For most systems, the compensation of local and global perturbations in accordance with these definitions requires different control actions vectors. Accordingly, the error signal can be divided into global and local components.

We will consider the local component of the error signal as the first corrective statistical error signal, and the control signals aimed at its minimization as the first control signals. Accordingly, the global component of the error signal will be considered the second corrective static error signal.

The drawing is a block diagram of an adaptation system for carrying out the proposed method.

It contains If-In subsystems. with control objects 2 y - 2 p, and. control units 3 - / -, shaper 4 classes, identification block 5, block 6, grouping, shaper 7 first statistical standards, block 8 forming second statistical standards, device 9 for determining the local mismatch component, key Yu, shaper 11 optimal process characteristics, device 12 determining the global error component, adaptive optimization block 13 and grouping block 14.

The adaptive control system works as follows. The signals associated with the parameters of the monitored output processes Xfewx, n (the index of the parameter of the output process), the controlled part of the disturbing action Fim, the signals of the parameters of the control object and the control unit p, as well as the signal of acceptable limit controls Vjo n form a first, multidimensional signal of state nor the system "((X, p, Xb (x., F-fc.,

, Vgon. ) from all systems 1 - i enters the shaper 4 classes.

in the class former, the multidimensional generalized signal Va is generated from the incoming first multidimensional signals. (Vj g.. V) and decomposes, by cluster analysis methods, into static homogeneous for each parameter of the output signal x. intermediate components; i is the parameter index of the output process.

From the first multidimensional signal

o. extract the components of the signals about the parameters of the object of the system, the controls, the signals of the monitored disturbances and the signals of the permissible controls and form the second multidimensional state signal from them

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Ouse systems (Prg Ffcn Voon), which, like the signals for which | -. ring it is formed by the signal component Vy.

In the class generator, for the multidimensional signal V, the statistical characteristics for each intermediate component of the signal Y are determined and the signals of the partitioning threshold levels are generated from the symbol V3 into groups for each parameter of the output signal, the system. The level signals go to the identification block 5. The same block receives the component of the ultrasonic signal V. | . At the same time making H1P. the V / n signal is fed to the input of the grouping unit 6. The other input of the b block receives the signal of the object parameters selected from the Vi signal. By comparing the Vj signal with the threshold level signals, the Y signal is identified with one of the signal classes of one of the output parameters process. Identification operation of each signal Vm

0 is repeated according to the number of parameters of the output process and each IL signal falls into m groups, where m is the number of parameters of the output process.

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The number of classes of output signals for each parameter is different (in the particular case it may coincide). Separate classes kugut exist for a long time.

0

In identifying vm for each i-th output parameter, the actual signal level of this parameter in the V signal is not taken into account. According to the results of id. .

5 unit 5 generates a switching signal, which is fed to the third. This input block b. According . with this signal, the block b groups the signals l-hklgg, o (l. (go to the classes

About signals of the t-th parameter) of the output process.

The grouped X {, s are received on the input of the former 7 first statistical standards; In the former 5, a statistic

model of the output signal for each group X y l i, group index (class).

When constructing a statistical model X (, (. For a group of systems, the complete statistical uncertainty in the distribution is replaced by parametric uncertainty followed by refinement of the distribution parameter, i.e. the distribution law and its parameters are determined and then refined. For many:. Processes with aftereffect gamma distribution was used as the initial distribution function

S - (, 1 - xnh r, -, (f (b-i) .l,

where, XibtixX - with expectation AND and variance b;

P mathematical, waiting for the output process of the group of systems. The coefficients o and 5 are determined by

by formulas;

about S - P.

In order to use the constructed model to control each particular system, its parameters are led to the parameters of the corresponding system in block 8, where a second statistical reference signal is formed and fed to the input of the device 9 for determining the local error component.

In device 9, calculate RdHsl | the probability of deviations between M Xfoiix f and M,; (; for each system, which, after the Lunkzio transformation, is used as the local component of the error signal and. For evaluation 4, for example, the function f / -

Onfu

(,, 7 ,,, P,

where -6 and w are scaling coefficients; R - probability of absence

mismatch; threshold value P The output signal of the device 9 is fed to the first input of the adaptive optimization unit 13, to the input of the key 10 and to the inputs of the control units 3 - 3j of systems - 1,

The input of the block 12 Formation of the global error component receives the second statistical reference signals and the input signal from block 11. The input signal X {); either specified outside the adaptation system and outputted from block 31 as a constant for each system level, or generated in block 11, based on the requirements im min Xy ,,. In this case, the shaper 11 determines the process characteristics that correspond to the calculated optimal value of the global control effect by building a statistical or simulation model that is tuned during the system operation and then used to generate the required input signal values. The output signal of the driver 11 is fed to the input of the device 12 for forming the global error component, where, by comparing the input signal and the second reference signal obtained in the drivers 8 and 11, it finds the global component

the error signal, which is fed to the second input of block 13.

The output signal of the switch 10 and the global component of the control action from the outputs of block 3 of the control systems 1 - 1 come in; block 14 grouping. From the output of block 14, the signals corresponding to the global component of the control action of systems whose local corresponding mismatches are equal to zero arrive at the third input of block 13 of adaptive optimization. At the same time, the first error correction statistical signal - the local component of the error signal is used to compare it with a threshold signal for (Normalization of the first control correction signals, which is generated in block 13 and fed to the inputs of the control units of the respective systems, from the output of the first (local) management systems that are enrolled

the correction signal, to the corresponding inputs of the adaptive optimization unit 13, the increment signals of the first control are received. By these

signals in block 13 in accordance

with the synchronization signals coming from the grouping unit 6 ,; forms from the first my correctional correction signal UN for each group of output signals ,,, 2 on

each parameter by the signals

corresponding measured increments of the first control signals and local deviations, and use the received signal to

correction signal adaptation and for-.

The mipoBaHHH resultant first control, providing

nit “J D. to

where to is the initial moment of occurrence of a local mismatch.

The global component of the control action is adapted by the second multidimensional correction signal lg, obtained by grouping each class of output signals and control actions of systems for each process - “For which 4 X for this process is zero, i.e. is within acceptable limits, and the minimum is determined, for example, by the Bayesian method.

Adapted components of the control action correction are supplied separately to the corresponding inputs of all blocks 3- - Rear control subsystems 1 | - one,. Thus, the task of adapting the control of non-stationary processes under conditions of uncertainty is solved by simultaneously adapting a large number of systems of the same type.

The effectiveness of the proposed method is enhanced by the separate formation and adaptation of the local and global components of the control action, aimed at changing the characteristics of the controlled process towards their optimal values, which ensures the effective use of the existing impact resource.

Increased accuracy is achieved by lowering; dispersion of controlled processes due to their separation; by searching for discontinuous-type nonlinearities during the separation of processes; lowering the variance of the estimate due to the use of correlated group samples; lowering the variance of the estimate by increasing the number of observations, which provides an increase in the accuracy of the estimate VJj times where and is the number of grouped realizations of the process, based on the requirements of statistical sufficiency; ft 20

The overall increase in the accuracy of determining the statistical model of the process is not less than 1-2 decimal orders.

The speed of the adaptation process is increased due to the possibility of using at the same time a number of steps to search for an extremum in the control actions both with active and passive learning of the adaptation system.

The system, built in accordance with the proposed method of adaptive control, enters the mode for several cycles.

These solutions are further adaptive, improving the algorithm of functioning in accordance with a change in its conditions.

Claims (3)

1. A method of adaptive control of systems under conditions of uncertainty, based on measuring for each system output signals, disturbances and signals corresponding to the parameters of the object and the position parameters of controls, generating the state of the system from the measured signals of the first multidimensional signal, measuring signals control, generating for each parameter of the output signal of each system a statistical reference output signal, generating error signals between the output signals of the systems and the statistical reference output and signals and using them to correct the control signals, characterized in that, in order to expand the field of application, to improve the accuracy and the speed of the method, in it, by the first multidimensional signals of the states of the systems, form a multidimensional generalized signal and decompose it into statistically homogeneous signals for each parameter: output signal, form for each system signals corresponding to the parameters of the object and parameters of the controls, perturbation signals and control limit signals the second multidimensional signal of the system state for which for each statistic a uniformly each signal of each parameter the output signal of a multi-iMepHoro generalized signal, form the threshold level signals, compare them with the second multidimensional signals of the system states, form according to the level of the group of first multidimensional signals, from which groups of signals corresponding to the object parameters and output system parameters are determined, the first statistical reference signals are determined from them, scaled by signal levels, corresponding to the object parameters and; of the system’s output signal, the second statistical reference signals compare them with the system’s output and input signals and form the first and second corrective statistical signals, respectively. mismatch signals. 2. The method according to claim 1, wherein the first correction statistical unbalance signal is compared for each system with the error threshold signal obtained by the signal, the system control signals are corrected, the signal control signals are measured, the corresponding measured increment signals of the system control signals, and the first statistical error signals form the first multidimensional correction signal of the system state. 3. Method POP1, characterized in that for each When the first corrective statistical signal of the error of the control signals and the values of the output signal parameters of the systems of the same group are equal to zero, a second, multidimensional correction signal of the system state is formed. Sources of information taken into account in the examination 1. Japanese Patent No. 52-31507, cl. G 05 B 13/02, published 1977. 2. Repin V.G., Tartakovsky G.P. Static synthesis with a priori uncertainty and adaptation of information systems. -M., Sov. Radio, 1977, p. 240-249 (prototype).