WO2007040425A1

WO2007040425A1 - Method for an object control system self-adjustment and a device for carrying out said method

Info

Publication number: WO2007040425A1
Application number: PCT/RU2006/000515
Authority: WO
Inventors: Valeriy Ivanovich Goncharov; Vladislav Aleksandrovich Rudnitskiy; Aleksey Sergeevich Udod
Original assignee: ZAKRYTOE AKTSIONERNOE OBSCHESTVO 'EleSi'
Priority date: 2005-10-05
Filing date: 2006-10-04
Publication date: 2007-04-12
Also published as: RU2005130752A; RU2304298C2

Abstract

The invention relates to automatic control and adjustment. The use of said invention in self-adapting systems and automatic control methods with a non-periodic signal makes it possible to improve the self adjustment accuracy and operating speed by using a system pattern in a non-parametric form in a self-adjusting circuit. The inventive method consists in transmitting a control action to an object, in determining parameters of the controlled object pattern according to the response thereof to the control action and in calculating the values of the control system adjustable parameters. For this purpose, said method also consists in determining digital characteristics of the input and output signals of the controlled object, in determining the transfer function of the controlled object pattern according to said signals and in forming a reference control system pattern in the form of the transfer function according to specified indexes, wherein adjustable parameters of the control system are determined on the base of the transfer function of the controlled object pattern and the reference control system pattern in an iterative manner with respect to the control system structure and parameters, according to the quality features of the transfer process thereof, wherein all signal conversions are performed according to an interpolation method.

Description

METHOD FOR SELF-ADJUSTING THE OBJECT MANAGEMENT SYSTEM AND THE DEVICE FOR ITS IMPLEMENTATION

FIELD OF THE INVENTION The invention relates to the field of automatic control and regulation of various objects, in particular to the field of adaptive systems and methods of automatic control with a test non-periodic signal.

State of the art

The invention can be used in systems for regulating technological parameters in the metallurgical, chemical, energy, oil and gas processing, food and other industries. A known method of self-tuning of automatic control systems, based on the receipt and use of the reaction of the control object as a whole to the trial effects [1]. The specified method of self-tuning consists of two stages. At the first stage, preliminary identification of the dynamic properties of the control object is carried out, determining the approximate values of the adjustable coefficients of the controller by generating a test harmonic signal. At the second stage, the dynamic properties of the control object are identified by supplying a test step signal to the control object and specifying the values of the controller coefficients. The method has known limitations and disadvantages, in particular the following. Firstly, it requires a long two-step self-tuning procedure. Secondly, the system is tuned in relation to an indirect indicator of the quality of the system — the degree of stability, which does not adequately characterize both the transition process occurring in the system and the control system itself Niya. Thirdly, it uses an approximate adjustment of the regulator by virtue of the adoption of a number of assumptions in obtaining design ratios. Fourth, the capabilities of the method are limited to calculating no more than three controller coefficients, while in practice there is a need to use more complex control laws than proportional-integro-differential (PID).

These limitations and disadvantages of the method reduce the accuracy of the system settings and its speed.

A known method of adjusting the controller of existing automatic systems [2], in which the identification of the control object is carried out by the transient response of a closed system obtained by applying a test step signal to the control object. In this method of adjusting the regulator, such an indirect parameter of the quality of the system as an indicator of oscillation is used as the main parameter, however, in general, the method does not allow to achieve high tuning accuracy.

The known method proposed in [3], based on the input of the control object to the step effect, the formation of the reaction of the object to the step effect and the derivative of this reaction. Using these functions, the parameters of the control object model are determined, which are converted into optimal settings of the PID controller. In this method, there is no lengthy two-step procedure. In this sense, it is more perfect than previous counterparts, but it also has its main disadvantages, which do not allow to increase the accuracy and speed of automatic system tuning.

The closest in technical essence and the achieved result to the claimed method of self-tuning of the object control system is the “Method of optimal automatic tuning control systems)) [4].

This method of optimal automatic tuning of the control system consists in translating the closed-loop control system into open mode, applying a test signal to the input of the object, measuring the parameters of the transient process, determining the parameters of the adopted model of the control object from them, determining the optimal controller settings from the model parameters and translating systems with optimal settings in the operating mode. A step signal with adjustable amplitude and polarity is used as a test signal. As the measured parameters of the transient process caused by the test signal, the maximum value of the derivative of the output of the object and the time of its achievement, the time of reaching the derivative of a certain fraction of the maximum value of the derivative, as well as the time at which the value of the derivative of the output of the object decreases to a certain fraction of the maximum value of the derivative.

The specified method improves the quality of self-tuning and regulation. But the basic analytical relations used in it, connecting the root frequency and time parameters of the system, are very approximate and, therefore, the system’s tuning with respect to the most important parameters - overshoot and regulation time is also very approximate, which reduces the accuracy of the method.

The optimal automatically adjusting general industrial regulator (OAOP regulator) [1] is known, which includes a control object, a mode control unit, a preliminary identification unit, a parameter estimation unit, and a settings calculation unit. Each of the three possible modes of operation of the OAOP controller is determined by the position of the switch slider. A disadvantage of the known controller is the implementation of a lengthy two-stage self-tuning procedure. At the same time, the adjustment of the controller does not provide sufficient accuracy, being quite approximate by virtue of the adoption of a number of assumptions in obtaining design ratios.

Known automatically tuning adaptive industrial controller (ANAP controller) [3], which includes a control object, a derivative evaluation unit, a parameter evaluation unit, a settings calculation unit, a mode control unit. ANAP regulator can operate in one of three modes: manual control; automatic adjustment of controller parameters; automatic regulation.

This controller does not have a two-stage setup procedure, however, it has the drawbacks of the controller [1], which do not allow to increase the accuracy and speed of automatic system settings.

The closest in technical essence and the achieved result to the claimed self-adjusting control system of an object is a control system that implements a method of optimal automatic tuning of the control system [4]. The well-known self-adjusting system for controlling an object contains a serially connected device for comparing a driving signal and a feedback signal, a key, a regulator, an adder and a control object output connected to a device for comparing a driving signal and a feedback signal, as well as a block for calculating the optimal settings, the output connected to controller, and a block for generating a test signal and identification of parameters, the output of which is connected to the input of the optimal settings calculation unit. The input of the test signal generation and parameter identification unit is connected with the output of the control object and the input of the comparison device signal and feedback signal. The unit for generating a test signal and parameter identification includes a control unit and a unit for obtaining parameters of the control object.

The disadvantage of this self-adjusting object control system is the lack of accuracy and speed of the system’s self-tuning, due to the fact that its tuning of the system with respect to the most important parameters - overshoot and regulation time is very approximate, which reduces its accuracy.

Disclosure of invention

The main task solved by the claimed group of inventions is to create a method for self-tuning the object control system and device for its implementation, which can improve the accuracy of self-tuning by using a non-parametric form of representing signal models, the system and its elements. At the same time, an increase in the speed of self-tuning of the object control system is achieved by reducing the amount of computation.

The problem is solved in that in the method of self-tuning the control system of the object, based on the supply of a control action on the object, determining the parameters of the model of the control object based on its response to the control action and calculating the values of the adjustable parameters of the control system, determine the numerical characteristics of the input and output signals control object, which find the transfer function of the model of the control object, form the model of the reference control system in the form of transfer functions based on predetermined indicators, and customizable control system parameters are determined based on the transfer function of the control object model and the transfer function of the model of the reference control system iteratively with respect to the structure and parameters of the control system according to the quality indicators of the transition process of the system, while all the transformations are carried out on the basis of the real interpolation method (VIM).

It is advisable that the reference model of the control system be formed on the basis of system quality indicators predefined by the operator. The optimal supply of control action on the object in the form of a test non-periodic signal.

In this case, a non-periodic test signal can be stepwise or linearly increasing. It is advisable to determine the adjustable parameters of the control system based on the transfer functions of the models of the control object and the reference model of the control system, presented in nonparametric form.

The adjustable parameters of the control system are determined on the basis of the transfer functions of the models of the control object and the reference model of the control system iteratively with respect to the structure and parameters of the custom control system until the specified coincidence of the reference and custom control system is achieved. The achievement of a given coincidence of the reference and custom systems is optimally fixed according to the criterion of overshoot with the minimum complexity of the control system.

The problem is also solved by the fact that the device for implementing the method of self-tuning the object control system contains a control object, a regulator, a device for comparing the driving signal and the feedback signal, one of the inputs of which is connected to the output of the control object, the optimal settings calculation unit, the first output connected to the first the input of the controller, the block receiving the model of the control object, the output connected to the first input of the block calculating the optimal settings, the self-tuning loop control unit and the adder connected by inputs to the controller output and the first output of the self-tuning loop control unit, and the output connected to the control object. New is that in the device for implementing the method, a unit for obtaining a numerical characteristic of the input signal of the control object, a block for obtaining a numerical characteristic of the output signal of the control object and a unit for constructing a reference model of the system, one of the inputs connected to the output of the control unit of the self-tuning circuit, the input of which is connected to the second output of the optimal settings calculation unit, and the output of the building block of the reference model of the system is connected to the second input of the optimal settings calculation unit The input, output and output of the control object are connected to the control unit model obtaining unit, respectively, through the unit for obtaining the numerical characteristic of the control object input signal and the control unit for obtaining the numerical characteristic of the control object output signal, and the regulator is connected to the output of the device for comparing the driving signal and the feedback signal communication, while the second and third inputs of the building block of the reference model of the system are intended to be connected to the sources of setting the quality indicators of the system and the type of controller, and the second input of the device for comparing the driving signal and the feedback signal is intended to be connected to the source of the driving signal.

Preferably, the self-tuning loop control unit is implemented as a series-connected key and a probe signal generator, wherein the output of the probe signal generator is the first output of the self-tuning loop control unit, the key input is the input of the self-tuning loop control unit, and the key output is the second output of the loop control unit samona- construction sites.

It is optimal to execute a block for constructing a reference model of the system in the form of series-connected block for calculating the coefficients of a reference model, a block for calculating the transition characteristics of a reference model of a system and a block for storing results, the output of which is the output of a block for constructing a reference model of the system, as well as a block for correcting specified parameters, input which is the first input of the unit for constructing the reference model of the system, and the output is connected to the input of the unit for calculating the coefficients of the reference model, while input calculation block rows reference model coefficients are second and third inputs of the block for constructing the reference system model. The unit for obtaining the numerical characteristic of the input signal of the control object is expediently performed with an analog-to-digital converter, a recording and filtering unit for sampling and a unit for calculating the value of the numerical characteristic of the input signal, the input of the analog-to-digital converter being the input of the block for obtaining the numerical characteristic of the input signal of the object control, and the output of the unit for calculating the value of the numerical characteristic of the input signal is the output of the unit numerical characteristics of the input signal of the control object.

The unit for obtaining the numerical characteristics of the output signal of the control object is preferably performed containing a series-connected analog-to-digital converter, a recording, filtering and storage unit for sampling and a unit for calculating the values of the numerical characteristics of the output signal, while the input of the analog-to-digital converter is the input of the block for obtaining the numerical characteristics of the output signal of the object control, and the output of the unit for calculating the value of the numerical characteristic of the output signal is the output unit for obtaining a numerical characteristic of the output signal management project.

The control object model obtaining unit is expediently implemented as a series-connected unit for calculating the transfer function coefficients of the control object model, the transition object calculation unit for the control object model and the comparison unit, while the inputs of the coefficient transfer coefficient calculation unit for the control object model are the inputs of the object model obtaining unit control, and the output of the comparison block is the output of the block receiving the model of the control object. The optimal settings calculation unit is optimally performed by containing the controller coefficient coefficients calculation unit, the control system coefficient calculation unit, the control system transition characteristic calculation unit, the comparison unit and the key, the output of which is the second output of the optimal settings calculation unit, as well as the results storage unit, the output of which is the first output of the optimal settings calculation unit, and the input is connected to the output of the comparison unit and to the key input, while input The odes of the controller coefficient calculator are the first and second inputs of the optimal settings calculator. The claimed method for self-tuning the object control system and the self-adjusting object management system for its implementation differ from the closest analogues, therefore, the claimed solutions satisfy the patentability condition of the invention of “novelty”. The analysis of the prior art on the conformity of the claimed solutions to the patentability condition of the invention “inventive step” showed the following.

In the presented method of self-tuning and the system operating on its basis, unlike the known ones, non-parametric the presentation form of signal models, the system and its elements, which allows to reduce the amount of calculations, create and implement an algorithm for tuning the system to direct quality indicators. In this case, not only a stepwise test signal, traditionally used in analogs, but also a linear, quadratically increasing, pulsed, etc. can be used.

In addition, the claimed invention allows for not only parametric, but also structural self-tuning of the regulator.

At the same time, the set parameters of the system can be used in the indicators of the quality of the system that are most understandable to the operator - overshoot, the transition process establishment time (regulation time), maximum slew rate and others.

The claimed inventions are so interconnected that they form a single inventive concept, therefore, this group of inventions satisfies the requirement of the unity of the invention.

Brief Description of the Drawings

The invention is illustrated by drawings, where in FIG. 1 shows a functional diagram of a self-adjusting object control system according to the proposed method, FIG. 2 - self-tuning loop control unit, in FIG. 3 is a block for constructing a reference model of the system, in FIG. 4 - a block for obtaining a numerical characteristic of the input signal, in FIG. 5 is a block for obtaining a numerical characteristic of the output signal; FIG. 6 is a block for obtaining a model of the control object, in FIG. 7 is a block for calculating optimal settings, in FIG. 8 is a transient graph of a control object and a model of a control object; FIG. 9 is a transient graph of a model of a reference system; FIG. 10 are graphs of the transient characteristics of the model of the reference system and the calculated transient characteristics of the model of the control system, on FIG. And - graphs of the transition characteristics of the reference model of the system and the customized model of the control system.

An example embodiment of the invention A self-adjusting object control system (Fig. 1), which implements the proposed method for self-tuning an object control system, comprises a control object 1, a controller 2, a device 3 for comparing a driving signal and a feedback signal, one of the outputs of which is connected to the output of the control object 1, unit 4 for calculating optimal settings, the first output connected to the first input of controller 2, unit 5 for obtaining a model of the control object, output connected to the first input of unit 4 for calculating optim lnyh settings loop self-tuning control unit 6 and an adder 7. The adder 7 inputs connected to the output control circuit 2 and the first output control unit 6 bootstrapping and output associated with the control object 1. The self-adjusting control system of the object also contains a block 8 for obtaining a numerical characteristic of the input signal of the control object 1, a block 9 for obtaining a numerical characteristic of the output signal of the control object 1, and a block 10 for constructing a reference model of the system, one of the inputs of which is connected to the output of the block 6 for controlling the self-tuning circuit. The input of the self-tuning loop control unit 6 is connected to the second output of the optimal settings calculating unit 4. The output of block 10 for constructing a reference model of the system is connected to the second input of block 4 for calculating optimal settings. The input and output of the control object 1 are connected to the block 5 for obtaining the model of the control object, respectively, through the block 8 for obtaining the numerical characteristics of the input signal of the control object and the block 9 for obtaining the numerical characteristics of the output signal for the control object, and the controller 2 is connected to the second input with the output of the device 3 comparing the driving signal and the feedback signal. The second and third inputs of block 10 for constructing a reference model of the system are intended to be connected to sources for specifying system quality indicators and specifying the type of controller that are external devices. The second input of the device 3 comparing the driving signal and the feedback signal is intended to be connected to the source of the driving signal, which is an external device.

Block 6 control loop self-tuning (Fig. 2) contains a series-connected key 11 and the generator 12 of the test signal. The output of the probe signal generator 12 is the first output of the self-adjusting loop control unit 6, the input of the key 1 1 is the input of the self-adjusting loop control unit 6, and the output of the key 11 is the second output of the self-adjusting loop control unit 6.

Block 10 to build a reference model of the system (Fig. 3) contains a series-connected block 13 for calculating the coefficients of the reference model of the system, block 14 for calculating the transition characteristics of the reference model and block 15 for storing the results, the output of which is the output of block 10 for building the reference model of the system, block 16 for setting indicators, the input of which is the first input of block 10 for constructing a reference model of the system. The output of the unit 16 for correction of the specified indicators is connected to the input of the unit 13 for calculating the coefficients of the reference model of the system, the inputs of the unit 13 for calculating the coefficients of the reference model of the system are the second and third inputs of the unit 10 for constructing the reference model of the system. Block 8 for obtaining a numerical characteristic of the input signal of the control object (Fig. 4) contains a series-connected analog-to-digital converter 17, a block 18 for recording and filtering samples and a block 19 for calculating the magnitude of the numerical characteristic of the input signal. The input of the analog-to-digital Converter 17 is the input of block 8 for obtaining the numerical characteristic of the input signal of the control object, and the output of block 19 for calculating the value of the numerical characteristic of the input signal is the output of block 8 for obtaining the numerical characteristic of the input signal of the control object.

The block 9 for obtaining the numerical characteristic of the output signal of the control object (Fig. 5) contains a series-connected analog-to-digital converter 20, a block 21 for recording, filtering and storing the sample and a block 22 for calculating the magnitude of the numerical characteristic of the output signal. The input of the analog-to-digital converter 20 is the input of the block 9 for obtaining the numerical characteristics of the output signal of the control object, and the output of the block 22 for calculating the values of the numerical characteristics of the output signal is the output of the block 9 for obtaining the numerical characteristics of the output signal of the control object.

Block 5 obtain the model of the control object (Fig. 6) contains series-connected block 23 for calculating the coefficients of the model of the control object, block 24 for calculating the transition characteristics of the model of the control object and block 25 for comparison. The inputs of the block 23 for calculating the coefficients of the model of the control object are the inputs of the block 5 for obtaining the model of the control object, and the output of the block 25 for comparison is the output of the block 5 for obtaining the model of the control object.

The optimal settings calculation unit 4 (Fig. 7) contains in series the controller coefficient calculation unit 26, the control system coefficient calculation unit 27, the control system transition characteristic calculation unit 28, the comparison unit 29 and the key 30, the output of which is the second output of the optimal calculation unit 4 settings. The optimal settings calculation unit 4 also includes a result storage unit 31, the output of which is the first output of the optimal settings calculation unit 4, and the input is connected to the output of the comparison unit 29 and to the input of the key 30. The inputs of the controller coefficient calculation unit 26 are the first and second inputs of the optimal settings calculation unit 4. The method of self-tuning of the object control system is implemented using the claimed self-tuning system as follows.

At the first stage, referred to as identification of the control object, the user sets the adequacy requirement in the form of a numerical value of the adequacy criterion for the transition characteristic of the control object model to its experimental characteristic. This value is entered into the comparison block 25 of the block 5 for obtaining the model of the control object and is used in the future to evaluate the result obtained in the identification. The control system is switched to the open state, for which the comparison device 3 is turned off and the controller 2 is transferred to the broadcast mode at its output of the input signal u (t), the value of which in this mode must be equal to zero.

To the input of the control object 1 through the comparison device 7 from the output of the probe signal generator 12, switched by the key 11 of the self-tuning loop control unit 6, a test non-periodic signal U _n p is supplied. It can be stepped linearly

melting or otherwise in shape. The signal polarity depends on the current state of the control object and, like its amplitude, must fit into the framework of the permissible norms of the technological process occurring in the control object. The amplitude of the signal can be equal to the nominal value of the input signal of the object or make up a fraction of it, for example, 5-10%. At the output of the control object 1, an output signal characterizing the transient process y (t) appears. The input and output signals of the control object 1 U _np and y (t) are given

to block 8 for obtaining a numerical characteristic of the input signal of the control object and block 9 for obtaining the numerical characteristic of the output signal of the control object, where they are processed by ADC blocks 17 and 20, respectively, the input signal is recorded and filtered in block 18, the output signal is recorded, filtered and stored in block 21 . After the end of the transient process of the signal y (t), the supply of the test signal U _{np is} stopped, and it has no effect on the control object

what influence. Further, to obtain mathematical models of signals in a special machine-oriented form - in the form of numerical characteristics, the result is respectively sent to block 19 for calculating the magnitude of the numerical characteristic of the input signal and block 22 for calculating the magnitude of the numerical characteristic of the output signal, which are elements of the corresponding blocks 8 and 9 for obtaining numbers - the total characteristics of the input and output signals.

The output signals of blocks 8 and 9 are fed to the inputs of the coefficient calculation unit 23 of the control object model included in the control object model receiving block 5, in the form of a transfer function with a pattern of a given order. In block 23, the coefficients of the transfer function are calculated, which then go to block 24 to calculate the transition characteristic of the model of the control object. In block 25, the obtained characteristic is checked for its experimental adequacy, stored in block 21 of block 9 for obtaining the numerical characteristics of the output signal. If the model does not satisfy the adequacy requirement, then the modeling process is repeated in block 23 for calculating the coefficients of the control object model with an increased order of the model transfer function template. Then again, the transition characteristic is calculated in block 24 the transition characteristic of the model of the control object and checking its adequacy to the experimental characteristic in the comparison block 25. If the result is unsatisfactory, the modeling procedure is repeated with a less stringent adequacy criterion, starting with a simple transfer function template in block 23. If the result is also in this If unsatisfactory, then the identification procedure is repeated from the stage of supplying to the input of the test object non-periodic signal U _n „and, further, in the given order. When put

As a result, the transfer function coefficients of the control object model go to the optimal settings calculating unit 4.

The next stage begins by entering into block 10 the desired quality indicators presented to the system — overshoot and regulation time, on the basis of which, in the coefficient calculation block 13 of the system model model, the transfer function coefficients of the system model are calculated and the system transfer standard function is obtained. The values of the coefficients of this function enter block 14 for calculating the transient response of the reference model of block 10, in which the transient response of the reference system is calculated, which comes in the form of a numerical sample to the block 15 for storing the results of block 10 for constructing the reference model of the system. In block 10, information is also entered about the type of controller with which the entire control system will be controlled. This information and the values of the required quality indicators are stored in the storage unit 15 of the results in the form of numerical values. At the next stage, the type of the transfer function of the controller and the value of its coefficients are determined. In block 26 calculating the coefficients of the control model, which is part of block 4 for calculating the optimal settings, the calculated coefficients of the control object from block 5 and data on the desired type of controller from block 10 are received. Further, in the block 26 for calculating the coefficient of the controller based on this data, the tuning of the coefficient of the controller takes place, the values of which are sent to the block 27 for calculating the coefficients of the control system, in which, based on the values of the coefficient of the controller and the transfer function of the control object, the control system is synthesized. The found transfer function coefficients of the control system are sent to the control system transient response calculator 28, and then the result is compared with the standard stored as a sample in the results storage block 15 of block 10 and evaluated for compliance with the quality indicators of the system stored as numerical values in block 15 In the case of an unsatisfactory result, a new iteration of the calculation of the coefficients of the controller and the coefficients of the control system, called parametric tuning with tem. If the parametric adjustment does not bring the desired results, in the block 26 of the calculation of the coefficients of the controller is an increase in the order of the structure of the controller. This procedure is the structural setting of the system, followed by the parametric setting described above. In the case of an unsatisfactory result, the key 30 included in block 4 is triggered, the signal from which is fed to the self-tuning loop control block 6, the key 11 of which sends a signal to the result correction block 16 of the given parameters of block 10, which increases the desired transition time and initiates the recalculation new model reference system. Further, the procedure for calculating the controller coefficients is repeated until a satisfactory result is obtained from the point of view of overshoot and the regulation time corrected by the block 16. In this part of the work of the method and device for its implementation, there are two features. The first is that the method allows you to customize systems with controllers of arbitrary order, including PID-type controllers as a special case. The second feature is the implementation of two iterative procedures. The first provides a parametric search for a solution, the second - structural. The goal of structural iterations is to find the simplest possible regulator at which the set quality indicators can be achieved. Such a technical solution minimizes computational costs and increases due to this accuracy, speed and reliability of the self-tuning loop and the system as a whole. After that, the coefficients of the controller that satisfy the set and adjusted indicators are recorded in the block 31 for storing the results of block 4, from where they are sent to the controller 2 for its reconfiguration. The comparison device 3 begins to calculate the error of the mismatch between the input value of the input signal u (t) and the current output signal y (t) of the control object, that is, the system enters the regulated mode with the new calculated coefficients of controller 2.

In the inventive method for self-tuning the control system of an object, three relatively independent procedures and their corresponding tasks can be distinguished: 1) identification of the control object;

2) obtaining the desired transfer function of the system;

3) determination of the type of the transfer function of the controller and the values of its coefficients.

For a more detailed explanation of the implementation of the method of self-tuning and system operation, we consider a sequence of signal transformations with a representation of the basic design ratios of the selected tasks. These transformations are carried out on the basis of the real interpolation method (VIM), the fundamentals of which are described below.

When considering signals and systems belonging to classes of non- intermittent, and solving the synthesis problems of such systems, it is advisable to use models in the field of images obtained on the basis of any integral transformations. The most common are the Laplace and Fourier transforms. They make it possible to solve all the basic problems of calculating dynamic systems in terms of image functions, which is much simpler than solving the same problems in the time domain. However, these transformations have drawbacks that are manifested in the hardware and software implementation of such methods — in numerical operations, it is necessary to perform transformations of the real and imaginary parts of the models under consideration, which entails a large amount of computation. This disadvantage is eliminated by using the real integral transformation

F (δ) = | f (t) e ^{~ δt} dt, δ e [C, oo], C> 0, (1)

About which associates the original function f (t) with the image F (δ). We note the main thing here: the obtained function F (δ) belongs to the class of image functions and, therefore, has marked advantages over time functions; at the same time, it is free from the difficulties of numerical operations on Fourier images F (jω) or Laplace F (p), which have the argument imaginary jω or complex p = δ + jω, respectively.

The conditions for the existence and uniqueness of the function F (δ) are determined by the convergence of the integral in (1). In the application to linear ACSs, when f (t) is its temporal dynamic characteristic, convergence is ensured by the choice of the corresponding value of parameter C. Thus, for a stable system with an impulse transition characteristic k (t) = f (t), one can take C = 0. In the case of Using the transition characteristic h (t) = f (t) of a stable system, the condition for the convergence of the integral is also determined quite simply: δ e (0, ∞] or C> 0.

To move from system models in terms of real image functions to their discrete representations and vice versa, oriented to digital structures, an interpolation approach is used. To this end, for the function F (δ), δ e [0, oo], the nodes δj, i = 1,2, .... and

find the values F (δj), i = i, η, η = m + n + l. The resulting set

is called the numerical characteristic of the function F (δ), and the number η of its elements is called the dimension of the frequency response.

For the effective use of the real functions F (δ) and their numerical characteristics, it is important to know their positive features and properties. Here are some. a) The functions F (δ) can be obtained by the formula of the direct δ transformation (1), as well as by the Laplace images F (p). In the latter case, the result can be obtained by formally replacing the variable p by δ e [C, ∞], C> 0, considering the transformation (1) as a special case of the Laplace transform. This feature is especially important because it allows one to use the entire existing Laplace originals and images correspondence library created to date to obtain F (δ). b) The functions F (δ) have graphical representations, which makes them and the actions on them more visual in comparison with the images F (p), which is important, for example, during commissioning. c) The functions F (δ) do not contain an imaginary component; therefore, the numerical methods of acting on them turn out to be approximately twice as large. more economical in comparison with the Fourier and Laplace images d) If the function f (t) in (1) is the impulse response of the system, then the image F (δ) has the meaning of the real transfer function W (δ).

The set of approaches, techniques, and algorithms for calculating and studying dynamical systems, based on the use of real transformation and interpolation procedures, is called the real interpolation method (VIM). More detailed information about the method and solving problems based on it are presented in [5]. The following shows the application of VIM to solve three main problems that arise during self-tuning - identification, formation of the desired transfer function and calculation of controller parameters.

Identification of the Management Object

To consider the first task, we turn to the part of the functional diagram shown in FIG. 1, including the control object 1, blocks 8 and 9, respectively, for obtaining the numerical characteristics of the input and output signals of the control object, block 5 for obtaining the model of the control object.

The identification task is implemented in a parametric setting and includes the following steps:

- determination by signals u (t) and y (t) of their numerical characteristics {U (δ _i )} _η , i = l, 2, ..., η and {Y (δ _i )} _η , i - l, 2, ..., η;

- calculation of the input and output signals {U (δ _i )} _η , i = l, 2 _v .., η and {Y (δ _| )} _η , i - l _> 2, ..., η, numerical character ¬

sticks of the control object {W _oy (δ _j )} _η ; - obtaining the real transfer function W (δ) of the control object by the numerical characteristic {W _oy (δi)} _η . Let the object is described by the transfer function (PF)

In order to simplify the explanations, we assume that the input signal of the system u (t) is absent, and a test signal and -, - ₉ (t) are supplied to the input of the control object. Then for signals u » _b (t) and y (t) there are their real images

U (d _j ) - е ^"51 '' - Δt _j , i = l, 2, ..., η, (3)

Y (δi) = Σ y (t _j ) - e ^{~ δitj} - Δt _j , i = l, 2, .., η, (4)

as well as the material transfer function of the control object

Expression (5) defines the elements of the numerical characteristic {W _oy (δ _i )} _η , therefore, we can consider the model of the control object in nonparametric form to be found.

At the second stage of parametric identification, it is necessary to obtain the coefficients of the real FS (2). To do this, we compose a system of linear algebraic equations (SLAE) for the unknown coefficients a _k , b _j , k = 1, 2, ... n, j = 0, 1, ... m:

_{W (δi} ) ₌ b _m δ _i ⁿ '-b b _m _ ₁ δ _i ° -' ₊ ... ₊ b _0> . ₌ a _n δ _l ¹ + a .-, δ, - ¹ + ... + l The left side of the SLAE is known - it is determined by the formula (5) for calculating the ele cops of the control object. The number of equations η in

SLAE is determined by the relation η = n + m + l; the coefficients a _k , b _j obtained as a result of solving the system of equations (6) are the coefficients of the real FS (2). To go over to the Laplace FS, it suffices to replace the real variable δ by the complex p. An analysis of the obtained result is performed in the time domain, for which the obtained transfer function of the control object model is subjected to the inverse Laplace transform and compared with the experimental characteristic y (t) using one of the known methods; the minimax adequacy criterion is used in the proposed algorithm. The minimax criterion operates on the error function

Δy (t) = y (t) - y _m (t), where y _m (t) is the transition characteristic of the control object model, y (t) is the experimental transition characteristic of the control object.

where t _a is the time during which the experiment was conducted, A _max is the maximum allowable value of the criterion in relative units.

To illustrate the health of the proposed method, consider a numerical example of identification. We set the value of the adequacy criterion A _max = 0.1. Let a stepped control signal U _pp , which causes a transient in it (graph 1, Fig. 8), be applied to the control object 1 of the open system. At the output of the object in the recording and filtering unit 18 of the sample, the transition characteristic of the signal voltage amplitude is recorded, in the form of a sample h _oyj (t _r ), r = 1, ... 99, from

table:

Replacement sheet The transfer function of the model of the control object is defined as

In order to reduce the amount of computation, the coefficient b ₀ can be found directly from the steady-state average value of the transition characteristic: b ₀ = 141, which can be obtained by applying a normalized step signal u (t) = l to the input of the control object. The remaining three coefficients bi, a ₂ , a _b are subject to determination; therefore, in block 8, according to the method described in [5], the book: V. Goncharov. Real interpolation method for the synthesis of automatic control systems. - Tomsk: Ed. TPU, 1995. 108 s, we define a system of three interpolation nodes with the following values:

δ ₂ = 3.9, δз = 5.85 and we find the values of the elements of the numerical characteristic of the input signal as the product of the input signal to the interpolation nodes: U (δi) = 1.25, U (δ ₂ ) = 1.86, U (δ ₃ ) = 3.75. In block 9 for obtaining the numerical characteristics of the output signal, using expression (4), we obtain the values of the elements of the numerical characteristics of the output signal: Y ^ ₁ ) = 26.2, Y (δ ₂ ) = 11.8, Y (δ ₃ ) = 2.4.

Next, in block 5 of obtaining the model of the control object according to (5), the SLAE is compiled and solved:

26.2 -1.25 = ^L25b ' ^{+ W}

1.25 ^ a ₂ + 1.25a _! + 1

As a result of solving the system of equations, the values of the desired coefficients are determined: a ₂ = 0.53, ai = 1.9, b ₂ = 0.82. Then, in block 24, according to the found coefficients of the transfer function of the model, its transition characteristic is calculated. In comparison block 25, the adequacy criterion equal to 0.031 is calculated by formula (7), which is less than the specified A _max = 0.1. The result of solving the identification problem is illustrated by graphs of the experimental and model transient characteristics, which are presented in Fig. 8.

Obtaining the desired transfer function of the system

This is the second of three main tasks. Its essence is the formation of the transfer function of the reference system, the properties of which should be approached in the process of tuning the main circuit of the system. The initial data for solving the problem are the system quality and accuracy indicators set by the operator at the commissioning stage, as well as the experimentally obtained current transfer function of the control object.

The task has two main stages. At the first, by the given quality indicators, for example, overshoot of σ and the transition process establishment time, the elements of the numerical characteristic of the reference system (W ^. (S ₁ ) J _{11 are} determined. At the second stage, the coefficients of the desired transfer function are found.

The calculation formula for the first stage is obtained on the basis of the known relationship between the transfer function and the transition characteristic and has the form

l ... η

(9) where the notation is introduced, the meaning of which is revealed by the dependencies h ^ (t) = k _r t + b _r , r = 0.3,

k _r = [h _w (t _{r + 1} ) - h _w (t _r )] / [t _{r + 1} - t _r ],

b _r = h _w (t _{r + 1} ) - k _r t _{r + 1} and the parameters indicated in the graph of Fig. 8. At the second stage, the coefficients of the desired transfer function are found

/ 3 / „4 Kv t + b _m _ _lP ^m - + ... + b ₀ a _n p + a _n _, p ⁿ Ч ... + 1 by solving the system of equations

The formal replacement of the variable δ by p leads to the Laplace transfer function

In the conditions of minimizing the computational costs during the self-tuning of the system in the future it will be advisable to use the transfer function of the open loop. It is found by the well-known opening relation

which simultaneously takes into account the requirement of astatism, if any.

Consider a calculated example of obtaining the desired transfer function. We set the quality indicators of the transition process (setting the desired quality indicators of the system, Fig. 1, block 10): overshoot σ ₃ = 0.1 ± 0.01, (in relative units), set time

lance t _γ ^C <2s. Closed loop transmission coefficient K = IOO. Structural tour desired transfer function

Since the coefficient b ₀ is found from the static equation (according to the steady-state value of the transition characteristic of the desired system) and is equal to 100, three PF coefficients are to be determined: a, a, a, b.

We define a system of three interpolation nodes with the following values: δi = 2.52, δ ₂ = 5.05, δ ₃ = 7.57. Using expression (9), in the block for calculating the transfer function coefficients of the system model 13, we obtain the values of the elements of the numerical characteristic: W ^ (O ₁ ) = 43.67,

W ^ (δ ₂ ) = 24.64, W ^ (δ ₃ ) = 16.62. We make SLAU:

2.52 ^ + 100

43.67 =

2.52 ⁱ a ₂ + 2.52a ₁ + l 5.05C + 100

24.64 =

5.05 ^ ₂ + 5.0Sa ₁ -H l 7.57C + 100

16.62 =

7.57 ² a ₂ + 7.57a _! + 1

and we find the unknown PF coefficients: a ₂ ⁼ 0.18, ai = 0.52, bi = 20.08

Using the obtained coefficients for verification by solving the inverse problem (calculating the transient response of the model with the found coefficients in block 14), we obtained the following results:

- overshoot σ = 0.09998;

- regulation time t ^ = 2.01 s;

- the transfer coefficient of a closed system K = IOO; Such parameters can be considered satisfactory, therefore, the problem is considered solved. The resulting coefficients are stored in block 15. Determination of the type of the transfer function of the controller and the values of its coefficients

The third, the last of the considered problems of adjusting the regulator, consists in calculating its parameters for which the system will have specified quality and accuracy indicators. The initial data for its solution are the previously obtained transfer functions of the reference system in the open state and the control object. The task of adjusting the controller is to solve the equation:

* £ (P) = 1 + W _p (p) - ^' W _oy (?) - K _oc , ⁽ П ⁾

where W ^ (p), W _p (p), W _oy (p) are the transfer functions of the desired (reference) closed system, controller, and system control object, respectively, K _oc is the feedback coefficient equal to the inverse value of the closed transfer coefficient system.

Computationally, it is more beneficial to use the open-loop synthesis equation

W ^ (P) - W _p (p) W _oy (P),

(12) where W ^ (p) is the transfer function of the open system.

The problem of finding the function W _p (p) has two parts: structural and parametric. Both are solved by a consistent approach to the desired result.

The structural part consists in finding the parameters μ, v of the transfer function of the controller

In order to obtain a rational solution by the criterion of computational costs, its search begins with a dynamic controller of minimal complexity: μ = v = 1 (PI controller). In this case, equation (12) takes the form

W ₃ P (P) = M ± bL _Woy (P). ₍₁₃ )

With such initial data, the problem is reduced to calculating the coefficients bi, b- To determine them, equation (13) is transferred on the basis of VIM to the real region by replacing p -> δ, δ е [0, ∞] and takes the form: _w * _{(δ) ==} biδ ± bo). about

This allows you to expand the equation into a system of linear algebraic equations for 2 unknown coefficients bi, bо, using the VIM discretization capabilities: _{wi (δi) =} biδi + b <μ _{i = i} ^

The δi values can be determined, for example, on a uniform grid using the δ * formula δ _j = - -, where δ _β is the upper boundary of the location of the interpolation nodes δ _j G [0, δ _a ], δ _g = δ _η , η = 2. The coefficients calculated in this way allow you to get the transfer function of the controller and a closed custom system. However, the properties of the system may not meet the requirements Well, for example, the value of the leading parameter of the system - overshoot - may go beyond the required limits. Therefore, a parametric adjustment of the solution is organized, which consists in changing, according to a certain rule, the values of the interpolation nodes. As a result, one of two situations will be achieved. The first is the overshoot of the custom system that matches the required with the given accuracy. In this case, the solution is considered to be found. The second situation is that the specified tuning accuracy has not been achieved. Then the order of the transfer function of the controller is automatically increased by one and the automatic iterative parametric tuning procedure is repeated. The sequential complication of the controller is the content of the structural iterative tuning procedure. Together, they ensure the achievement of the set values of the system parameters. As an illustrative example, we consider the problem of obtaining controller coefficients when the transfer functions of the reference system and the control object are known (from the examples discussed above), and the transfer function of the controller has the form

(fourteen)

The regulator should provide overshoot of the system σ _c = σ ₃ +0.1. The transfer function of the controller can be represented as:

moreover, the controller coefficient b ₀ can be found in the block 26 for calculating the controller coefficients, as the ratio of the corresponding coefficients of the desired open transfer function and the transfer function of the control object model: bо = 312.38 / 141 = 2.21. So thus, only one coefficient bi can be determined.

The first value of the interpolation node at the first iteration δi = l, 5 is automatically calculated taking into account the previously obtained control time t ^ = 2.01 s. We calculate the values of the elements of numerical characteristics included in expression (15):

- W ₁ M = 28.08;

- W ₆ (O ₁ ) = 7.89;

Having obtained the equation for an unknown coefficient

_ __ 1.5b _t + 2.21 _. . _ 7.89 = ^ι , we define it: bi = 6.42.

The data goes to block 27, where, according to formula (11), there is the transfer function of the closed system and, further, to block 24, where its transition characteristic is located. Overshoot is defined as the maximum value of the transition characteristic of the control model relative to its steady-state value and is equal to σ = 0.21, which is significantly greater than the required value. This indicates the need for parametric settings. As part of its implementation, an iterative change in the value of the interpolation node occurs. At each iteration (l ... i), the numerical characteristics are calculated, and the unknown coefficient of the controller is found. Then, the data enters the control system coefficient calculation unit 27, where the transfer function of the closed-loop system is located, and, further, the transition characteristic calculation unit 24 of the control object model, where its transition characteristic is used to calculate the regulation. In the considered example, at the ith iteration, the value of the interpolation node is δi = 0.95. We calculate the values of the elements of numerical characteristics included in expression (15): - W ^ ₁ ) = 241.36;

W ₁₆ (O ₁ ) = 41.4;

- W ₆ ^ ₁ ) = 5.83;

We solve the equation for an unknown coefficient:

5.83 = - - - - and we find:

Once again, we find a transitional character

The system с s logic with such a regulator setting, we obtain overshoot σ = 0.16, which is less than that obtained at the first iteration, but more than required. The transient response graphs of the reference and synthesized systems are shown in FIG. 10. A further change in the values of the interpolation node in the considered example does not lead to the desired result, therefore, it is necessary to go to the structural adjustment procedure, for this purpose, in the block for calculating the coefficients of the controller 26, the order of the structure of the controller increases:

(16)

The coefficient b _{0 of the} controller, as before, can be found immediately, as the ratio of the corresponding coefficients of the desired PF and PF model of the control object: b ₀ = 312.38 / 141 = 2.21. Thus, three coefficients b ₂ , bi, a ₂ are subject to determination.

We define a system of three interpolation nodes with the following values: δi = 1.75, δg = 3.5, δz = 5.25. We calculate the values of the elements of numerical characteristics:

- W ^P (δ ₂ ) = 213.9, W ^P (δ ₂ ) = 180.56, W ^P (δ ₃ ) = 163.74; - W _oy (δ ₂ ) = 23.86, W _oy (δ ₂ ) = 10.H, W _oy (δ ₃ ) = 5.7;

- W _p (δ ₂ ) = 8.96, W _p (δ ₂ ) = 17.86, W _p (δ ₃ ) = 28.72; We make SLAU:

and we find the unknown PF coefficients: b ₂ = 0.445, bi = 3.246, and ag = 0.019. By replacing the real variable δ by the complex p, we pass to the equation of the closed system and find the transition characteristic. Its graph is shown in FIG. eleven.

The obtained overshoot of the synthesized system σ _c = 0.0909 and the transition process time t ^ = 2.002 s satisfy the initial conditions, therefore, the problem is solved and the found coefficients go to block 2 of the controller.

Industrial applicability The inventive method of self-tuning and a device for its implementation can improve the speed of calculations and the accuracy of the system by using a non-parametric form for representing signal models, the system and its elements, reducing the amount of computation and implementing the system tuning algorithm for direct quality indicators. The self-tuning method and device for its implementation can be widely used in the field of automatic control and regulation of various objects, in particular in the field of adaptive systems and automatic control methods with a trial non-periodic signal. Sources of information from the prior art

[1] Shubladze A.M., Popadko B.E., Gulyaev SV., Shubladze A.A. Optimal, automatically tuned general industrial regulator (OAOP regulator) // Means of measurement, automation, telemechanization and communication. - 2002.- Ns 7. - S. 2-5.

[2] Man H.B., Cheong L.S. Adjustment of regulators according to the transient response of a closed system with a refined model of an object // Thermal Engineering. - Jfe 7. - 1998 .-- S. 55-58. [3] Shubladze A.M., Gulyaev SV., Olypvang V.R., Shubladze A.A. Automatically tuned adaptive industrial controller (ANAP regulator) // Devices and Systems. Management, control, diagnostics. - 2005. - -Ne s. - C 32-35.

[4] “Method for optimal automatic tuning of the control system)) [4] RF patent Ne 2243584, IPC G05B 13/00, publ. 2004.12.27].

[5] Goncharov V. I. Real interpolation method for the synthesis of automatic control systems. - Book, Tomsk: Ed. TPU, 1995.

Claims

Claim

1. The method of self-adjustment of the control system of the object, based on the filing of the control action on the object, determining the parameters of the model of the control object based on its reaction to the control

5 the impact and calculation of the values of the adjustable parameters of the control system, characterized in that the numerical characteristics of the input and output signals of the control object are determined, by which the transfer function of the control object model is found, the model of the reference control system is formed in the form of the transfer function based on specified parameters, and custom control system parameters are determined based on the transfer function of the model of the control object and the transfer function of the model of the reference control system I iteratively with respect to the structure and parameters of the management system according to the transitional quality indicators

15 of the system process, while all signal transformations are carried out on the basis of the real interpolation method (VIM).

2. The method of self-tuning the object control system according to claim 1, characterized in that the model of the reference control system is formed on the basis of system quality indicators predefined by the operator 0.

3. The method of self-tuning of the object control system according to claim 1, characterized in that the control action on the object is carried out in the form of a test non-periodic signal.

4. The method of self-tuning of the object control system according to 3, 5, characterized in that the test non-periodic signal is stepwise or linearly increasing.

5. The method of self-tuning of the object control system according to claim 1, characterized in that the customizable parameters of the control system are determined on the basis of the transfer functions of the models of the control object and the reference control system presented in

5 nonparametric form.

6. The method of self-tuning the object management system according to claim 1, characterized in that the customizable parameters of the control system are determined on the basis of the transfer functions of the models of the control object and the reference control system iteratively with respect to the structure and parameters of the custom control system until a specified coincidence of the reference and custom control systems.

7. A method for self-tuning an object management system according to claim 1, characterized in that achieving a predetermined match between the reference and

15 customizable systems are fixed according to the criterion of overshoot with the minimum complexity of the control system.

8. A self-adjusting object control system containing a control object, a regulator, a device for comparing the driving signal and the feedback signal, one of the inputs of which is connected to the output 0 of the control object, the optimal settings calculation unit, the first output is connected to the first input of the controller, the object model obtaining unit control, an output connected to the first input of the optimal settings calculation unit, a self-tuning loop control unit and an adder, inputs connected to the controller output and 5 first outputs by the control unit of the self-tuning loop, and the output connected with the control object, characterized in that a unit for obtaining the numerical characteristic of the input signal of the object is introduced into it control unit for obtaining a numerical characteristic of the output signal of the control object and the unit for constructing the reference model of the system, one of the inputs connected to the output of the control unit for the self-tuning circuit, the input of which is connected to the second output 5 of the optimal settings calculation unit, and the output of the unit for constructing the reference model of the system is connected to the second the input of the unit for calculating the optimal settings, the input and output of the control object are connected to the block receiving the model of the control object, respectively, through the block receiving h techniques, are characteristics of the input signal w object control unit and obtaining a numerical output characteristics of the control object, the regulator second input connected to the output comparator setpoint signal and the feedback signal, wherein the second and third inputs of building block reference model system designed for connection to a source of reference

15 indicators of the quality of the system and the task of the type of controller, and the second input of the device comparing the driving signal and the feedback signal is intended to be connected to the source of the driving signal.

9. The self-adjusting object control system according to claim 8, characterized in that the self-adjusting loop control unit 0 contains a key and a test signal generator connected in series, wherein the output of the test signal generator is the first output of the self-adjusting loop control unit, the key input is the input of the loop control unit self-tuning, and the key output is the second output of the self-tuning loop control unit. 5

10. A self-adjusting object management system according to claim 8, characterized in that the unit for constructing a reference model of the system comprises series-connected unit for calculating the coefficients a reference model of the system, a unit for calculating the transition characteristics of the reference model and a storage unit for the results, the output of which is the output of the building block of the reference model of the system, as well as a correction block of specified indicators, the input of which is the first input 5 of the building block of the reference model of the system, and the output is connected to the input of the block the calculation of the coefficients of the reference model of the system, while the inputs of the block for calculating the coefficients of the reference model of the system are the second and third inputs of the block for constructing the reference model of the system.

11. The self-adjusting object control system according to claim 8, characterized in that the unit for obtaining the numerical characteristics of the input signal of the control object contains a series-connected analog-to-digital converter, a recording and filtering unit for sampling, and a unit for calculating the values of the numerical characteristics of the input signal, while the input is analog digital

15 of the converter is the input of the block for obtaining the numerical characteristics of the input signal of the control object, and the output of the block for calculating the values of the numerical characteristics of the input signal is the output of the block for obtaining the numerical characteristics of the input signal of the control object. 0

12. The self-adjusting object control system according to claim 8, characterized in that the block for obtaining a numerical characteristic of the output signal of the control object contains a series-connected analog-digital converter, a block for recording, filtering and storing the sample and a block for calculating the value of the numerical 5 characteristic of the output signal, the input is analog -digital converter is the input of the block receiving the numerical characteristics of the output signal of the control object, and the output of the block calculating the magnitude of the numerical characteristics of the output signal is the output of the block for obtaining the numerical characteristics of the output signal of the control object.

13. A self-adjusting object control system according to claim 8, 5, characterized in that the control object model obtaining unit comprises successively connected control object model coefficient calculation unit, a control object model transition characteristic calculating unit and a comparison unit, while inputs of the object model coefficient calculating unit the controls are ι the inputs of the control unit model receiving unit, and the output of the comparison unit is the output of the control unit model receiving unit.

14. A self-adjusting object management system according to claim 8, characterized in that the optimal settings calculating unit comprises series-connected coefficients calculating unit

15 controller, a control system coefficient calculation unit, a control system transition characteristic calculation unit, a comparison unit and a key whose output is the second output of the optimal settings calculation unit, as well as a results storage unit, the output of which is the first output of the optimal settings calculation unit 0, and the input connected to the output of the comparison unit and to the input of the key, while the inputs of the unit for calculating the coefficient of the controller are the first and second inputs of the unit for calculating the optimal settings.

5

0