Adaptive control system with two-stage identifier and indirect standard model

FIELD: automatic control.

SUBSTANCE: process of dynamic identification is organized in two steps. At first step object control efficiency matrix estimate is calculated. At second step - matrix of own dynamic properties of object is estimated. System has adder, first and second adjusters, low frequency filter, control object, second step block of current identification, adjusters control block, block of first step of current identification, band filters block.

EFFECT: higher quality, broader functional capabilities, higher efficiency.

3 dwg

The present invention relates to the field of automatic control systems of dynamic objects with uncontrolled disturbances, unknown variable parameters, in which the spectrum of natural frequencies of the control circuit exceeds the working range (fundamental) frequency of the object itself. It is assumed that the ratio of the ranges of operating frequencies of the object and the range of control signals is known. About also known maximum rate of change of the parameters of the object.

The prototype of the present invention is a devil search adaptive control system with ID and implicit reference model described in the invention [1]. Structural diagram of an adaptive control system for objects with uncontrolled perturbations includes an adder, two controllers (one in forward and one in reverse communication), low pass filter, the control object and the contour adaptation. The latter, in turn, consists of a block of the current identification block priori information about matrix management effectiveness of the object and tuner controls.

Consider the construction of such a control system for the next task. Let the control object (OS) at the current time interval t∈[t₀that∞) is described in the following matrix differential equation

where x∈Rⁿ- directly measurable state vector OS; u∈R^m- control vector (control law, ZU); f is the vector of uncontrollable external disturbances, limited by the norm; And, In a matrix of unknown parameters OS (matrix of its own internal dynamics and efficiency of management objects) with the appropriate dimensions in the General case variables over time and across the state;directly measured or calculated analytically for x(t).

An adaptive system should form such a control law so that the OS behave like the reference model (EM), which is specified implicitly in the form of the following differential equations

where x_mthe state vector of the model; u_m- limited normal input

the impact model; dimensions correspond to equation (1); And_mand In_m- matrix of the model parameters in the General case, the variables time, and the operator And_mis asymptotically stable.

About the quality of the adaptive control system will be judged by the vector magnitude e=x-x_mthat will call the error adaptation. Accurate monitoring of the shelter for EM can be ensured only when the condition of full compliance models [2]

rankB=rank(B,A_m-A)=rank(B,B_m)=rank(B,f),

or, mo is the same,

where B⁺- a pseudo-inverse matrix In [3]. If the condition (3) operation, which we call exact:

will provide the asymptotic properties of the error adaptation, which follows from the joint consideration of equalities (1) and (2)[1].

By the condition of the matrix a, and the external disturbance f is not measured, so instead of (4) real control law will be in the form

whereand- evaluation of the matrices a and B, which are delivered by the unit current identification.

As the current algorithm identification is used recurrent algorithm type stochastic approximation, which is described as follows [4]:

where- evaluation of the matrix C;- block matrix of unknown parameters; i is the number of discrete time increments;the discrepancy, hereinafter referred to as error identification (not to be confused with the error estimation of object parameters);- extended state vector OS (the set of variables involved in the identification); G_iin the General case, the variable is positively opredelenijaja matrix [n+m) or a positive scalar.

Suppose that the following norms of vectors and matrices is limited:- this is true for the vast majority of practical problems. Then we can show that for sufficiently large norm of the matrix G over timewithout any additional conditions. In contrast, the parameter estimates to converge to the true values requires compliance with a number of conditions, including the absence of uncontrollable external disturbances [4].

In the works [1, 5, 6] it is shown that under the conditions

or

in a closed equation for the dynamics of the error adaptation system using a memory (5) has the form

The left part of the differential equation (9) is stable, so when- to achieve adaptation goals:.

To comply with conditions (7) or (8) in the invention [1] proposed in the structural diagram of the system control unit priori information about matrix management effectiveness of the entity that issues in the current block identification information about the matrix B₀of size nxm. This matrix takes into account a priori information about matrix management effectiveness in compliance with R the ties [1]

.

In the block of the current identity matrix of B₀used for matrix correctionto the adjusted scoreto satisfy the conditions(7), (8).

However disclosed in the prototype [1] approach has the following disadvantages:

1. It is assumed the presence of a priori information about matrix management effectiveness, which is not always the case. For example, at the stage of the flight maneuverable aircraft at supercritical angles of attack, when the management effectiveness varies greatly, and complex ambiguous dependencies.

2. The measurement or calculation of the derivative.

The objective of the invention is to remedy these disadvantages.

It is recommended to use filtered signals, and the identification process will be divided into two stages:

1. The determination of the estimated matrix management effectiveness. To generate this stage it is expedient in the block diagram of the system to allocate a separate block procedure evaluation matrix management effectiveness. The system can include a block of bandpass frequency filters.

2. Receive an evaluation matrix native speakers OS. This stage teleshop the knowledge to organize in the current block identification prototype which later will be called a block of the second stage current identification.

Explain the need for the proposed changes.

Obviously, block a priori information about matrix management effectiveness of the object is not needed, if you provide sufficient accuracy specified matrix:. In the limitand conditions (7), (8) are performed automatically. Thus, the dynamic equation of the error adaptation will be even simpler than the expression (9), [6]

To improve the accuracycontributes to the following:

1. In contrast to the measurement component of the state vector, which often contains considerable dynamic, fluctuating and constant errors, the measurement component of the vector control is ensured with high accuracy. For example, the measurement of the angular position of the control surface of the aircraft using a position sensor with digital output is carried out with an accuracy of angular minutes [7].

2. For a real technical system control frequency band control signals, as a rule, considerably wider than the frequency range of the dynamics of the shelter. The latter is, most often, the low-frequency link.

3. The accuracy of the estimated parameters depends on the quantity. The more parameters includes a mathematical model of the OS, the harder it is to achieve high accuracy of their estimation and Vice versa [8]. If OS (1) to evaluate only the elements of the matrix b, then the number of evaluations is significantly reduced and thereby facilitates the accurate definition.

To explain the phrase, let's consider one of the rows of the system (1)

where the index k indicates the number of lines of equation (1). Response(the term of the regression analysis) is a response to all signals in the right-hand side of equation (10). To reduce the number of estimated parameters must be extracted from the signal response component, which is the reaction only on the control signals.

For this purpose we use the fact that differences in the spectra of operating frequencies of the OS and control signals. The opportunity to skip all the variables of equation (10) through a band-pass filter, the amplitude-frequency characteristic (AFC), depicted in figure 1. Figure 1 is denoted by: A₀-Frequency response of the shelter; A_yspectrum control signals; A_PF-Frequency response of bandpass filter. While ensuring the narrowness of the frequency response of the filter, the latter transmits a signal only with frequency ω_PFwhich will be called a frequency selection filter.

To provide the most simple implementation of such a bandpass filter according to the scheme, from which is given in figure 2,and. In the figure W_F1, W_F2W'_F2W'_F2- the transfer function of the oscillatory parts with different relative attenuation coefficients:

where p is the operator of differentiation; ω_nφ- the natural frequency of the bandpass filter; ξ_1,ξ₂the relative attenuation coefficients, such thatSuperscript "PF" indicates the corresponding output signals of the band pass filter.

The frequency response of the oscillating links {_F1And_F2and receive bandpass filter (A_PF) with respect to u andshown in figure 2,B.

Equation (10), recorded from the output signals of the bandpass filter will be

where g_k- hindrance due to incomplete suppression of the signals of its own internal dynamics of the object at the bandpass filter and the external disturbances.

As you can see, the number of estimated parameters in equation (12) is much smaller than in the model (10).

Custom model for the current identity, respectively, will have the form [8]

The algorithm first stage in accordance with the expressions (6), (12) and (13) has the form

wherepositively ODA is divided matrix.

Natural practical requirement to consider using an adaptive management approach is the requirement of smallness of the norm interference g on frequency allocation. For the OS with scalar control algorithm identification is greatly simplified, since in this case, instead of (12) will be

It follows that to improve accuracyyou want therani.e. that the relationit was big enough. The latter can be used in the system as follows: calculate the proposed approach estimates do not constantly, but only when the norm of the vector u^PFexceeds an experimentally set threshold value.

The second stage is based on the assessmentdelivered the first stage, and is intended for assessment. It may be determined in accordance with the algorithm (6) based on:

whereG_2i- positive definite matrix.

Since the condition x not measured, we will offer a second stage to build on these dependencies, but filtered the s signals:

where- output vector signal filter is a real differentiating element with transfer functionwhen its input is- the output vector signals of the filter aperiodic link with transfer functionwhen the input serves u_iand x_i; τ - the time constant of the filters is selected sufficiently low to run ratio

where a,b are arbitrary elements of matrices a And C.

In the last ratio is easy to show that equation (1) corresponds to the following entry

pointing to the possibility of building identification on these filtered signals.

For the implementation of the considered approach is required following changes to the adaptive control system proposed in the prototype [1].

As the identification process takes place in two stages, you must block the current identification of the prototype is divided into two blocks: the first phase, which will be the evaluation of matrix management effectiveness of the facility; the block of the second stage is to estimate the matrix of its own internal dynamics of the shelter.

The unit of the first stage Ident is the codification includes a logical device, running the algorithm for the identification of this phase only when exceeding the norm of the vector u^PFa predetermined threshold value. Also the system is made to a block of bandpass filters based on the links (11)designed for high frequency bandpass selection control signals and the derivative of the state vector of the shelter.

As with the process of identifying the conditions for the evaluation of matrix management efficiency with high accuracy, the unit priori information about matrix management effectiveness of the object becomes unnecessary and adaptive systems it is excluded. Not also require the correction procedure of evaluation.

Figure 3 presents a structural diagram of an adaptive control system with two-stage ID and implicit reference model.

Structural diagram contains the adder 1, the first 2 and second 3 regulators, filter 4 low frequencies, the object 5 control unit 6 of the second stage current identification, block 7 settings regulators, block 8 of the first stage of the current identification block 9 bandpass filters.

The adaptive system works as follows. Specifies the impact in the form of a signalis fed to the first input of the adder 1. To the second input of the adder receives a signalc you are the ode of the second regulator 3. The output of the adder is connected to the first input of the first controller 2, the controller generates the control law in accordance with addictions

The output of the first regulator connected to the input of the filter 4 low frequencies that is configured to cut off the high frequencies. The output of the filter is connected to the input of the object 5 management and to the first input unit 6 of the second stage current identification and to the first input of block 9 of bandpass filters.

From the output of the control object is removed information about the measured value of the state vector (x_i). The output of the control object associated with the second input unit 6 of the second stage current identification, with the second input of the second regulator 3 and the second input unit 9 bandpass filters. Bandpass filters have the structure of figure 2,and is based on links with the transfer function (11). They are separated from the control signals u(t) and the derivativecomponents in a narrow range of frequencies around the frequency of selection of each filter ω_PFforming signalsandFrequency ω_PFis selected in advance by the source a priori information to meet the ratios of the frequency response of its own internal dynamics of the object and the range of control signals (figure 1).

From the output unit 9 bandpass filters the signal is s andenter in block 8 of the first stage current identification. In this block calculates the evaluation matrix management effectiveness. She goes through the first output unit 8 in block 6 of the second stage current identification on its third input.

Unit 6 of the second stage current identification signals u_iand x_iwith the control object, known evaluationcoming from the block of the first stage current identification on the basis of the relations (15) filters the signals, and generates the current evaluation. The filtering is based on the real differentiating and aperiodic chains with continuous time, satisfying the condition (16) and selected based on a priori information about the maximum rate of change of the parameters of the object.

The current algorithms identify blocks 6, 8 belong to the class of algorithms of stochastic approximation, in which the most efficient use of recurrent method of least squares with forgetting factor [8].

The output of the second stage current of identification, through which issued assessmentandassociated with unit 7 the knobs. This block computes the matrix and. For the implementation of pseudouridine matrix can be used iterative method Greville [3]. The first output unit 7 is connected with the second input of the first regulator, it is passed to the matrix. The second output unit 7 is connected with the first input of the second regulator, it is passed to the matrix.

LITERATURE

1. Beeches V.N., Kruglov, S. p. Adaptive control system with ID and implicit reference model. - RF patent for the invention №2108612; Appl. 14.09.94.; Priority 14.09.94; Publ. 10.04.98., Bull. No. 10. (prototype).

2. Utkin V.. Sliding modes in optimization and control. - M.: Nauka, 1981.

3. Gantmacher FR Theory of matrices. - M.: Science, CH. nat. Ed. Mat. lit., 1988.

4. Tsypkin AS fundamentals of information theory to identify. - M.: Science, CH. nat. Ed. - Mat. lit., 1984.

5. Beeches V.N., Kruglov, S. p., Reshetnyak, H.E. Adaptability of a linear dynamic system with an identifier and a reference model // Automatics and telemechanics, 1994. No. 3, S. 99-107.

6. Bronnikov, A. M., Kruglov, S. p. Simplified terms of adaptability of the control system with an identifier and a reference model // Automatics and telemechanics, 1998. No. 7, S. 107-117.

7. Beeches NR. Integrated flight and navigation system. Part 2. Flight system. - M.: WEA, 1986.

8. Ljung L. system Identification. Teorias user: TRANS. from English. Ed. Jazzymina. - M.: Nauka, 1991.

Adaptive control system of a two-part identifier and an implicit reference model containing an adder, a first input of which is connected to define the impact and the output to the first input of the first regulator, the output of which is connected to the input of the low pass filter, the output of which is connected to the input of the control object and to the first input of the current block identification, the output of the control object connected to the second input of the current block identification and to the first input of the second encoder output block current identity is connected to the input of the tuner knobs, the first output of which is connected to the second input of the first regulator and the second output to the second input of the second regulator, the output of which is connected to the second input of the adder, wherein the block of the current object identification consists of three blocks: block bandpass filters, block of the first stage current identify and block the second phase of the current identity, the first unit of bandpass filters and block the second phase of the current identity is connected to the output of the low pass filter, a second input unit of bandpass filters and block the second phase of the current identity is connected to the output of the control object, the output of bandpass filters connected to the input of block Pervov the phase current identification, the output of which is connected to the third input of the second stage current identification, the output of which is connected to the tuner controls.