RU2343524C1 - Adaptive control system - Google Patents

Abstract

FIELD: physics; control.

SUBSTANCE: invention is related to the field of automatics and may be used for control of chemical, power-producing, electromechanical and other objects with alternating or non-stationary parameters. Adaptive control system contains regulator, summator, control object, three amplitude and phase meters, unit of phase frequency self-tuning, generator, computer unit, computer of amplitude-phase characteristic, unit of amplitude self-tuning. Connection of mentioned elements of adaptive system is executed according to application documents.

EFFECT: exclusion of band-stop filter from circuit; expansion of amplitude range of operation; make it possible to operate with low amplitude at the output from control object, expansion of application field.

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Description

The invention relates to electrical self-adjusting control systems, and in particular to the field of adaptive control systems with a test harmonic signal, and is intended to control chemical, energy, electromechanical and other objects with variable or non-stationary parameters.

The closest in technical essence to the proposed solution is a self-adjusting control system with a harmonic test signal (RF patent No. 2068196, class G05B 13/02), containing a controller, a control object, the output of which is connected to the first input of the amplitude and phase meter, the first input of which connected to the first input of the computing unit, the output of which is connected to the input of the tuning parameters of the controller, the signal input of which is connected to the output of the comparison device, the first input of which is the input of the system we, the adder and generator of trial harmonic oscillations, a phase adjustment block, the input of which is connected to the second output of the amplitude and phase meter, a blocking filter and a block filter coefficient calculation unit, the input of which is connected to the output of the phase adjustment block, connected to the second input of the computing block and to the input of the generator of trial harmonic oscillations, the output of which is connected to the second input of the amplitude and phase meter and to the first input of the adder, the second input of which is connected to the output of the regulator, and the output to the input of the control object, the output of which is connected to the information input of the blocking filter, connected by the output to the second input of the comparison device, and the control input to the output of the block calculating the coefficients of the blocking filter.

The disadvantages of the known device are connected with the fact that the controller settings are determined by searching for one “characteristic” point of the amplitude-phase characteristic (AFC) of the control object, in particular, the point whose phase is -π and then using the empirical Ziegler-Nichols method for calculating PID- regulator. At the same time, in the known device it is practically impossible to assess the quality of the controller settings obtained during adaptation related to the operation of the system as a whole, namely: to evaluate the most important indicator of the functioning of the control system - stability margins in amplitude and phase. Thus, the known device does not continuously monitor the results of the obtained optimal settings, that is, it does not control the AFC of the open-loop control system at the frequency of test oscillations.

When carrying out the adaptation process, a priori data are required at least about the gain of the control object. They are necessary to set a suitable amplitude of test oscillations supplied by the generator of sinusoidal oscillations to the input of the control object. The amplitude of the test harmonic at the input of the object should be, on the one hand, sufficient to highlight the test harmonic in the output signal of the object against the background of noise and, on the other hand, not so large as to bring the object out of normal operation. This circumstance limits the scope of the known device.

The objective of the invention is the provision and continuous monitoring of the given stability margins in the system with optimal settings of the PID controller while simultaneously implementing an identityless approach to constructing an adaptive control system when the mathematical model of the control object is not used explicitly anywhere in the system’s functioning,

The technical result is the exclusion of the blocking filter from the circuit and the negative effects of the self-tuning process associated with it, as well as the expansion of the amplitude range of operation by organizing a special stabilization circuit for the amplitude of the test harmonic at the output of the control object, which allows working with a small amplitude at the output of the control object, and, how consequence, the expansion of the scope of the adaptive system.

This result is achieved by the fact that in an adaptive control system containing a regulator, the first input of which is connected to the input of the adaptive control system, and the output is through a series-connected adder, a control object to the first input of the first amplitude and phase meter, a phase-locked loop, the output of which is connected to the input of the generator and through the computing unit to the second input of the regulator, the output of the generator is connected to the second input of the adder and the second input of the first meter of amplitude and phase, introduced the second amplitude and phase meter, the first and second inputs of which are connected to the output of the adder and the output of the generator, respectively, the amplitude-phase characteristic calculator, the amplitude output of which is connected to the second input of the computing unit, and the first and second inputs are connected to the first and second outputs of the second amplitude meter and phase, the phase output of the amplitude-phase characteristic calculator is connected to the input of the phase-locked loop, the third amplitude and phase meter, the first and second inputs of which are connected to the output of the controller and the output of the generator, respectively, and the outputs of the amplitude and phase are connected to the third and fourth inputs of the computer of the amplitude-phase characteristic, the amplitude auto-tuning unit connected between the amplitude output of the first amplitude and phase meter and the second input of the generator, and the output of the control object is connected to the third input of the regulator.

In addition, the controller is based on a digital high-speed PID controller,

- the first and second and third amplitude and phase meters are based on Fourier filters.

The invention is illustrated using the drawings, where in Fig.1. shows a structural diagram of an adaptive control system, Fig.2. - the schedule of the adaptive control system during self-tuning, Fig.3 - schedule of the adaptive control system when practicing master actions.

The adaptive control system contains a controller 1, the first input of which is connected to the input of the adaptive control system, and the output is connected through an adder 2 in series, the control object 3 is connected to the first input of the first 4 amplitude and phase meters, phase-locked loop 5 (BFAC), the output of which connected to the input of the generator 6 and through the computing unit 7 to the second input of the controller 1, the output of the generator is connected to the second input of the adder 2 and the second input of the first meter of amplitude and phase, the second 8 meter of amplitude and phase, the first and second inputs of which are connected to the output of the adder and the output of the generator, respectively, the calculator 9 amplitude-phase characteristics, the amplitude output of which is connected to the second input of the computing unit, and the first and second inputs are connected to the first and second outputs of the second amplitude and phase meter, phase output the amplitude-phase characteristic calculator is connected to the input of the phase-locked loop, the third 10 amplitude and phase meter, the first and second inputs of which are connected to the output of the controller and the output to the generator, respectively, and the outputs of the amplitude and phase are connected to the third and fourth inputs of the calculator of the amplitude-phase characteristic, the amplitude automatic adjustment unit 11 connected between the amplitude output of the first amplitude and phase meter and the second input of the generator. The output of the control object is connected to the third input of the controller. In this case, the controller is based on a digital high-speed PID controller, and the first second and third amplitude and phase meters are based on Fourier filters.

For most industrial control objects, the AFC vector of an open optimally tuned system occupies the position W _pc (jω) = 0.8 · е ^{-j · 2.62} at a frequency corresponding to the period Т _rez = mT _and where, in the absence of any a priori information about the object’s dynamics, the calculated value m it is advisable to choose m≈3.5 [1].

Therefore, the adaptation circuit of the proposed adaptive system monitors and stabilizes the vector of the amplitude-phase characteristic (AFC) of the open-loop control system in a given position W _r.c. (jω) = 0.8 · е ^{-j · 2.62} , unlike the prototype, without the use of a blocking filter in the structure of the main control loop. To evaluate the open-loop phase response vector, a new signal sampling point has been added: PID controller output U _p . This signal analyzes the third amplitude and phase meter (third Fourier filter).

Adaptive control system operates as follows.

The input of the control object receives the sum of the control and trial harmonic, generated by the generator, signals U _p (t) + U _g (t). The peculiarity of the system’s operation is the need to set up the PID controller’s preliminary settings; otherwise, it is impossible to evaluate the vector of the AFX system. The second amplitude and phase calculator (second Fourier filter) evaluates the steady-state values of the amplitude R _I and phase ϕ _{I of} test oscillations at the input of the control object U (t). The third Fourier filter estimates R _p and ϕ _p in the output signal U _p (t) of the controller. Then, the AFC calculator determines the vector of the complex characteristic of the open control loop R _c , ϕ _c at the frequency of the test signal ω. The use of two Fourier filters is necessary for estimating the AFX vector in a closed loop.

Search and tracking of the frequency at which the phase shift of the system ϕ _s is equal to ϕ _s = -2.62 rad is carried out by the phase locked loop (BFAC). The calculation unit calculates the PID settings k _p, T _u, T _d when the phase φ _with a certain accuracy value _of φ = -2.62 rad by the formulas:

;

;

,

;

;

,

where j is the number of the current period of adjustment of the controller,

- значение амплитуды вектора АФХ системы, в котором его надо стабилизировать,

- the value of the amplitude of the vector of the AFC of the system in which it must be stabilized,

T _and and T _d - the settings of the adaptive control system, normalized by the quantization period T _q ,

N _j = 2π / (ωT _q ) is the normalized period of trial oscillations,

m - is selected in the region of 3.5.

Thus, the controller settings depend on their previous values.

The third 10 Fourier filter estimates the values of the amplitude R _p and phase ϕ _{p of the} harmonic with the frequency of test oscillations ω at the output of the regulator.

If we denote the controller output signal V = U _p , and the generator output signal χ = U _g , then the controller output operator relative to the generator is determined by the following expression:

.

.

The dependence of the phase on the frequency of the test sinusoid ω at the output of the regulator has the form:

φ _p (ω) = arg {Ф _χv (jω)} = arg {-W _pid (jω) W _oy (jω)} - arg {1 + W _pid (jω) W _oy (jω)}.

The following difference:

φ _p (ω) -φ _in (ω) = arg {-W _pid (jω) W _oy (jω)} = arg {W _pid (jω) W _oy (jω)} - π, whence φ _c (ω) = arg {W _pid (jω) W _oy (jω)} = φ _p (ω) -φ _in (ω) + π.

Therefore, the computer 9 amplitude-phase characteristics to obtain on the j-th cycle of self-tuning an unbiased estimate of the phase of the AFC vector of an open system should use the following algorithm:

.

.

диапазона изменения выходной переменной. БАА по текущей оценке амплитуды R_вых(j) на j-м цикле адаптации изменяет амплитуду пробной синусоиды генератора:In addition to the main blocks, the adaptive controller also includes a stabilization circuit for the amplitude of the test oscillations. It consists of the first Fourier filter and the amplitude auto-tuning block (BAA). Such a circuit is necessary, since when controlling a technological process with variable parameters, its gain can vary within wide limits, while it is desirable that the level of test harmonic at the output of the object does not exceed a predetermined value

range of variation of the output variable. BAA according to the current estimate of the amplitude R _o (j) on the j-th adaptation cycle changes the amplitude of the probe sine wave of the generator:

.

.

The work of the blocks included in the structure of the control system can be described as follows.

The generator 6 trial harmonic oscillations generates a test signal:

U _g [k] = R _g sin (δ [k]),

where k is the current number of the quantization period;

R _g - the specified value of the amplitude of the test harmonic;

δ [k] is the discrete time of the trial oscillation generator, depending on the current value of the normalized oscillation period N _j and determined by the relation: δ [k] = δ [k] + 2π / N _j , moreover, if δ [k] ≥2π, then δ [k] = δ [k] -2π.

N _j is the normalized period, which is associated with the frequency of test oscillations by the ratio:

ω = 2π / (N _j T _q ),

where T _q is the quantization period.

Amplitude and phase meters are discrete Fourier filters, which determine the amplitude of R (j) and phase φ (j) of the harmonic component in the signal S [k] according to the formulas from the m-periods of trial oscillations on the jth adaptation cycle:

where R _s (j), R _c (j) is the sine and cosine components of the signal Y [k];

m is the number of analyzed oscillation periods, varying which can be achieved to increase the noise immunity of the adaptation circuit, depending on the "noise" Y [k].

The output signal of the control object Y [k] (S [k] = Y [k]) acts as the analyzed signal S [k] for the first Fourier filter (block 4). When the adaptive control system operates in real time, the current signal values from the output of the control object Y [k] are obtained by analog-to-digital conversion. For the second Fourier filter (block 8), the analyzed signal is the input of the control object U [k] (S [k] = U [k]). For the third Fourier filter (block 10) - U _p [k] (S [k] = U _p [k]).

The duration of the sequence analyzed on the jth cycle, during which the generator frequency does not change, is mN _j T _q .

Block 5 phase adjustment works, in the simplest case, according to the integral control law, since jumps in the test frequency are undesirable. It is, by changing the frequency of the oscillator ω monitors the phase shift between the harmonic test frequencies at the input level of the control object and the same harmonic frequencies, the controller output _of φ = -2.62 rad. The frequency phase adjustment block implements the following function:

N _{j + 1} = N _j {βφ (j) / φ _s - (β-1)},

where β is selected in the range of 0.5 ÷ 1.5, which ensures stable operation of the adaptation circuit for objects with different values of delay.

Controller 1 implements the digital high-speed PID controller algorithm with filtering the D component. It is obtained by discretizing the corresponding continuous PID controller, and the control law is as follows:

where k _p is the transfer coefficient of the controller, T _and is the time constant of the controller isodrome, T _∂ is the time constant of the differentiation of the controller.

The input of the control object 3 is the sum of the signals from the output of the regulator U _p (t) and the trial harmonic effect U _g (t) from the generator of trial harmonic oscillations, the frequency of which can vary.

The work of the adaptive control system was investigated on a computer model. Figure 2 shows a graph of self-tuning of an adaptive PI controller (with the D component turned off, Td = 0) with stabilization of the open-loop phase characteristic vector when controlling the object. On the graph: N - normalized period of trial oscillations; R _g - the amplitude of the test signal; Kp, Ti, TD - PID controller settings; k is the transmission coefficient of the control object; T1 is the first time constant of the object; R _o - the amplitude of the oscillations at the output of the object; Ph is the phase of the AFC vector of the object.

The following initial parameters of the PI controller were established: k _p = 0.8, T _and = 3200 s. These parameters are far from their optimal values determined as a result of self-tuning and presented in the upper right corner of the graph: k _p = 1.5, T _and = 297.14 s. The graph also shows: Rs and PHs - respectively, the amplitude and phase of the vector of the AFC of the open-loop control system at the frequency of test oscillations. The quantization period in the system is T _q = 20 s.

Figure 3 shows a graph of the development of the adaptive task controller. At the same time, the self-tuning loop continued to work, which is an integral condition for managing objects with variable parameters.

The graph reveals the features of the adaptive controller with stabilization of the open-loop phase characteristic vector: at large jumps of the driving influence, the estimates of the vector of the phase characteristic curve are also thrown, after which several periods of test oscillations are required to restore the true values of the amplitude and phase. This is due to the fact that with a similar construction of the adaptation algorithm, the frequency of test oscillations is close to the resonance frequency of the system, with which transients in the system proceed. This fact slightly reduces the speed of the self-tuning loop, however, in general, the graphs show the qualitative dynamics of the main loop of the control system.

The presented graphs confirm the operability of the adaptive control system when controlling objects with variable parameters, even under the most complex parametric disturbances in the form of jumps.

Thus, the proposed adaptive control system provides continuous monitoring of the specified stability margins in the system at the optimal settings of the PID controller while simultaneously implementing an identityless approach to constructing an adaptive control system, i.e. when the system operates, the mathematical model of the control object is not used explicitly anywhere. In the proposed adaptive control system, a blocking filter and the negative effects of the self-adjustment process associated with its presence are excluded from the circuit, and the adaptive control system has a wider amplitude range of operation compared to the prototype, which allows working with a small amplitude at the input of the control object and, as a result , expand the scope of the adaptive control system.

Literature

1. Rotach V.Ya. Calculation of the dynamics of industrial automatic control systems, M .: Energy, 1973, 440 p.

Claims (3)

1. Adaptive control system, including a controller, the first input of which is connected to the input of the adaptive control system, and the output through a series-connected adder, a control object to the first input of the first amplitude and phase meter, a phase-locked loop, the output of which is connected to the generator input and through computing unit to the second input of the regulator, the output of the generator is connected to the second input of the adder and the second input of the first meter of amplitude and phase, characterized in that the second measurement amplitude and phase amplifier, the first and second inputs of which are connected to the output of the adder and the output of the generator, respectively, the amplitude-phase characteristic computer, the amplitude output of which is connected to the second input of the computing unit, and the first and second inputs are connected to the first and second outputs of the second amplitude meter and phase, the phase output of the amplitude-phase characteristic calculator is connected to the input of the phase-locked loop, the third amplitude and phase meter, the first and second inputs of which are connected to the output the regulator and the generator output, respectively, and the amplitude and phase outputs are connected to the third and fourth inputs of the amplitude-phase characteristic calculator, the amplitude auto-tuning unit connected between the amplitude output of the first amplitude and phase meter and the second generator input, and the output of the control object is connected to the third input regulator. 2. The adaptive control system according to claim 1, characterized in that the controller is based on a digital high-speed PID controller. 3. The adaptive control system according to claim 1, characterized in that the first, second, and third amplitude and phase meters are based on Fourier filters.

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