RU2099766C1 - Method for functional diagnostics of linear control systems - Google Patents

Abstract

FIELD: automatics, possibly testing and fault detection of linear automatic control systems. SUBSTANCE: method is realized with use of dynamic model of tested system. Method comprises steps of multiply summing and integrating input and output signals of linear units. Output signals of said model are used for testing operating efficiency of the whole system by means of comparing current values with preset threshold value. EFFECT: enhanced reliability of diagnostics. 5 dwg

Description

 The invention relates to the field of automation and can find application in monitoring systems and troubleshooting of linear automatic control systems.

 There is a known method for diagnosing linear dynamic objects, the troubleshooting of which is carried out under the assumption that only single faults can occur in the object (USSR author's certificate N 1462254, class G 05 D 23/02, 1987). The occurrence of multiple defects can lead to diagnostic errors during the implementation of this method.

где a_ki, b_ki коэффициенты передаточной функции 1-го динамического элемента, входящего в диагностируемую систему, вид передаточной функции которого принимается:

k максимальный порядок передаточной функции; γ параметр, характеризующий инерционные свойства контрольного устройства; m_i - коэффициенты, определяющие вклад каждого звена в контрольное соотношение.Closest to the proposed method, the technical solution is a method for diagnosing linear dynamic objects (A. s. USSR N 1300419, class G 05 B 23/02, 1987), based on the use of a control ratio of the following form:

where a _ki , b _{ki are the} coefficients of the transfer function of the 1st dynamic element included in the diagnosed system, the form of the transfer function of which is taken:

k maximum transfer function order; γ parameter characterizing the inertial properties of the control device; m _i are the coefficients that determine the contribution of each link to the control ratio.

 The application of the method is limited to considering malfunctions that distort one of the coefficients of the entire set of controlled dynamic elements. However, the real structural defect of the element in the vast majority of cases leads to a simultaneous change in the values of several coefficients of the transfer function (for example, a change in the insulation resistance of the PI controller capacitor leads to a simultaneous change in the gain and time constant). Therefore, when deviating from the nominal value of several coefficients, errors in determining the location of the defect are possible.

 Implementation of the relation (1) for monitoring the operability can lead to the conclusion that the system is operable when multiple defects occur in it. We show this by example. Consider the structural diagram of the system shown in FIG. one.

Применим контрольное соотношение вида (1), для простоты примем, что контрольное устройство безынерционно ( γ 0):
D = (x₁-ε•a₁)+(x₂-x₁•a₂)+(x₃-a₃x₁) (2)
Определим реальные сигналы для этого случая:

где g значение входного сигнала.Let all three links with transfer functions a ₁ , a ₂ , a ₃ (inertialess links) be controlled. In this case, it is necessary to control the signals ex ₁ , x ₂ , x ₃ . Let the nominal values of the parameters a ₁ a ₂ a ₃ 1. The transfer function of a closed system

We apply the control relation of the form (1), for simplicity we assume that the control device is inertialess (γ 0):
D = (x ₁ -ε • a ₁ ) + (x ₂ -x ₁ • a ₂ ) + (x ₃ -a ₃ x ₁ ) (2)
Define real signals for this case:

where g is the value of the input signal.

Пусть теперь в системе возникли кратные дефекты и параметры приняли новые значения
α₁= a₁,α₂= a₂+Δa;α₃= a₃-Δa.
Примем Δa 0,5. Передаточная функция замкнутой системы при наличии двух неисправностей будет иметь значение:

т. е. W₃ > W_3ном и система потеряла работоспособность. Определим реальные сигналы для этого случая

Подставим полученные значения сигналов в контрольное соотношение (2):

Использование контрольного соотношения вида (2) приводит к ошибке контроля. Система считается работоспособной, хотя значение передаточной функции замкнутой системы изменилось на 100%
Легко обобщить полученные результаты и на коэффициенты при ненулевых степенях P (постоянные времени). Появление пары кратных дефектов для постоянных времени также приводит к их компенсации, поскольку в сумму контрольного соотношения соответствующие им слагаемые войдут с противоположными знаками.Substitute the obtained values in relation (2):

Let now multiple defects appear in the system and the parameters take new values
α ₁ = a ₁ , α ₂ = a ₂ + Δa; α ₃ = a ₃ -Δa.
Take Δa 0.5. The transfer function of a closed system in the presence of two faults will matter:

i.e., W ₃ > W _3nom and the system has lost working capacity. Define real signals for this case

Substitute the obtained signal values in the control relation (2):

Using a control relation of the form (2) leads to a control error. The system is considered operational, although the value of the transfer function of a closed system has changed by 100%
It is easy to generalize the results obtained to coefficients for nonzero powers of P (time constants). The appearance of a pair of multiple defects for time constants also leads to their compensation, since the corresponding terms will be included in the sum of the control relation with opposite signs.

 The control ratio in the known method is calculated using a set of integrators unlimited (and therefore, a long time). In the presence of a zero drift of operational amplifiers and integration of errors due to an inadequate model object, the control parameter may exceed the threshold value in the absence of defects.

 In addition, the known method has another significant drawback, which is obvious from the following reasoning.

При отсутствии неисправностей в звене и адекватной модели имеем

Пусть изменение технического состояния звена привело к изменению выходного сигнала y' y + Δy.In expression (1), we take n 1 (control of one link), γ 0 (inertialess control device). Imagine the signal D in the following form:
D = F _a y (t) -F _b x (t), (3)
where y (t) is the output signal of the link;
x (t) link input;
F _a , F _b linear operators of the following form:

In the absence of malfunctions in the link and an adequate model, we have

Let the change in the technical condition of the link lead to a change in the output signal y 'y + Δy.

In this case
Δ ′ = F _a y′-F _b x = F _a y + F _a Δy-F _b x = F _a Δy.
That is, the value of the control signal is determined by the coefficients of the diagnostic model a _i and the signal Δy which, in turn, depends on the input signal x. Thus, with the same deviation of the coefficients of the monitored link from the nominal, but for different levels of the input signal, the value of y will be different. This fact makes it difficult to use the known method for functional diagnosis. In this sense, an optimal control device would be the one whose output signal would be proportional to the degree of deviation of the transfer function coefficients from the nominal value and would not depend on the amplitude of the input signal.

 The technical problem to which the invention is directed is to expand the functionality of the method and increase the reliability of diagnosis.

 This problem is solved by the fact that in the method of functional diagnosis of linear control systems based on the use of a dynamic model of the system, multiple summing and integration of input and output signals of linear blocks, according to the invention, the diagnostic time interval Δtg equal to the duration of the system transition process, the time interval Δt equal to the longest transient time across the entire set of blocks, the input and output signals of a closed control system are supplied to the dynamic model of this system, the output signals of the model are repeatedly summed and integrated with zero initial conditions during the Δtg control signal after the (m + 1) th summation, where m is the system order, they are used to monitor the operability of the entire control system by comparing with a predetermined threshold value, the above operations are repeated periodically, if the control signal exceeds the threshold value, a decision is made about the presence of one or more defects in the system, the input and output signals each block of the system is fed to its dynamic model, from the output of which they are summed and integrated K times with zero initial conditions for the interval Δt, the control signal value is determined for each block and the presence of a defect in the block is determined by comparison with the threshold value.

A new set of actions is proposed to solve the problem, expanding the functionality of the method and increasing the reliability of diagnosis:
1. Determine the nominal values of the transfer coefficients of the closed-loop automatic control system α _i , β _i and the transfer coefficients of the blocks included in the system a _ij , b _ij .

2. Determine the duration of the transient system t _n .

3. In order to exclude the influence of zero drift of the operational amplifiers of the integrators, the performance check is carried out periodically with the preliminary setting of zero initial conditions of the integrators. The turn-on time of the integrators (calculation duration Δ) is set equal to the duration of the transient process t _n , which allows you to take into account all the features of the dynamics of the controlled system.

где F_a, F_b операторы, определяемые выражениями (4).4. The control signal D is obtained by implementing the ratio on the integro-adders

where F _a , F _{b are the} operators defined by expressions (4).

где Y₀(t) значение выходного сигнала при отсутствии неисправностей (поскольку F_aY₀(t)≡ F_b•X(t). Подставляя в (6) и учитывая тождество, получим:

Таким образом, контрольное соотношение (5) представляет собой относительное интегральное изменение выходного сигнала звена, которое уже не зависит от амплитуды входного сигнала, а определяется степенью изменения технического состояния.In the expression (5) in the numerator is written the control ratio used in the known method, and the denominator can be represented in another form:

where Y ₀ (t) is the value of the output signal in the absence of faults (since F _a Y ₀ (t) ≡ F _b • X (t). Substituting in (6) and taking into account the identity, we obtain:

Thus, the control relation (5) represents the relative integral change in the output signal of the link, which no longer depends on the amplitude of the input signal, but is determined by the degree of change in the technical condition.

 The implementation of the control ratio is shown in FIG. 2, where 1 is a controlled unit; 2, 3 blocks containing integro-adders that implement relations (4), 4 dividing device. In FIG. 3, 4 show the implementation of blocks 2 and 3, respectively.

где n число контролируемых динамических элементов.5. The troubleshooting start only when the value of the signal Δ modulo exceeded the preset threshold value D _max
6. Troubleshooting is carried out by alternately determining the control signals Δ _i for each of the links included in the system:

where n is the number of controlled dynamic elements.

If Δ _i exceeds the threshold value Δ _max , the 1st element is considered faulty.

 7. The time for determining the control relation (integration time) is set equal to the greatest duration of the transient process over the entire set of dynamic elements.

 The implementation of this sequence of actions allows us to determine malfunctions of arbitrary multiplicity and better takes into account the peculiarities of the manifestation of defects of individual blocks (with a simultaneous change in the coefficients). The frequency of control eliminates the accumulation of errors by analog devices of the control circuit.

 Comparison of the above set of actions (1 7) on the object of diagnosis with the prototype leads to the conclusion that all 7 operations separately, and therefore, especially their combination, are absent in the prototype and in the prior art.

 The method of functional diagnosis is as follows.

При контроле работоспособности системы периодически контролируются сигналы g и x₂ системы, вычисляется контрольное соотношение вида
Δ = (0,5g-x₂)/0,5g. и сравнивается с заранее установленным пороговым значением Δ_max Примем Δ_max= 0,1
Рассмотрим теперь появление в системе кратных дефектов
α₁= a_1ном;α₂= a_2ном+Δa;α₃= a_3ном-Δa,Δa = 0,5
Этот случай был проанализирован ранее применительно к прототипу. Передаточная функция замкнутой системы при наличии дефектов будет иметь значение

Реально контролируемый сигнал в этом случае будет иметь значение:

Подставим эту величину в контрольное соотношение и получим:
Δ = (0,5g-g)/0,5g>Δ_max
Поскольку

выносим решение о наличии одного или нескольких дефектов в системе и приступаем к их поиску. Для этого контролируем сигналы ε x₁, x₂, x₃ и подставляем их в соответствующие контрольные соотношения. Реально контролируемые сигналы будут иметь значения:

Подставим полученные значения сигналов в соответствующие контрольные соотношения:

Сравнивая с пороговым значением Δ_max выносим решение о наличии неисправностей в блоках 2 и 3.Consider a diagnostic object with a block diagram shown in FIG. 1. Let a _1nom a _2nom a _3nom 1. The nominal value of the transfer function of a closed system:

When monitoring the health of the system, the signals g and x _{2 of the} system are periodically monitored, a control relation of the form is calculated
Δ = (0.5g-x ₂ ) / 0.5g. and compared with a predetermined threshold value Δ _max Take Δ _max = 0.1
We now consider the appearance of multiple defects in the system
α ₁ = a _1nom ; α ₂ = a _2nom + Δa; α ₃ = a _3nom -Δa, Δa = 0.5
This case has been analyzed previously in relation to the prototype. The transfer function of a closed system in the presence of defects will matter

A really controlled signal in this case will matter:

Substitute this value in the control ratio and get:
Δ = (0.5g-g) / 0.5g> Δ _max
Because the

we make a decision on the presence of one or more defects in the system and proceed to their search. To do this, we control the signals ε x ₁ , x ₂ , x ₃ and substitute them in the corresponding control ratios. Actually controlled signals will have the following meanings:

Substitute the obtained signal values in the corresponding control ratios:

Comparing with the threshold value Δ _max we make a decision on the presence of malfunctions in blocks 2 and 3.

Note that the values of Δ ₂ and Δ ₃ in the presence of defects do not depend on the level of the input signal and are determined by the degree of deviation of the coefficient from the nominal.

а в качестве дефекта рассматривалось отклонение постоянной времени T₁ на 100 и 200% На графике по оси абсцисс показана амплитуда входного сигнала, а по оси ординат: Δ₁ максимальное на интервале моделирования значение контрольного сигнала при диагностировании по прототипу; Δ₂ максимальное значение контрольного сигнала при диагностировании по предлагаемому способу. Графики иллюстрируют достоинство предлагаемого способа независимость контрольного сигнала от амплитуды входного сигнала. Зависимости

соответствуют отклонению T₁ на 100% зависимости

- отклонению T₁ на 200% Таким образом, максимальное значение контрольного сигнала, полученного по предлагаемому способу, не зависит от амплитуды входного сигнала и пропорционально степени отклонения параметра передаточной функции от номинального значения.In FIG. 5 presents the results of simulation on a PC of diagnosing an object described by an oscillating link with a transfer function of the form

and as a defect, the deviation of the time constant T ₁ by 100 and 200% was considered. The graph on the abscissa shows the amplitude of the input signal, and on the ordinate: Δ _{1 the} maximum value of the control signal in the simulation interval when diagnosing by prototype; Δ _{2 the} maximum value of the control signal when diagnosing the proposed method. The graphs illustrate the advantage of the proposed method, the independence of the control signal from the amplitude of the input signal. Dependencies

correspond to the deviation T ₁ 100% dependence

- deviation of T ₁ by 200% Thus, the maximum value of the control signal obtained by the proposed method does not depend on the amplitude of the input signal and is proportional to the degree of deviation of the parameter of the transfer function from the nominal value.

Claims (1)

A method for the functional diagnosis of linear control systems based on the use of the nominal coefficients a _{i j} , b _{i j of the} transfer functions of the linear blocks of the system, the multiple summation and integration of the input and output signals of the linear blocks, characterized in that they fix the diagnostic time interval Δt _g equal to the transition time the process of the system, the time interval for diagnosing linear blocks Δt, equal to the longest transient time for the entire set of blocks, orders of number the factor K _i and the denominator n _{i of the} transfer functions of the blocks and the whole system, preliminarily determine the nominal transfer coefficients of the entire system b _i , a _i as the gear ratios of the integrators of two integro-summing blocks, for which the input signal of the entire system is simultaneously fed to the first inputs of the last K integrators of the first integrosumming block, where K is the order of the numerator of the transfer function of the entire system, initial approximations of the coefficients are preliminarily set as gear coefficients of the integrators islitelya transfer function of the whole system, the second inputs of the integrators is fed the output signals of the preceding integrator, the output of the last integrator is summed with the input signal of a closed system by feeding it to a second input of the adder with the initial approximation coefficients b _k, the output of the entire system simultaneously fed to the first inputs of the last n integrators of the second integro-summing block, where n is the order of the denominator of the transfer function of the entire system, as the gear coefficients of the integrators The initial approximations of the coefficients of the denominator of the transfer function of the entire system are established, the output signals of the previous integrators are fed to the second inputs of the integrators, the output signal of the last integrator is fed to the first input of the adder, the second input of which with the transmission coefficient equal to the initial approximation a _n , the output signal of the system, outputs of the two adders fed to the inputs of the comparison element, repeatedly firing integrators with zero initial conditions at time Δt _g, alter Prevalence you transfer the integrators and the second inputs of the two adders, achieving the minimum modulo value at the output of the comparison element, then fix the transfer coefficients of the integrators as the nominal values of the transfer coefficients of the entire system, go on to determine the nominal transfer coefficients of the individual linear blocks, for which the input signal i of the th block is simultaneously fed to the first inputs of the last K _i integrators of the first integro-summing block, where K _{i is the} order of the numerator of the transfer function OK, the initial approximations of the coefficients of the numerator of the transfer function of the i-th block are preliminarily set as the transfer coefficients of the integrators, the output signals of the previous integrators are fed to the second inputs of the integrators, the output signal of the last integrator is summed with the input signal of the i-th block supplied to the second input of the adder with the initial approximation coefficient b _i K _i, the output signal of i-th block are simultaneously fed to the first inputs the last n _i integrosummiruyuschego second integrator unit, where n _i procedure the denominator of the transfer function of the i-th block, the initial approximations of the coefficients of the denominator of the transfer function of the i-th block are preliminarily set as the gear coefficients of the integrators, the output signals of the previous integrators are fed to the second inputs of the integrators, the output signal of the last integrator is fed to the first input of the adder, to the second input of which with a transmission coefficient equal to the initial approximation a _i n _i , the output signal of the i-th block is supplied, the output signals of two adders are fed to the inputs of the comparison element I, repeatedly launching integrators with zero initial conditions for the time Δt, change the gear ratios of the integrators and second inputs of the two adders, achieving the minimum modulus of the signal at the output of the comparison element, and then fix the gear ratios of the integrators as the nominal values of the transfer function coefficients of the ith block , the above operations are performed for each of the blocks of the system, when diagnosing the input signal of the system is simultaneously fed to the first inputs of the last K integrators of the first th integrosummiruyuschego block coefficients equal coefficients b _i of the numerator of the transfer function of the closed system, the second inputs of the integrators is fed the output signals of the previous integrators last integrator output signal is summed with the closed system input signal supplied to the second input of the adder with b _k factor, the output signal of the closed systems simultaneously feed the first inputs of n integrators of the second integro-summing unit with coefficients a _i , output signals are fed to the second inputs of integrators previous integrators, the output signal of the last integrator is fed to the first input of the adder, to the second input of which an output signal is supplied with the coefficient a _n , the output signals of two adders are fed to the inputs of the comparison element, the signal from the output of the comparison element is fed to the first input of the dividing device, to the second input which serves as a signal from the output of the first adder, the output signal Δ of the dividing device is used to monitor the health of the entire system by comparing its module with a predetermined threshold value According to this, the above operations are repeated periodically, starting the integrators for a time Dt _g with zero initial conditions, in the event that the control signal exceeds the threshold value, they proceed to troubleshooting, for which, using the input and output signals of each block, they determine their technical condition by implementing them over time Δt of the above-described sequence of operations using the nominal transfer coefficients a _{i j} , b _{i j} .

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