RU2474856C1 - Method for adaptive three-position control - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: one of potential values of control action is applied at extreme positions in order to return the controlled value to dead zone of the controller, and when the controlled value lies within the dead zone, control is carried out using pulse width modulated pulses with adapted duration and period.

EFFECT: improved quality of control by keeping the controlled value in the dead zone of the controller and control is especially efficient for objects with a load which sporadically or slowly varies in a wide range.

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Description

The invention relates to automation methods, and in particular to a method of adaptive three-position regulation. It can be used to automate the operation of heating furnaces, extruders and injection molding machines, reactors, household and industrial refrigerators and other objects for positional regulation of one technological quantity (temperature, pressure, etc.) in them by applying positional control actions of the “on” type "/"turned off".

There is a method of three-position regulation with fixed positions of the regulator (see, for example, A. A. Kampe-Nemm “Automatic two-position regulation.” M .: Nauka, 1967, 160 s.), Which does not provide sufficiently high-quality regulation.

Improvements in quality can be achieved by creating positional control systems using regulators with an average regulator position that adapts to the load of the object, changing towards the operating extreme position analog (see ed. St. USSR No. 675399, class G05B 11/56, 1979) or discrete (see ed. St. USSR No. 1554628, cl. G05B 11/56, 1989 or ed. St. USSR No. 1802606, cl. G05B 11/18, 1992) method.

A characteristic feature of this class of systems is the adaptation of the middle position of their regulator to the extreme values, and with the discrete method of adjusting the middle position to the extreme one, either a reversible stepper motor (ed. St. No. 1554628) or a reversible counter and a counting result converter (counter code) are used into a discrete signal (ed. St. No. 1802606) based on a digital-to-analog converter (DAC).

In other words, in this class of adaptive positional control systems, the power supplied to the control object when the controlled variable is in the deadband of the controller, i.e. when the controller is in the middle position, it is determined by the signal level of this position.

A common drawback of this class of adaptive positional control systems is the difficulty of using a middle position signal located between the values of the extreme position signals in a specific executive device of the control object, for example, an electric heater of a heat furnace or a compressor cooler engine, due to the complexity of pairing a controller operating in the middle position with them, since these actuators are most convenient to use in the “on” / “off” modes.

Quality indicators can be improved by applying the regulatory methods used in the inventions of RF patents No. 2047210, class. G05B 11/18, 1995 and No. 2408913, IPC G05B 11/18, 2010, which were selected as prototype patents. They use the signal of the middle position, equal in level to the signals of only the extreme positions, which is supplied by pulses, and the adaptation of the average position of the three-position controller is provided in the first case by changing the duty cycle of these signals with a constant period of their repetition, and in the second case also by changing the duty cycle, but by changing the repetition period of these pulses.

The disadvantage of these methods is the fixation of one of the parameters of the supplied pulses: either the period or the duration of the pulses, which leads to the necessity of calculating and choosing this parameter correctly for the corresponding changes in the load on the control object. Also, the invariability of the selected parameter during the operation of the object with large, compared with the calculated, changes in the load can lead to degeneration of the considered methods in a conventional non-adaptive on-off mode with an ambiguity zone of regulation. In addition, the implementation of these methods provides for the adaptation of the variable parameters of the pulses with only a certain step, which leads to the need to choose the step and the associated problems: a small step leads to a large adaptation time, and when using a large step, the value of the pulse parameter adapted to the load is obtained more roughly and less accurate.

A method is proposed in which a signal of the middle position is used, equal in level to the signals of only the extreme positions, which is supplied by PWM pulses having a variable duration and pause. Thus, in contrast to prototype patents, the disadvantage associated with the fixity of one of the pulse parameters is eliminated: both the pulse duration and the pulse repetition period are adapted. In addition, the disadvantage associated with the discrete step of changing the parameters of the pulses in the prototype patents is eliminated.

In other words, if the adjustable value goes beyond the dead band of the regulator, then one of the control actions of the extreme positions is used to return it to the zone. On the other hand, when the controlled variable is within the dead band, the regulation is carried out by PWM pulses. In this case, the adaptation of the pulse duration in the current period is carried out on the basis of the dependence of the achieved minimum value of the controlled variable (or maximum, if the supplied pulse leads to an increase in the controlled variable) and the pulse duration in the previous period; The pulse period is adapted by changing the pause between them, the calculation of which in the current period is carried out similarly based on the dependence of the achieved maximum value of the controlled variable (or the minimum, if the absence of a pulse leads to a decrease in the controlled variable) and the duration of the pause in the previous period.

Consider the essence of the method by the example of a cooled object, in which the regulation of the value of X, for example, temperature, is carried out by controlling actions u ₀ and u ₁ , where u ₁ corresponds to the selection of energy due to the internal control action, and u ₀ to the flow of energy due to the external environment. As such an object, one can consider a refrigerator for which X is the temperature inside the refrigerator, u ₁ is the compressor enable signal, u ₀ is when the compressor is turned off. For heated objects, in which u ₁ corresponds to the influx of energy, and u ₀ to the outflow of energy, in the proposed method it is enough to change the type of control action: “off”, change to “on”, and “on” - to “off”.

In the initial period of the change in the controlled variable from one extreme position to the other and back to the first, regulation takes place in the usual on-off manner with an ambiguity zone. The pulse duration in this case corresponds to the time of the change in the controlled variable from the upper value of the control zone to the lower, and the pause between pulses corresponds to the time of the change from the lower value to the upper. In subsequent periods, adaptation of the duration of the pulses and their period occurs due to a change in the pauses between them, based on the relationship between the influx and outflow of energy with the behavior of the controlled variable.

The adaptation is based on the assumption of a linear dependence of the change in the controlled variable ΔX on the change in the energy of the object ΔQ:

where K is the coefficient of proportionality. Such a dependence is characteristic of thermal objects whose adjustable value is temperature (a change in temperature ΔT is associated with a change in the amount of body heat ΔQ through heat capacity C: ΔQ = CΔT); objects in which the fluid level is regulated (a change in the fluid volume ΔV for cylindrical or parallelepiped tanks is proportional to a change in the level ΔH: ΔV = SΔH, where S is the cross-sectional area of the tank).

привело к изменению регулируемой величины на

как показано на фиг.1,a.Assuming that the influx of energy from the external environment to the moment t ₀ was approximately equal to the outflow of energy caused by the control action u ₁ , i.e. the changes in the controlled variable were insignificant, we can say that the change in the energy of the control object caused by the control action u ₁ over time

led to a change in the controlled variable by

as shown in figure 1, a.

The change in the energy of the control object is associated with a change in the influx and outflow of energy per unit time:

where N ₀ is the outflow of energy per unit time caused by the control action; N ₁ - the influx of energy per unit time due to the external environment. Further calculations are performed for a slowly changing object load, i.e. if N ₁ ≈const and N ₂ ≈const for at least two periods of change in the controlled variable.

, т.е. в нулевом периоде, когда действует обыкновенное позиционное регулирование с зоной неоднозначности, равно:According to (1), the amount of energy taken from the object during the time

, i.e. in the zero period, when ordinary positional regulation with an ambiguity zone is valid, it is equal to:

Given the relationship between the change in the energy of the object with its inflow and outflow (2), from equality (3) we have:

до уровня X_min за время

, можно получить:Similarly, for the next, first, regulation period, in which it is necessary to make a change in the controlled variable from the value

to level X _min in time

, available:

, соответствующего началу импульса, до уровня X_min нижнего значения зоны регулирования:Expressing K from equality (4) for the zero period and substituting it into equality (5) for the first period, we obtain the pulse duration for the first regulation period at which the controlled quantity under the influence of the control action u ₁ changes from the level

corresponding to the beginning of the pulse to the level X _{min of the} lower value of the regulation zone:

The adaptation of pauses between pulses occurs by analogy with the adaptation of pulse durations. The duration of the pause in the first regulation period is calculated based on the duration of the pause of the zero period, as well as the previous and required changes in the controlled variable in the zero and first regulation periods (Fig. 1, b):

- продолжительность паузы в нулевом периоде, когда действует обыкновенное позиционное регулирование с зоной неоднозначности;

- адаптированная продолжительность паузы в первом периоде регулирования.Where

- the duration of the pause in the zero period, when ordinary positional regulation with an ambiguity zone is valid;

- adapted pause duration in the first regulatory period.

From relations (6) and (7), we obtain the dependences for determining the adapted pulse and pause durations for the i-th period based on data on the change in the controlled variable in the previous (i-1) -th period:

и

, а

и

. Также следует учитывать, что поскольку объекты, к которым применяется рассматриваемый способ регулирования, обладают внутренним запаздыванием, время начала и прекращения импульса следует считать соответственно с момента убывания и возрастания регулируемой величины, находящейся в средней позиции диапазона регулирования.The calculated dependences (8) and (9) make it possible to take into account various variants of the ratio of the initial level of the controlled variable, the minimum and maximum achieved values of the controlled variable with respect to the minimum and maximum boundary of the deadband. Those. in contrast to the situation shown in figure 1, in the General case, for example, may be

and

, but

and

. It should also be taken into account that since the objects to which the control method under consideration is applied have an internal delay, the start and stop time of the pulse should be considered, respectively, from the moment the adjustable value decreases and increases, which is in the middle position of the control range.

The implementation of the proposed method of regulation is described in the block diagram shown in figure 2. It contains a block 1, which decodes the block diagram shown in figure 3, upon receipt of the job deadband controller [X _min ; X _max ] and X _max , the current value of the controlled variable X and the type of static characteristics Revers, "direct" or "Reverse". Figure 4 shows the block diagram for decoding block 2 - the formation of control actions in extreme positions and PWM pulses in the middle position. The adaptation of the duration of the pulses and the pause between them occurs if the current period is not the first (block 3 of figure 2). The adaptation process in accordance with block 4 of FIG. 2 decodes the block diagram shown in FIG. 5, and finding the values necessary in the adaptation process (block 5 of FIG. 2) decodes the block diagram shown in FIG. 6. According to block 6 in figure 2, if the system stops, for example, in the case of manual shutdown of the controller included in the control system, with a firmware program that implements the proposed adaptive control method, the program stops. Otherwise, there is a return to block 1 of FIG. 2, and the control process continues.

According to the flowchart of FIG. 3, at the beginning, the value of the lower X _min and upper X _max boundaries of the deadband of the controller, the current value of the controlled variable X and the setting of the “direct” or “inverse” static characteristic of the Revers controller are set (block 7 of FIG. 3). If the specified static characteristic is “direct”, the logical variable Revers is set to the value “TRUE”. Moreover, in accordance with block 8 of Fig. 3, the type of control action u ₀ , which is also a logical variable, will take the value "TRUE", and u ₁ - "FALSE". In this case, if the control action U at the current moment of time is equal to U = u ₀ , then this will correspond to the activation of the actuator, and U = u ₁ to the disconnection. To implement the “reverse” static characteristic of the controller, the variable Revers is set to the value “FALSE”. Then the control action U = u ₀ will correspond to the actuator being in the “off” mode, and U = u ₁ - “on”. After that, the value of the onstart logical variable is checked (block 9 of Fig. 3), and if it is TRUE, which corresponds to the start of a program that implements a three-position adaptive control method, the initial values of the variables (block 10 of Fig. 3) are used, which are used when the program is running .

Blocks 11-18 of figure 4 describe the formation of control actions when the controlled variable is in the extreme positions of the controller. In block 11 of FIG. 4, it is checked whether the value of the controlled variable X at the current time is smaller than the lower limit of the dead zone X _min , and if so, according to the block 12 of FIG. 4, a control action U is applied to return the value X to the middle position equal to U = u ₀ . In this case, the time moment f _{stop of} the pulse _stop is equal to the value of the TIME system time at the current moment (block 13 of FIG. 4), and the time t _off elapsed from the time t _stop is reset (block 14 of FIG. 4). In another case, if X> X _max , which is checked in block 15 of Fig. 4, the value X is returned to the middle position by the control action U = u ₁ (block 16 of Fig. 4), the time moment t _{start of} the momentum _start is equal to the value of the system TIME time at the current moment (block 17 of FIG. 4), and the time t _on elapsed from time t _start is reset (block 18 of FIG. 4).

In blocks 19 and 20 of FIG. 4, it is realized for the case of a cooled control object that the time moment of the start of the pulse supply f _{start is found} , which is equal to the current system time (block 20 of FIG. 4) under the condition that the current control action must be equal to U = u ₁ and after the last switching of the control action from the value U = u _{0, the} purpose of U = u _{1 the} adjustable value did not change, i.e. the logical variable X _change has the value “FALSE”, or the adjustable value at the current time has a value greater than the value of the controlled variable X ₀₁ at the time of switching (block 19 of FIG. 4). Similarly, in blocks 21 and 22 of FIG. 4, the determination of the time t _stop corresponding to the start of a pause is described.

Blocks 23-26 of FIG. 4 describe the termination of the pulse when the time t _on elapsed since the start of the pulse becomes longer than the adapted pulse duration t _imp (block 23 of FIG. 4). In this case, the control action is switched to U = u ₀ , the moment of time f _stop , corresponding to the beginning of the pause, is equal to the current value of the system time TIME, and the time t _on is reset (blocks 24-26 of figure 4). Similarly, in blocks 27-30 of FIG. 4, the end of a pause is described when the time t _off elapsed from the moment the pulse is stopped becomes longer than the adapted pause duration t _relax (block 27 of FIG. 4).

The time t _{on is} calculated under the condition that the control action is equal to U = u ₁ (block 31 of FIG. 4) as the difference between the current time of the system time TIME and the time of the start of the pulse f _start (block 32 of FIG. 4), and the time t _off - as the difference between the current moment of the TIME system time and the moment of the start time of the pause t _stop (block 34 of figure 4), provided that the control action is equal to U = u ₀ (block 33 of figure 4).

равнялось

, а управляющим воздействием в текущий момент времени U является U=u₁ (блок 35 фиг.5). При этом рассчитывается продолжительность импульса в предыдущем периоде как разность между моментом времени t₁₀ последнего изменения управляющего воздействия с u₁ на u₀ и моментом времени

начала подачи предыдущего импульса (блок 36 фиг.5). Нахождение адаптированного значения продолжительности импульса на основании соотношения (8) описывается блоком 37 фиг.5, в котором через X₀₁ обозначено значение регулируемой величины X в момент времени t₀₁ последнего изменения управляющего воздействия с u₀ на u₁. По аналогии в блоках 38-40 фиг.5 описывается адаптация паузы t_relax между импульсами при смене управляющего воздействия с u₁ на u₀.The block diagram shown in FIG. 5 describes the adaptation of the durations of pulses and pauses based on relations (8) and (9). The adaptation of the pulse duration t _imp occurs when the control action changes from u ₀ to u ₁ , i.e. if the value of the control action at the previous time

was equal

, and the control action at the current moment of time U is U = u ₁ (block 35 of FIG. 5). In this case, the pulse duration in the previous period is calculated as the difference between the time t _{10 of the} last change in the control action from u ₁ to u ₀ and the time

the beginning of the previous pulse (block 36 of figure 5). Finding the adapted value of the pulse duration based on relation (8) is described by block 37 of Fig. 5, in which X ₀₁ denotes the value of the controlled variable X at time t _{01 of the} last change in the control action from u ₀ to u ₁ . By analogy, in blocks 38-40 of FIG. 5, adaptation of the pause t _relax between pulses is described when the control action is changed from u ₁ to u ₀ .

, t₁₀, X₁₀ и X_change при смене управляющего воздействия с u₁ на u₀ (блок 41 фиг.6). Аналогично, в блоках 47-50 производится присваивание значений переменным

, t₀₁, X₀₁ и X_change при смене управляющего воздействия с u₀ на u₁ (блок 46 фиг.6). Блоки 51-54 фиг.6 описывают нахождение минимального

и максимального

достигаемого значения регулируемой величины в процессе функционирования. Блоки 55 и 56 фиг.6 предназначены для подсчета переключений управляющего воздействия ChangeU, что необходимо для определения количества поданных ШИМ-импульсов. В блоке 57 фиг.6 происходит переприсваивание переменной

таким образом, что в следующем цикле, реализуемом блок-схемой фиг.2, значение переменной

будет равно текущему значению управляющего воздействия U. Блоки 58 и 59 фиг.6 реализуют присваивание значения «ИСТИНА» переменной X_change (блок 59 фиг.6) при изменении регулируемой величины (блок 58 фиг.6), т.е. в случае если текущее значение регулируемой величины X не равно значению регулируемой величины

в предыдущем цикле, реализованном в блок-схеме фиг.2. В блоке 60 фиг.6 реализовано переприсваивание переменной

таким образом, что в следующем цикле, реализуемом блок-схемой фиг.2, значение переменной

будет равно текущему значению регулируемой величины X. Аналогично в блоках 61 и 62 фиг.6 находятся моменты прекращения

и начала

подачи предыдущего импульса. Наконец, в блоке 63 фиг.6 переменной onstart присваивается значение «ЛОЖЬ», в соответствии с которым при проверке этой переменной в последующих циклах работы программы инициализация начальных значений переменных (блок 10 фиг.3) не происходит.The block diagram shown in Fig.6, describes the finding of the values necessary in the process of control and adaptation. In blocks 42-45 of Fig.6, the assignment of values to variables is implemented

, t ₁₀ , X ₁₀ and X _change when changing the control action from u ₁ to u ₀ (block 41 of FIG. 6). Similarly, in blocks 47-50, values are assigned to variables

, t ₀₁ , X ₀₁ and X _change when changing the control action from u ₀ to u ₁ (block 46 of Fig.6). Blocks 51-54 of FIG. 6 describe finding a minimum

and maximum

the achieved value of the controlled variable during operation. Blocks 55 and 56 of FIG. 6 are intended for counting control switching changes ChangeU, which is necessary to determine the number of PWM pulses applied. In block 57 of FIG. 6, the variable is reassigned

so that in the next cycle implemented by the flowchart of figure 2, the value of the variable

will be equal to the current value of the control action U. Blocks 58 and 59 of FIG. 6 implement the assignment of the value “TRUE” to the variable X _change (block 59 of FIG. 6) when the controlled variable changes (block 58 of FIG. 6), i.e. if the current value of the controlled variable X is not equal to the value of the controlled variable

in the previous cycle, implemented in the block diagram of figure 2. In block 60 of FIG. 6, variable reassignment is implemented

so that in the next cycle implemented by the flowchart of figure 2, the value of the variable

will be equal to the current value of the controlled variable X. Similarly, in blocks 61 and 62 of Fig.6 are the moments of termination

and start

supply of the previous impulse. Finally, in block 63 of FIG. 6, the onstart variable is assigned the value “FALSE”, according to which, when checking this variable in subsequent cycles of the program, the initialization of the initial values of the variables (block 10 of FIG. 3) does not occur.

An adaptive three-position control method was used in the control program for a household refrigerator. The controlled value was the temperature in the refrigerator, the control actions corresponded to the "on" / "off" of the refrigerator compressor. The obtained results of changing the controlled variable for a non-adaptive on-off with an ambiguity zone (Fig. 7, a) and for the adaptive three-position method (Fig. 7, b) showed an improvement in the quality of regulation by minimizing the run-out of the controlled variable outside the control range, which is provided by adaptive change in characteristics control pulses.

Claims (1)

An adaptive three-position control method, in which one of the potential values of the control actions is applied at the extreme positions to return the controlled variable to the regulator dead band, and when the controlled variable is within the dead band, the regulation is performed by PWM pulses, characterized in that both the duration and the length are adapted and the period of the PWM pulses based on the dependencies of the achieved minimum / maximum values of the controlled variable and for a long time STI pulse and a pause in the previous period, which are determined on the basis of the following relationships:

Where

- pulse duration after adaptation in the current period;

- the duration of the pulse before adaptation in the previous period;

- the value of the controlled variable before the start of the pulse in the current period;

- the value of the controlled variable before the start of the pulse in the previous period;
X _min is the lower boundary of the dead band of the regulator;

- the measured minimum value of the controlled variable in the previous period;

- the duration of the pause after adaptation in the current period;

- the length of the pause before adaptation in the previous period;

- the value of the adjustable value before the pause in the current period;

- the value of the controlled variable before the pause in the previous period;
X _max is the upper limit of the dead band of the regulator;

- the measured maximum value of the controlled variable in the previous period.

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