DE19617384A1 - Regulator of mixt. ratio of two gas vol. flows through Venturi nozzle - Google Patents

Abstract

Two gas flows enter the nozzle at different points, and their pressures and temps. are measured. The distance of the needle is set by an adjustor (M) in conjunction with a regulator (contr) having adjustable gain. The gain is determined by a monitor (sup) which detects oscillations of the control quantities and sets up a measure of oscillation. The monitor is based on a fuzzy controller. The regulator may be similar or may be a proportional or proportional-integral controller.

Description

The invention relates to the regulation of one if possible constant mixing ratio of two gas volume flows, one of which is subject to fluctuations and the other or the mixture volume flow is readjusted. For the Re Gas volume flows are generally nozzles suitable. A gas under pressure, which at for example can also be sucked in by a compressor, is reduced by reducing a nozzle cross section in its Flow rate is limited and thus the volume flow of gas adjustable. A special design of a Dü se represents the Venturi nozzle, in which by means of a nozzle the flow cross section is narrowed and thus the Volume flow of the gas flowing through can be determined. When regulating the mixing ratio of two gas volumes menströmen the problem arises that at least one Vo lumen flow cannot be influenced in its fluctuation behavior and that the other gas volume flow depends on the behavior of the the former must be adjusted so that the mixing ratio remains as constant as possible. Depending on the structure of the mix arrangement The two volume flows can be controlled according to the regulation be merged or it will through the venturi nozzle the mixed gas volume flow is already regulated.

Current flow ratio regulations are based on linea Ren PID controllers, which have the disadvantage that rise time and Overshoot range cannot be set separately. Furthermore the setting of classic PID controllers for non-linear Control systems made so that they radio even in the borderline case can function. That usually means a lazy sprun response of the control loop. A one-line monitoring by Limit vibrations are generally not known. There are on the other hand, known online tuning algorithms, which according to be  the controller parameters set according to the Leave the tuning process constant [2, 3].

The object underlying the invention is to egg ne arrangement and a method for controlling the mixing ratio ratio of two gas volume flows through a Venturi nozzle to specify, at which the desired set current ratio after the smallest possible number of Set time steps without overshoot. Furthermore should the parameterization should be designed so that this rule and the control procedure for possible faults, Pa parameter changes and model uncertainties is so robust that the stability of the control loop is not violated and the rule goodness is not significantly disturbed. Another subtask which is to be solved by the invention consists in that the increase caused by parameter changes Circular reinforcements, which in turn lead to limit vibrations can be recognized and quickly eliminated.

This task is for the arrangement according to the characteristics of the Claim 1 and for the method according to the features of claim 5 solved.

Further developments of the invention result from the dependent Claims.

A particular advantage of the arrangement according to the invention is that means are provided with which Schwin conditions of the control loop are monitored and independently can be regulated by forming a measure of vibration and the gain factor of the adjustable controller is adjusted accordingly.

Another advantage of the arrangement according to the invention is in that it can be used for a wide variety of controllers.  

Another advantage of the arrangement according to the invention is in that almost any combination of different Chen controllers for regulating and monitoring the Regulator can be provided.

Can be particularly advantageous for the arrangement according to the invention as a monitor or as a controller or as both fuzzy Regulator [1] can be used. So you get a quick one re step response of the control loop and limit vibrations can steamed faster.

Is particularly advantageous in a Ver drive to regulate the mixing ratio of two gas vo lumen flows through a venturi nozzle usually scatter size monitored and as a measure of the tendency of the Control loop used.

The spread over several time intervals is particularly advantageous sections of the control loop are determined and, if a limit is exceeded, the gain factor of the connected NEN controller reduces the tendency to oscillate dampen circle.

The gain factor of the controller is preferably at Un exceeding a limit it for the scatter again increases so that the control loop or controller is always optimal can react quickly to pending parameter changes.

The controller of the control loop is preferably controlled by a Sliding mode fuzzy controller controls which rules to control the gain factor both the current Gain factor, as well as the currently determined scatter consider. In this way, a particularly optimal one Behavior of the control loop guaranteed.

In the following, the invention is based on figures purifies.  

Fig. 1 shows an example of a mixture structure with a Venturi nozzle.

Fig. 2 shows a detailed view of a Venturi nozzle. Fig. 3 gives an example of the dependency of a special len design of a Venturi nozzle between needle immersion depth and volume flow.

Fig. 4 shows a timing diagram for various stages of a control process.

Fig. 5 shows an example of a control cycle according to the invention.

Fig. 6 illustrates different time periods during control operation.

Fig. 7 shows an example of fuzzy rules for a monitor.

Fig. 8 shows an example of fuzzy sets for a controller.

Fig. 9 shows an example of fuzzy sets for a monitor.

Fig. 1 shows an example of a gas mixing arrangement with a venturi nozzle. A similar nozzle arrangement is also given, for example, in [4]. For example, a pure gas flow enters on the left side of the arrangement and a mixed gas flow emerges on the right side. On the right side of FIG. 1 there is, for example, a compressor VP, with which the gas is sucked in through the venturi nozzle Vent. From the first gas volume flow that occurs on the left, 15 characteristic parameters for determining the volume flow are determined at one point, for example. Here the P and T are the pressure and the temperature. The mixing ratio x to be regulated is established in that, for example, a further gas is supplied to the first gas volume flow through a pipe Abg. From the gas mixture, for example, characteristic parameters for determining this gas volume flow are determined at point 17 . The pressure and temperature T and P are also determined here. A defined volume flow of the gas mixture is then removed through a further line Abga.

However, the invention is not intended to relate solely to sol restrict arrangements in which a pure gas volume menstrom is supplied whose characteristic values are determined and then the characteristics of the mixture are determined. It is also quite conceivable that the characteristic values of the pure volume flow can be determined and then a mixture instead finds. The way the mixing is done and which parameters are determined at what time plays for the essential thought of which of the invention underlying, no role.

The task of an exhaust gas test system, for which one he use arrangement according to the invention advantageously for example can, it is, the exhaust gases of a fuel-powered driving to analyze their pollutants.

The An is an essential part of such a system suction device.

Here, for example, exhaust gas and fresh air are mixed via a Venturi nozzle and this diluted exhaust gas is sent as a sample to an analysis station. However, the invention can also be used in all other technical applications in which an accurate mixing ratio of two gaseous or vaporous substances is important and is not limited to exhaust gas analysis alone. For example, it is conceivable that a stoichiometric mixture of reaction gases is set using the invention in order to achieve the most complete chemical reaction possible. One of these gases can preferably be supplied as a reaction gas from another chemical process, so that its volume flow is subject to fluctuations. Sensors at the entry point of the dilution _air and at the exit point of the mixture make it possible to determine the throughput of the dilution _air V _air and the throughput of the mixture V _Gem . The difference between the two forms the throughput of the undiluted exhaust gas V _{exhaust gas} .

If the total throughput V _Gem is kept constant by a suction power once set and, on the other hand, the throughput of the undiluted exhaust gas V _{exhaust gas} varies due to different operating conditions, the degree of dilution of the exhaust gas-air mixture also varies. However, this is disadvantageous for the subsequent analysis process. Therefore the task is the relationship

to keep constant. With the help of a nozzle needle control it is now possible to vary the total throughput V _{Gem of} the mixture.

But that it is also possible to a certain ratio x _to adjust. This setting of x _should be adjusted depending on the speed of the exhaust gas volume V _{exhaust gas} = V _Gem - V _air regulated, which corresponds to a flow ratio measurement. With the controlled Venturi nozzle, the control finds a non-linear controlled system, which at best can be linearized at certain operating points. Experience has also shown that the identification of the route parameters is fraught with uncertainties. Furthermore, there are strong disturbances in the control loop, which also intervene in the control loop in a non-linear manner. With kept constant V _{Gem exhaust gas} varies with varying V V indirectly _air, the non-linear received in the ratio (1). It is therefore advisable to use a control strategy that adapts to the non-linear system and is also robust against disturbances and parameter changes.

Fuzzy control offers such a control strategy on.

With the invention, therefore, a fuzzy Control strategy designed to solve the above problem of through flow ratio control triggers. This draft regulation was first tested on a simple process model and then Implemented and tested on the real system.

The invention further provides a fuzzy supervisor Available, the detected vibrations and by Removed the change in the loop gain.  

The nozzle is preferably used as a static approximation, Modeled nonlinear transfer element. Due to the Shape of the nozzle and the setting of the compressor VP that the When the mixture is sucked in, the air / exhaust gas mixture emerges at the nozzle outlet at the speed of sound.

The volume _flow rates V _air and V _Gem can then be determined indirectly via the parameters pressure p and absolute temperature T, which are measured by sensors at the points marked on the nozzle, using the following equation:

Here B (1) is a parameter which depends on the immersion depth l of the nozzle needle (see FIG. 2), but also on its shape and also on the type of nozzle. However, the latter two parameters are constant for a specific system, so that only a dependency on l remains for the constant B, which, however, i. is generally non-linear (see Fig. 3). For the course of the volumes V _air and V _Gem , qualitatively similar curves result for constant pressure and temperature. In the case of variable pressure or temperature and variable immersion depth l, the nozzle thus has a non-linear transfer characteristic of the 3rd order. The dead time of the nozzle, which occurs between the measurement at the nozzle inlet and at the nozzle outlet, was preferably neglected because of its insignificance compared to the other time constants.

If pressure and temperature are assumed to be constant,

T₀ = 193.15 K
p₀ = 101.33 Kpa.

then V only depends on the position-dependent parameter B (1). This dependence is shown in the calibration curve in FIG. 3.

Fig. 2 shows a detailed arrangement of the Venturi nozzle. Here, for example, the point 17 is shown, at which a pressure measurement PM and a temperature measurement TM take place. For example, these characteristics are determined for the mixed gas volume flow. From this, the volume flow can then be derived using simple thermodynamic basic equations. In this example, the nozzle needle is moved with the help of a servo motor M, which can be a stepping motor, for example, into or out of the nozzle opening. As a measure of the opening of the nozzle, the immersion depth l of the nozzle needle nozzles in the nozzle Vent is used here. The skilled person is of course clear that he can move the nozzle itself instead of the nozzle needle, in order to achieve a reduction in the area through which flow can be achieved.

Fig. 3 gives an example of the dependency of a proportionality constant B (1) on the immersion depth l of the nozzle needle in the Venturi nozzle. These proportionality constants are different for all different designs of Venturi nozzles. However, they have a similar non-linear course depending on l. When dimensioning the control, it should preferably be ensured that one does not move in the edge areas of the curve, since undefined states occur when the corresponding limit values are exceeded or fallen short of. These limits are (l₀, B₁₀) on one side and (l₁₀, B₀) on the other side of the curve. Preferably, the control should always be in the middle of the curve so that there is as much scope for parameter changes as possible.

If the calibration curve is the result of averaging between support points, the behavior of the nozzle between the support points must also be modeled. For this purpose, linear interpolation can advantageously be carried out between the support points. Preferably, the calibration curve should be limited in the design of the control system in such a way that positioning outside the boundary points is prevented. A stepper motor is preferably used as the motor, which can be modeled in its closest approximation, as shown in FIG. 4.

Fig. 4 illustrates the time dependencies in the control of the needle immersion depth with the help of a step motor. For example, a target length l _{should be} set to who. A command must first be sent to the motor, which takes the time period T _trans . The motor then takes time to start up and reach its target speed. This time is called T _Ramp . During the period of the adjustment process T _plateau , the motor moves at a constant speed. Then the time must be taken into account, which the motor needs to get back to speed 0. This is also referred to as T _Ramp , but can be different from the T _Ramp mentioned at the beginning if the motor has a non-symmetrical behavior when starting up or shutting down. The motor is preferably given a target position in the form of a serial telegram. For example, the transmission of the telegram to the motor controller requires a time to increase the motor angle or the motor position. Until it reaches the target position, the frequency ramp is preferably lowered again, so that a new position can only be controlled after a further 400 ms. In Fig. 4 this fact is shown. The stepper motor used in the first implementation cannot be stopped between receiving the setpoint and setting the setpoint. In this case, measurements at the nozzle cannot be reacted to during this time. In the control engineering sense, this means that the motor represents a dead time element with a dead time of

T _total = T _trans + 2T _ramp + T _plateau (3)

in which

The speed v _motor is a constant variable that occurs at a predetermined step frequency. Thus, the stepper motor is a dead time element with a by Eq. Dead time described variable (3) _to the setpoint value L depends.

Fig. 5 shows an example of a ses Regelkrei invention. For example, the depth of immersion of a needle in a venturi nozzle vent is to be regulated thereby. With the help of this Venturi nozzle, the mixing ratio x of two gas volume flows is to be checked. In this embodiment or in this example of regulation, the regulation is carried out in such a way that the mixing ratio is controlled via the mixed gas volume flow. To determine the individual gas volume flows, their characteristic data are determined and these are fed to the controller. On the left side of the control loop, the command variable x _k ^{d is} supplied as the desired mixing ratio. The control difference e _{xk is formed} with an x _k obtained in the control loop and fed to a controller contr. This controller can either be designed as a fuzzy controller, as a proportional controller or as a proportional integral controller or in another way. It is important that the gain factor of the controller can be adjusted. The controller determines a change in length Δl _k ^d from the input variables, ie the control difference and the set gain factor, for adjusting the Venturi nozzle. This is fed, for example, to a motor controller of a stepper motor M, which carries out an adjustment l _{k of} the nozzle needle of the Venturi nozzle. This leads to a total volume flow V _totk via the proportional relationship between the volume flow and the immersion _{depth of the needle} in the Venturi nozzle. From this total volume flow, the gas volume flow V _airk supplied to the left of the Ven turi nozzle is subtracted and the other volume flow V _{exk is obtained} . With the help of these two gas volume flows, the new mixing ratio x _{k is} formed and the control loop is run through again. To set the gain of the controller, a supervisor is provided, which can control the gain of the controller by means of a change in the gain factor ΔK. Depending on which type of controller is provided, the supervisor can also query the current amplification factor from the controller and include this in his assessment of the oscillation behavior of the control loop and the changes to be carried out.

As shown in Fig. 5 in a rough model of the control loop, the controlled system according to the invention preferably consists of the controlled Venturi nozzle Vent with suction device, the motor M, which changes the volume throughput of the nozzle by moving the nozzle needle, temperature and pressure sensors, with help of which the individual flows are determined and the controller contr, as well as supervisor or supervisor sup.

To be able to carry out a stability analysis and for a sensible initial dimensioning of the controller for the Pra xisfall, a simple model of the Venturi Designed nozzle plus stepper motor. The model of the step motor tors consists of a variable dead time with integrator. The dynamic behavior is then given by the following equation wrote

in which
l _{k + 1} - penetration depth of the nozzle needle at time k + 1
Δl _i ^d - motor input.

This results in a simple difference equation for the depth of penetration

l _{k + 1} - l _k = Δl _k ^d (5).

A conversion of (5) into a difference equation for the Mixing ratio

results only from a linearization of the characteristic V _Gemk (l _k ). With the assumption = = const you get the difference equation of the open circle

x _{k + 1} - x _k = A (x _k ) Δl _k ^d (6)

With

Because of the non-linearity of the static nozzle curve bie a controller form that uses SMFC (sliding mode fuzzy Controller) and is characterized by a very simple Structure distinguished. This type of controller shows a very robu behavior, especially in the presence of non-linearity The basics of these fuzzy controllers are set out in [1] represents and are assumed in the following.

An SMFC, which is soft, is preferably introduced Has a characteristic between its limits. Such a The controller can be described analytically as follows

Δl _k ^d = K · C _fuzz · sgn (s _k ); K, C _fuzz <0 (8)

in which case s _k = x _k - x _k ^d and x _k ^{d is} the target value. C _fuzz analytically describes the course of the controller characteristic for positive x _k and results from the choice of the position and form of the membership functions.

A typical fuzzy rule set for use in the Erfin manure is for example

R _i : IF s _k = LS ⁱ THEN Δl _k ^d = LU ⁱ

With

LS 1 = PB
LS² = PM
LS³ = PS
LS⁴ = Z
LS⁵ = NS
LS⁶ = NM
LS⁷ = NB
LU¹ = NB
LU² = NM
LU³ = NS
LU⁴ = Z
LU⁵ = PS
LU⁶ = PM
LU⁷ = PB

and P - positive, N - negative, Z - zero, B - big, M - medi um, S - small.

Fig. 8 shows examples of such membership functions for the input s _k = x _k - x _k ^d = Ax _k and the output .DELTA.l _k ^d.

The input value of the SMFC is first standardized (scaled) and then according to the input membership functions fuzzified. After processing through the fuzzy rules the result is defuzzified (e.g. Center of Gravity- Method) and then standardized. The result is then on given the stepper motor.

The controller is now preferably set so that both glo Bale stability is guaranteed as well as limit vibrations with a small amplitude can be avoided.

The following dimensioning rule applies for sufficient compliance with global stability
With

With

D <| x ^d _{k + 1} - x _k ^d |,

0 <A _min | A (x _k ) | A _max ,

η - positive safety distance.

In the vicinity of s _k = 0, the controller ( 8 ) is to be regarded as linear.

Δl _k ^d = K · C (x _k ^d ) · (x _k - x _k ^d ) (11)

where C (x _k ^d ) is the gain of the SMFC in a close vicinity of s _k = 0. For small s _k , the SMFC is advantageously designed so that the following condition applies

0 <A (x _k ) · K · C (x _k ^d ) <-1 (12).

This is immediately obvious if one enters (11) into (6) sets and for the regulated system the following differences equation obtained

x _{k + 1} = (1 + A (x _k ) · K · C (x _k ^d )) x _k - A (x _k ) · K · C (x _k ^d ) · x _k ^d (13).

This is a first order filter equation with the parameter A (x _k ) · K · C (x _k ^d ), for which stability is only guaranteed if (12) applies. In general, during the control process, the non-linear transfer characteristic of the nozzle changes so that the overall gain of the system changes. This can cause undesirable vibrations that can be eliminated by reducing the overall gain. This is done according to the invention by reducing the controller gain with the help of a supervisor sup, which detects the vibrations and reduces the controller gain accordingly. According to the invention, the scatter is a favorable measure of vibration

where n is the number of measured values used is. On the one hand, it is important to have a sufficiently large size number n must be taken into account so that the scatter σ² get acceptable confidence. On the other hand, n must not be large so that the supervisor sup opens quickly enough Disturbances can react.

According to the invention, the controller can be monitored with a conventional supervisor. This preferably begins to reduce the controller gain as soon as a maximum σ² _{max has been} exceeded. For the sake of simplicity, for example, the controller gain is gradually reduced with a constant gain change until it falls below σ² _max . If σ² falls below a lower limit σ² _min , the gain is preferably increased step by step until σ² _{min has} been exceeded again. The controller gain K is in turn also limited, for example, by an upper and a lower barrier.

K _min KK _max .

This will make the control loop and maintain its stability.

A fuzzy supervisor has compared to the conventional Supervisor the benefits of that

• 1. no sharp bounds need to be used for σ²,
• 2. no constant step size ΔK has to be used,
• 3. the current controller gain is taken into account can.

A higher control quality can therefore be achieved if a fuzzy supervisor is used. The inputs of the fuz zy supervisors are preferred σ² and K. The output is the change ΔK. The other advantages of this supervi sors are

• 1. Continuous consideration of σ² in a pre given interval
• 2. Automatic adaptation of the step size ΔK to the size σ²,
• 3. Including the size of the controller gain K.

The fuzzy supervisor strategy can be used, for example The following rules can be summarized:

1. IF K is (MEDIUM or HIGH) AND σ² is (MEDIUM or HIGH) THEN REDUCE K
2. IF K is LOW AND σ² is (MEDIUM or HIGH) THEN DO NOT CHANGE K
3. IF K is HIGH AND σ² is LOW THEN DO NOT CHANGE K
4. IF K is (LOW or MEDIUM) AND σ² is LOW THEN INCREASE K.

Rule 2 states that a low K no longer reduces should be.

Rule 3 states that with a low scatter σ², ie vibrations that are not present, the controller gain K can be increased up to a maximum K _max .

Fig. 7 shows an example of the corresponding control table le, and Fig. 9 shows an example of the membership functions for the inputs and the output.

In Fig. 7, the control table of the supervisor means STREU = σ², N_U = K and DN_U = ΔK.

Fig. 6 shows the chronological course of a measuring process of the invention or of the assembly. The measuring process of the individual volume flows is preferably carried out continuously in the form of sampling steps. At a point 1, for example, the pressure and the temperature of the respective gas volume flow are determined. The ratio of the two volume flows is then formed in Verh. The controller contr then defines a target adjustment length target of the nozzle needle of the venturi nozzle. This setpoint adjustment length setpoint is then transmitted to motor M. The transmission and movement of the motor up to point 2 then take place. The transmission is marked with over and the procedure with Verf. The entire intermediate measurements Z, which take place during this period, are not used, for example. The control can only be carried out again on the basis of new measured values after the set target state has been reached.

The system to be controlled is preferably a scanning system with variable sampling time. The timing of the regulation will through the components

• - volume measurement
• - ratio formation of the measured volumes
• - Calculation of the control algorithm and supervisor
• - Setting a new nozzle needle position

determines how this is illustrated in FIG. 6 over time.

The travel time of the motor can range from T _total = 100 ms to T _total = 1 s, for example.

Fig. 6 clearly shows that a new measurement only begins when the movement of the motor has been completed. In the meantime, however, further measurements can be carried out, which can be used for trend recording of the volume values in a finer time cycle. However, this only makes sense if the measured intermediate values of the volumes from the previous cycle are processed in the current cycle.

Fig. 7 shows an example of fuzzy rules with which the supervisor can control the gain of the controller. Identical names in FIGS. 8 and 9 have the same meaning as those in FIG. 7

literature

[1] Patent application: Control method for dynamic n-order systems.
Boarding school Publication: WO 93/11473
[2] B. Porter, AH Jones, CB McKeeown: Real-time expert tuners for PI controllers.
IEE Proceedings, m Vol. 134, Pt. D, No.4, July 1987, pp. 260-263
[3] Li Zheng: A Practical Guide to Tune of Proportional and Integral (PI) - like Fuzzy Controllers.
IEEE International Conf. on Fuzzy Systems FUZZ-IEEE 92, San Diego, Proceedings pp. 633-640
[4] DE 42 37 009 A1

Claims (8)

1. Arrangement for regulating the mixing ratio of two gas volume flows through a Venturi nozzle via its nozzle needle,

• a) in which the two gas volume flows enter the venturi nozzle (vent) at different points,
• b) in which at least first measuring means (P, T, 15 ) are provided for determining parameters of the first volume flow,
• c) in which at least second measuring means (P, T, 17 ) are provided for determining parameters of the second volume flow,
• d) where at least means for determining the mixing ratio are provided on the basis of the parameters measured by the measuring means,
• e) at least the actuating means (M) for adjusting the nozzle needle distance (l) of the venturi nozzle are provided in accordance with an actuating variable,
• f) at least one controller (contr) with an adjustable amplification factor is provided, which is the manipulated variable dependent on the amplification factor as a function of the re-difference, formed from the supplied mixing ratio and certain mixing ratio, and the known relationships between the volume flow change and the nozzle displacement adjustment range of venturi nozzles issues
• g) and in which at least one monitor (sup) is provided for setting the gain factor, which has means for detecting vibrations of the manipulated variable and forming a vibration measure which changes the gain factor as a function of the vibration measure.

2. Arrangement according to claim 1, in which as a supervisor (sup) a fuzzy controller and as a controller (contr) a fuzzy controller or a P or PI controller is provided. 3. Arrangement according to claim 1, in which as a monitor Threshold value monitor for the vibration level and as a controller a fuzzy controller is provided.   4. Arrangement according to claim 2 or 3, in which at least one Fuzzy controller designed as a fuzzy sliding mode controller is. 5. Method for controlling the mixing ratio of two gas volume flows through a Venturi nozzle,

• a) in which parameters of the two gas volume flows are determined to determine the volume flows and the current mixing ratio is determined therefrom,
• b) in which the control difference is formed from the current mixing ratio and a supplied target mixing ratio and a control variable dependent on a gain factor for adjusting the venturi nozzle is formed by using the known relationships between volume flow change and nozzle needle adjustment path of venturi nozzles will,
• c) and in which the temporal course of the manipulated variable is monitored, for which purpose the scatter of the manipulated variable is determined over time periods and the amplification factor is changed as a function of the scatter
• 6. The method according to claim 5, in which at least one limit value for the scatter is determined and monitored and the gain factor is reduced if the limit value is exceeded.

7. The method according to claim 5, wherein at least one Threshold for the spread is determined and monitored and if the gain falls below the limit factor is increased. 8. The method of claim 5, wherein the gain factor is formed by linguistic variables that represent the Mark the amplification factor and the scatter, with Hil fe are evaluated by linguistic rules.   9. The method according to claim 8, with the following linguistic set of rules: 1. IF K is (MEDIUM or HIGH) AND σ² is (MEDIUM or HIGH) THEN REDUCE K
2. IF K is LOW AND σ² is (MEDIUM or HIGH) THEN DO NOT CHANGE K
3. IF K is HIGH AND σ² is LOW THEN DO NOT CHANGE K
4. IF K is (LOW or MEDIUM) AND σ² is LOW THEN INCREASE K.
with K: gain factor
σ²: scatter