DE3108470A1 - Method for controlling the supply and removal of energy, and use of the method - Google Patents

Abstract

A method is proposed for the time-and energy-optimal control of the supply and removal of energy for heating up or cooling down a material phase. Taking account of the fact that it must hold to a first approximation that: - the energy (v(n)) absorbed or dissipated per time unit by the material phase at an instant is proportional to the energy difference ( DELTA T(n)) between the material phase and the heating or cooling members; - this energy difference ( DELTA T(n)) present at an instant is inversely proportional to the energy (v(n-1)) previously absorbed per time unit a system of equations for determining the furnace control steps (TH) is evaluated working backwards from measurements of the phase-specific capacity for the supply or dissipation of energy at the start of the method (T(o), v(o), TH(o)) and a stipulation of the phase end temperature (Tm(n)) to be achieved, as well as from the furnace temperature (TH(n)) then to be set. The furnace is driven in accordance with this using the staircase characteristic obtained. In order to refine the method, when carrying out the control the behaviour of the material phase can be further observed in order continuously to adapt the still remaining controlled variables from deviations which arise with respect to the computed characteristic. <IMAGE>

Description

Method for controlling the energy supply resp. -Discharge

and use of the method The present invention relates to a method for time- and energy-optimal control of the energy supply resp. -Discharge for heating up resp. Cooling down a matter phase and using the method.

The object of the invention is to supply or remove energy to control a phase of matter to be heated or cooled in such a way that the the desired goal is achieved in an energy- and time-optimized manner. That for example when raising a matter phase from an initial to a higher final temperature the heating elements provided for this purpose are operated differently with the same end effect can, for example, by heating up to the full capacity of the intended Heating elements at the beginning in order to lower the heating energy again towards the end of the process, is known. That, however, the resulting losses are extremely different will be, results from the fact that the radiation losses of the Heating organs approximately with the fourth power of their temperature difference with respect to the environment increase so that when the heating elements are adjusted to temperatures which are too high for the momentary absorption capacity of the matter phase, the energy largely used to warm up the environment.

The task mentioned is achieved by a method of the type mentioned at the beginning solved, in which one - at the beginning characteristic data for the energy absorption - or -Delivery behavior of the matter phase is determined - from this and the knowledge at least an energy state of the phase to be reached or to be passed through necessary energy supply or discharge function is calculated in the time and - the heating resp. Controls cooling organs according to the function found.

The invention is then illustrated, for example, with the aid of figures explained.

They show: FIG. 1 the step-by-step backward computation characteristic Control data with selected time increments of the same length, in the time-temperature coordinate system and the resulting temperature / time staircase control function for a furnace, FIG. 2 shows a representation analogous to FIG. 1, with the specification of a characteristic intermediate temperature value and a control condition to be complied with after it has been reached, FIG. 3 shows a representation analogous to FIGS. 1 and 2, with the provision of, for example, three temporally extended Control steps.

As already mentioned, the procedure described below works basically a matter of a phase of matter from an initial temperature to a final temperature to bring them, either from their edge surface by means of heating or cooling elements heated resp. cools or by means of radiation, for example microwave energy, heats up. In the following, the description is based on the first-mentioned processes, where the difference between the two mentioned is primarily that in the case of the former, according to the heat diffusion equation, it must be taken into account that up to a homogeneous temperature distribution within the matter phase when applying a external temperature step is reached, a certain time can elapse, whereas the homogeneity conditions are different when heated by means of radiant energy usually set much more quickly.

The invention is initially based on the basic knowledge that there is the way one phase of matter moves from a first temperature to a second is brought, there is a way that requires minimal energy consumption and thereby allows the temperature difference to pass through in an optimally short time. This is for example thus plausible that radiation losses with temperature, for example of heating elements rise very rapidly compared to the ambient temperature, and that it therefore makes little sense to heat up a material phase, for example, in such a way that that from the beginning full heating power of the intended heating elements is switched on.

Thermodynamic calculations of such an optimum lead to Conclusion that the mentioned energy and time-optimized way then is at least approximately complied with if the following criteria are taken into account become: 1. The amount absorbed by the matter phase at a point in time per unit of time resp. The energy emitted is, in a first approximation, proportional to the energy difference between matter phase and heating resp.

Cooling organs at this point.

II. This energy difference between Matter phase and heating resp.

On the other hand, cooling organs is inversely proportional to a first approximation to the energy previously absorbed per unit of time.

By adhering to these conditions at least approximately found the mentioned time-allergy-optimal way.

Implemented in practice, these findings can now be used for control purposes the heating elements for a phase of matter, as shown with reference to FIG. 1, use.

At the beginning of the process, the heating elements for the matter phase applied with a temperature step TH (o). After an initial phase, depending on the matter phase of more or less uncontrolled settling of its temperature, the temperature Trn (t) of the matter phase begins to rise to the temperature value to strive towards the heating elements TH (o). At a point in time t0 at which the dynamic Behavior of Trn (t) has become more or less steady, the rate of temperature rise will be v (o) the matter phase and the then prevailing excess temperature AT (o) of the heating elements measured in terms of the matter phase. To ensure that the entire phase has an at least almost homogeneous temperature, is thereby for example measured by means of a thermoelectric sensor inside the phase.

It can be seen that according to (I) the temperature rise rate v (t) corresponds to the matter phase of the energy absorbed by the latter per unit of time. Likewise, the excess temperature AT (t) corresponds to the heating elements with regard to the matter phase the energy difference between heating elements and matter phase.

It is now required that after the shortest possible time t the material phase has reached the final temperature Trn (n) n, with a furnace capacity of TH (n) then switched on (according to a given AT (n)), for example corresponding to its full output. The time interval t -t is divided into n small, equal time segments of length At, with the numbering from 1 to n. In the time segment n we can write according to (I): v (n) = v (o) T (n) (l, n) From (II) we get: The rate of rise v (n) can be further expressed as: v (n) At = {TH (n) - # T (n)} - {TH (n-1) - # T (n-1)} (3, n) This results in only three equations for the 5 unknown quantities v (n), TH (n-2), AT (n-2), TH (nl) and AT (nl). In the time segment nl the following result analogously: v (nl) At = {TH (n-1) - # T (n-1)} - {TH (n-2) - # T (n-2)} (3, nl) This results in a total of up to and looking backwards with time segment nl, six equations for a total of 8 unknowns. These equations can be found in an analogous way up to the second step, i.e. step no. 2. There they are: v (2) * At = {TH (2) - # T (2)} - {TH (l) -AT (l)} (3,1) In total there are 3 (n-1) equations for 3 ( nl) Unknowns with the quantities TH (o), AT (o) assumed to be known in the period no. 0 in (2,1).

From this it can be seen, however, that a time-energy-optimized way is only with n 3 2 can be found at all, i.e. at least two control steps are required are provided, in addition to step no. O, in which the material phase characteristic Data are determined.

As shown in Fig. 1, time is thus stepping backwards the above system of equations solved and the heating elements according to the values found for TH controlled 0. The values for TH are given in k.

With very small, practically infinitesimal step lengths At becomes thus created a quasi-continuous control process.

It is immediately evident1 that the method described is excellent suitable for computer control, which means that it is also practically continuous Temperature control of the heating or cooling elements can be easily achieved, depending on computational effort by a correspondingly small choice of At.

Cases may now arise in which other or additional conditions must be made to the temperature control of the material. This is one example in the heat treatment of metals such as aluminum. Here the task arises the temperature of the metal phase to a certain one in the best possible time and energy To lead temperature threshold to then as quickly as possible by a final temperature level to increase. This last requirement arises from the fact that during the transfer of the metal in such a treatment into a deeper energy state Potential threshold has to be overcome, but which it has to be overcome as quickly as possible is applicable.

A slight modification of the method shown in FIG. 1, for such a case is shown in FIG. Again, be at the beginning of the process, first of all, the characteristic absorption quantities of the matter phase determined, namely at the time dead the rate of temperature rise v (o), with corresponding excess temperature AT (o). It is also known, for example from metallurgical knowledge that at the end of the heat treatment the metal must have reached the temperature T (n) for the fastest possible, ultimate When this temperature is reached, only the maximum furnace capacity T (n) is available or an oven temperature T (n) determined from other criteria is used shall be. Knowing that from a roughly known temperature T $, for example, the desired recrystallization begins, and that from then on is to be operated with the given or determined furnace capacity, is described below this characteristic temperature value T5 is specified.

In analogy to (ln), here too, according to (1), v (n) = v (o). AT (n) (l, n) 'L \ T (o) calculated This gives the length At, now variable, to Provided that At is approximately the same length n, as the further steps At or the latter are selected, the equations (2, n) and (3, n) result again, with which the equation system as shown with reference to FIG. 1 becomes solvable.

It is now entirely possible that in practice the management of the heating elements is too expensive in many individual intervals At: Only a few, e.g. a total of three steps are provided for the heating element control, i.e. next to the measurement step 0 is followed by a step '1' and the end step '2'. In addition, it is with using the method shown in Fig. 2 is quite possible that according to the available or given heating element capacities TH (n) the resulting At becomes relatively long, which results in the linear interpolation between Trn (n) and Ts becomes too imprecise. It will now be made in the following with reference to Fig. 3 on the above This is a procedure based on explanations, but simplified for this purpose, wherein the first approximate statements made under (I) and (II) to a second Approximation can be corrected. This has proven to be particularly necessary because the few time steps involved in such a heat treatment process can stretch for hours.

Again, at the beginning of the process through the oven there is a temperature step TH (o) is applied and after an irregular oscillation of Tin (t) the excess temperature AT (o) and the rate of temperature rise characteristic of the absorption capacity v (o) measured. Furthermore, the end temperature is Um (2), as is the one to be applied at the end Furnace capacity TH (2) given. It is also known that from the temperature T5 the desired Recrystallization sets in and that from this moment on with maximum or otherwise given Furnace capacity is to be heated according to Ph (2).

Because according to the available or specified furnace capacity TH (2) for a relatively long time, for example 30 minutes with this power will have to be heated in order to start T (2) as quickly as possible from T5 m, an as yet undetermined number of small time intervals AT, determined according to FIG. 3.

Corresponding to the numbering k entered backwards in Fig. 3 of the time segments of the same length AT, according to the condition (I) corrected in a second approximation: the speed vk is calculated for each of these time segments.

The scaling of the right factor is preferably determined as follows. From dT v (o) = (5) dt, dT 2 dTE is selected as the temperature unit, dt = dt E as Time unit and v (o) 3 VE as a speed unit. Thus, the scaling quantities preferably chosen to be Sv = 1 (6) v (o) ST = 1 / dTE.

The speed vk is calculated until the following applies: = minimum and greater than zero (7), ie until the reference value Ts is reached as precisely as possible from above. This results in the number of steps x to be provided.

In Fig. 3, x = 4 is shown. With x = 5 the condition (7) already no longer fulfilled.

Now is according to the mean speed v (2) in the time segment '2' of the total length x AT is calculated.

The length of this time segment is designated in FIG. 3 as At 2 and results from # t2 = x. ## (9) Since in the case described here only two actual furnace control periods are provided, corresponding to n - 2, the conditions in middle time segment '1' can be determined. The easiest way to do this is as follows: It is assumed that the time segments At2 to Atl must behave in the same way as the energies to be absorbed in the respective time segments, i.e. in time segment No. 1 it becomes one of the middle for time segment No. 2 calculated speeds v (2) corresponding speed assumed. Then the number y of time steps of length AT results in the middle section No. 1 The calculated value T'S and not the T to be achieved is preferably used. The number of steps y sought results from (10).

Now formula (II) resp. (2, n) specified in a second approximation, applied as follows: where: #Tm (2) = {TH (2) -ET (2)} - {TH (l) -AT (l)} = fTH (2) - # T (2)} - {TH (s1) -AT (s')} H and analogously for AT (1).

m Expression (11) says that the temperature difference between the Matter phase and the heating resp. Cooling organs, at the end of an observed period of time vice versa proportional to the chord length e between the matter temperature at the beginning and at the end of this section is, viewed in the temperature-time diagram, as well as proportional is the length of the period under consideration.

AT (2) is that in time segment 2, AT (1) that in In In segment 1 absorbed energy, which corresponds to the temperature difference between Ts and X (o). The 5 scaling size results from the introduced convention: S t in addition From (11) AT (l) is determined, with which the furnace temperature T (1) from T (1) = T '+ AT (l) in the middle section 1 ge-H 5 is given.

It goes without saying that depending on the considerations regarding of the savings / effort ratio, the methods presented are combined can.

In summary, the method shown is based on the fact that at the beginning the characteristic absorption behavior of the heat to be treated Matter phase is determined, and that taking into account (I) and (II) of the optimal absorption path to be traversed in time with the correspondingly required Energy supplies is calculated in such a way that desired final ratios and / or Intermediate ratios can be achieved.

A further refinement of the procedure now results from that during the actual execution of the procedure i.e. during the previously calculated parameters for the furnace control are already used, the actual ratios T (t) that are established are continuously with the ones calculated in advance TARGET ratios are compared to each time the backward calculation in this way again to ensure that the actual conditions that arise in reality are used as new specifications are used and continuously corrected tax data are calculated from this. It results practically an adaptive tax resp. Control procedure by first Phase a system identification takes place at the beginning of the procedure, from this a first one Proximity control function in the form of the gradually necessary energy supplies TH is calculated, the energy supply is real according to these calculated values is controlled, then it is observed how accurately the system of the calculated hypothesis follows in order to continuously calculate the previously calculated tax values from observed deviations adapt. The proposed method can in principle be used anywhere where it is a matter of heating or cooling phases of matter. The resulting savings but justify the effort, especially with such large systems, as for the continuous heat treatment of metals, using computers, respectively. Microcomputers.

Already rough pre-calculations, as shown with reference to FIG. 3 without observing the system during the actual control phase and adapting the control parameters result in significant energy and time savings According to initial experience, up to more than 50% power savings.

Claims (10)

Patent claims Process for time and energy-optimized control the energy supply resp. - Discharge for heating up resp. Cooling of a matter phase, characterized in that one - to Beginning of characteristic data for the energy "absorption or release behavior the matter phase determines - from it and the knowledge of at least one to be achieved or energy state of the phase to be passed through the necessary energy supply or -AbfUhrfunktion calculated in the time and - the heating resp. Cooling organs after the found function controls. 2. The method according to claim 1, characterized in that - the Matter phase a temperature step (TH (o)) of the heating resp. Undergoes cooling organs, - because the rate of temperature change per unit of time (v (o)) of the matter phase as a measure for the energy absorption respectively. - Measures dispensing ability, - taking into account, that as a first approximation a) the current energy intake or output (v (t)) of the matter phase per unit of time proportional to the instantaneous temperature difference (AT (t)) between her and the heating resp. Is cooling organs, and that b) this temperature difference inversely proportional to the previously recorded or given per unit of time Energy, from the measured rate of temperature change (v (o)) and given intermediate or target values for the matter phase, the temperature steps necessary in time (TH (n)) for the heating resp. Cooling organs calculated. 3. The method according to claim 1, characterized in that during the control of the heating resp. Cooling elements according to the pre-calculated function The course of the matter phase temperature (Tm (t)) is observed and if there are deviations from calculated course, the control steps still to be carried out are adaptively recalculated. 4. The method according to claim 2, characterized in that a system of equations of equation triple for each for time segments of predetermined length (At) according to: v (n) = v (o) bT (n) AT (o) v (n) At = {TH (n) - # T (n)} - {TH (n-1) - # T (n-1)}, where: v (o) is the measured rate of temperature change of the matter phase; v (n) the expected rate of temperature change in time segment (n); AT (n) is the temperature difference between the matter phase and heating resp. Cooling elements in time step (s); AT (o) the temperature difference between the matter phase and heating resp. Cooling organs when measuring the rate of temperature change (v (o)); TH (n) the heating resp. Cooling element temperature in time step (s); TH (nl) the temperature of the heating resp. Cooling organs in the immediately earlier time step (nl); AT (nl) is the temperature difference between the matter phase and heating resp. Cooling organs in the immediately earlier time step (nl); AT (n-2) this temperature difference in the second earlier time step (n-2); TH (n-2) the temperature of the Hei: - resp. Cooling organs in the second earlier time step (n-2). 5. The method according to claim 2, characterized in that the final temperature to be reached (T (n)) of the material phase as well as the then to be set Heating element resp. Cooling organ temperature (TH (n)) specifies. 6. The method according to claim 2, characterized in that with the final temperature to be reached (Tm (n)) of the matter phase is then present Heating resp. Cooling organ temperature (TH (n1) specifies as well as a temperature support value (Ts) for the material phase temperature from which it is reached with the specified heating resp. Radiator temperature (Tg (n)) is to be controlled. 7. The method according to claim 2, characterized in that it is used in a second approximation that the temperature difference (AT (n)) between the matter phase and the heating respectively. Cooling organs at the end of an observed period of time (Y * ET) inversely proportional to the length of the chord is between the matter temperature at the beginning and the end of this section, in the temperature-time diagram and is proportional to the length (y) of the time section under consideration. 8. The method according to claim 2, characterized in that it is taken into account in a second approximation that in a time segment with constant heating or cooling organ temperature (TH (n)) when this time segment (ate) is subdivided into a plurality of sub-time segments (AT) Energy absorption or release of the matter phase in each subsection according to: behaves, where: v rate of energy intake or output in the sub-period k counted from the end of the period; AT (n) temperature difference between matter phase and heating resp. Cooling elements at the end of the subdivided time period (x.6); AT (o) k temperature difference between matter phase and heating resp. Cooling organs when recording v (o), raised to the power of the number of sub-time segments counted backwards (AT) from the end of the considered time segment (X-AT) to the considered sub-time segment. 9. Use of the method according to claim 1 for furnace control of heat treatment systems for metal, in particular for aluminum. 10. Use of the method according to claim 1 for computer control of heating or cooling elements.