CN115963874B - Temperature tracking control method - Google Patents
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Abstract
The invention discloses a temperature tracking control method, which relates to the technical field of automatic control and is applied to a temperature control system, and the method comprises the following steps: determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set; based on temperature data, a temperature-power function formula and a preset temperature track of the heating cavity at n sampling moments, introducing the output power limit constraint of the heating body, calculating a plurality of optimal output powers of the heating body in a preset future time period by taking the minimum temperature error as a target, and further determining a plurality of corresponding temperature data; and when the n sampling moments are not preset end moments of the preset temperature track, updating the n temperature data sets and the output power sets, and returning to the step of determining the temperature-power function formula. The invention can realize temperature control based on temperature track tracking and has higher robustness.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a temperature tracking control method.
Background
Temperature control is a very important part of many production and processing fields, and temperature affects many physical processes and chemical reactions. In the industries of metallurgy, chemical industry, machinery and the like, various heating systems such as a heat treatment furnace, a superheated steam furnace, a reaction kettle and the like are widely used, and the heating systems have the characteristics of thermal inertia, hysteresis, time variability and the like, so that the temperature of the heating systems is difficult to accurately and quickly control. On the other hand, with the complexity of the production process and the increase in the continuity of the process, the control of the temperature is not only to the set value and then to be maintained, but also in some cases, the temperature is required to be changed along a predetermined trajectory with time, that is, temperature tracking is required. For example, in the dyeing process, if the temperature of the dye liquor can maintain a specific heating curve, a better dyeing effect can be obtained; the heat treatment of the steel needs to strictly control the heating rate, the cooling rate, the heat preservation temperature, the heat preservation time and the like, so that various performances of the steel can achieve the expected effect; in the battery charging process, the loss of the battery can be reduced, the charging time can be shortened, the safety of the charging process can be improved and the like by designing and controlling a charging temperature curve. Therefore, temperature tracking control is becoming more and more important in various industries.
At present, most temperature control methods are based on fixed target temperature, and almost no requirement exists on the relation between temperature and time in the process of increasing or decreasing the temperature from the initial temperature to the target temperature, so the adopted control method is generally PID control, the response time is longer, the shortest time can only reach the second level, and meanwhile, constraint conditions cannot be added; or the system temperature is controlled by the thermal expansion and contraction properties of the materials. Obviously, the existing method cannot truly realize temperature track tracking control fundamentally.
Disclosure of Invention
The invention aims to provide a temperature tracking control method which can realize temperature control based on temperature track tracking and has higher robustness.
In order to achieve the above object, the present invention provides the following solutions:
the temperature tracking control method is applied to a temperature control system, wherein the temperature control system comprises a heating body and a heating cavity, and a working medium is arranged in the heating cavity;
the temperature tracking control method comprises the following steps:
acquiring a preset temperature track corresponding to the working medium, a temperature data set of the heating cavity in a preset time period and an output power set of the heating body in the preset time period;
determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set;
introducing output power limit constraint of the heating element based on temperature data of the heating element cavity at n sampling moments, the temperature-power function formula and the preset temperature track, and calculating a plurality of optimal output powers of the heating element in a preset future time period by taking the minimum temperature error as a target; the initial time of the preset future time period is n sampling times;
determining a plurality of temperature data of the corresponding heating cavity in a preset future time period based on a plurality of optimal output powers of the heating body in the preset future time period;
outputting the optimal output power of the heating body at n sampling moments and the temperature data of the corresponding heating cavity, and exiting temperature tracking when the n sampling moments are preset end moments of the preset temperature track; when the n sampling moments are not the preset end moments of the preset temperature track, updating n to n+1, updating the temperature data set to a plurality of temperature data of the heating cavity in a preset future time period, updating the output power set to a plurality of optimal output powers of the heating body in the preset future time period, and returning to the step of determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set.
Optionally, determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set specifically includes:
calculating a temperature control time lag according to the temperature data set;
fitting the temperature data set and the output power set by adopting a least square method to obtain a first temperature power correlation coefficient and a second temperature power correlation coefficient;
and determining a temperature-power function formula corresponding to the temperature control system according to the first temperature power correlation coefficient, the second temperature power correlation coefficient and the time lag of the temperature control system.
Optionally, based on temperature data of the heating cavity at n sampling moments, the temperature-power function formula and the preset temperature track, introducing an output power limit constraint of the heating body, and calculating a plurality of optimal output powers of the heating body in a preset future time period with minimum temperature error as a target, wherein the method specifically comprises the following steps:
acquiring temperature data of the heating cavity at n sampling moments and a preset future time period;
calculating a plurality of predicted temperature data in the preset future time period based on the temperature-power function formula and the temperature data of the heating cavity at n sampling moments;
determining a plurality of theoretical temperature data over the preset future time period based on the preset temperature trajectory;
establishing a temperature error objective function according to the plurality of predicted temperature data and the plurality of theoretical temperature data;
establishing the limit value constraint of the output power of the heating element;
and determining a plurality of optimal output powers of the heating element in a preset future time period by taking the minimum value of the temperature error objective function as a target based on the output power limit constraint.
Optionally, determining a plurality of temperature data of the corresponding heating cavity in a preset future time period based on a plurality of optimal output powers of the heating body in the preset future time period specifically includes:
aiming at the optimal output power of the heating body at n sampling moments, the temperature data of the corresponding heating cavity is the temperature data of the heating cavity acquired at n+1 sampling moments.
Optionally, the temperature tracking control method further includes:
and displaying the optimal output power of the heating body at a plurality of moments and the temperature data of the corresponding heating cavity in a form of tracking a temperature track curve.
In order to achieve the above purpose, the present invention also provides the following technical solutions:
according to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a temperature tracking control method, which is characterized in that a temperature-power function formula corresponding to a temperature control system is determined according to a known temperature data set and an output power set; and then introducing the output power limit constraint of the heating element based on the temperature data, the temperature-power function formula and the preset temperature track of the known heating element cavity at n times of sampling time, calculating a plurality of optimal output powers of the heating element in a preset future time period with the minimum temperature error as a target, and then determining the temperature data of the corresponding heating element cavity in the preset future time period, thereby obtaining the optimal output power of the heating element at n times of sampling time and the temperature data of the corresponding heating element cavity. The above process is iterated repeatedly, so that accurate tracking of the preset temperature track can be realized. Namely, as for an arbitrary continuous temperature track (temperature track in a preset future time period) of the temperature control system, the temperature control method can quickly and accurately track as long as the temperature track meets the limit requirement (output power limit constraint) of the input power of the system. In addition, aiming at the time variability of the system, the temperature tracking control method can update key parameters of the reactive system in real time, and ensure the instant authenticity of the system property; more importantly, the method provided by the invention has strong anti-interference capability and good robustness in the temperature control process.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a temperature tracking control method of the present invention;
FIG. 2 is a schematic diagram of a temperature control system of the present invention;
FIG. 3 is a preset temperature trace R (t) corresponding to a working medium according to an embodiment of the present invention;
FIG. 4 is a trace temperature trace curve T (T) for an example of the invention;
FIG. 5 is a graph showing the deviation of the trace temperature trace curve from the preset temperature trace in the embodiment of the present invention.
Symbol description:
1-a heating cavity; 2-working medium; 3-a heating element; 4-thermocouple thermometer; 5-controller.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a temperature tracking control method, which can track and control any temperature track on the premise of meeting the power requirement of any temperature control system, and has high control precision and high response speed. Meanwhile, the control algorithm has stronger prediction and adaptation capability and stronger anti-interference capability.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 1, the present invention proposes a temperature tracking control method, which is applied to a temperature control system. As shown in fig. 2, the temperature control system comprises a heating body 3 and a heating cavity 1, wherein a working medium 2 and a thermocouple thermometer 4 are arranged in the heating cavity 1, the thermocouple thermometer 4 is immersed in the working medium 2, and the thermocouple thermometer 4 and the heating body 3 are electrically connected with a controller 5.
The temperature control system works under certain air pressure (usually standard atmospheric pressure), and the temperature change delta T in the heating cavity 1 and the heat delta Q generated by the heating body 3 i The relation between the heat quantity delta Qo radiated outside the heating cavity 1 is as follows:
C p ΔT＝ΔQ i -ΔQ o
wherein C is p Is the isobaric heat capacity of the temperature control system.
Writing the above to a differential form, the following formula applies:
wherein t is time, subscript n is sampling number, P is power, h is interface heat exchange coefficient, A is effective surface area of heating cavity 1; t (T) R Is ambient temperature, typically room temperature. In general, for a particular temperature control system, the sampling time interval t n+1 -t n The above-mentioned differential form of the formula can be put into the following formula, taking the constant Δt as a unit of time:
T n+1 ＝aT n +bP′ n
in the method, in the process of the invention,P′ n ＝P n +hAT R 。
considering that the heat generated by the heating element 3 is conducted to the thermometer for a certain time, namely temperature control time lag, the formula T is given by n+1 ＝aT n +bP′ n The adjustment is as follows:
T n+1 ＝aT n +bP′ n-d ；
wherein the temperature control time lag is d, and the coefficients a and b reflect the properties of the system, namely C in the formula of the differential form p H and A. In fact, for a truly controlled temperature control system, its properties change over time, instantaneously, so equation T n+1 ＝aT n +bP′ n-d A and b in (a) are also variables.
To sum up, if at n sampling moments, the temperature of the temperature control system is T n Temperature T at n+1 sampling times n+1 Coefficients a and b depending on the nature of the reaction system, and the power P 'of the heating element at the n-d sampling time' n-d This is an overall implementation method of temperature trajectory tracking control.
From this, the temperature tracking control method of the present invention includes:
step 100, acquiring a preset temperature track corresponding to the working medium, a temperature data set of the heating cavity in a preset time period and an output power set of the heating body in the preset time period.
And 200, determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set.
Step 200 specifically includes:
1) Calculating a temperature control time lag according to the temperature data set; the invention considers the time lag of the device and can conveniently add the constraint. Specifically, the heating element 3 of the temperature control system is turned on to output a certain power, and if the temperature rise is detected by the dΔt thermometer for a certain period of time, the temperature control time lag is d.
2) And fitting the temperature data set and the output power set by adopting a least square method to obtain a first temperature power correlation coefficient and a second temperature power correlation coefficient. Specifically, the heating element 3 works for a certain period of time with a certain power, and according to the acquired temperature data set and output power set, the coefficient a and the coefficient b of the initial stage of the system are obtained by using least square fitting.
3) And determining a temperature-power function formula corresponding to the temperature control system according to the first temperature power correlation coefficient, the second temperature power correlation coefficient and the time lag of the temperature control system.
Specifically, if n < d, then P' n-d ＝hAT R 。
If n > d, the temperature-power function formula is:
T n+1 ＝aT n +bP′ n-d ；
wherein a represents a first temperature power correlation coefficient, b represents a second temperature power correlation coefficient, T n+1 Representing temperature data in the heating cavity at n+1 sampling moments, T n Representing temperature data in the heating cavity at n sampling moments, P' n-d The output power of the heating element at the sampling time of n-d times is represented, and d represents temperature control time lag.
Step 300, introducing output power limit constraint of the heating element based on temperature data of the heating element cavity at n sampling moments, the temperature-power function formula and the preset temperature track, and calculating a plurality of optimal output powers of the heating element in a preset future time period with minimum temperature error as a target; the initial time of the preset future time period is n sampling times;
specifically, the formula T will be n+1 ＝aT n +bP′ n-d Written as a function:
T n+1 ＝f(T n ，P′ n-d )。
from the recurrence relation:
T n+1+d ＝f(T n+d ，P′ n )
T n+2+d ＝f(T n+d+1 ，P′ n+1 )
…
T n+1+d+m ＝f(T n+d+m ，P′ n+m )；
wherein m is the number of time units in a preset future time period.
Taking into account the non-negativity and the finite nature of the power P, P is less than or equal to P under the condition of 0 m (P m Maximum power of the heating element), the temperature error objective function is constructed as follows:
wherein J represents the value of the temperature error objective function, T n+i Representing predicted temperature data obtained according to a temperature-power function formula at n+i sampling moments, R n+i Representing theoretical temperature data obtained according to a preset temperature track at n+i sampling moments, wherein sigma is a penalty factor, and U=max (0, -P) +max (0, P-P) m ) P represents the power of the heating element at n sampling times, P m Indicating a preset maximum power of the heating element.
Specifically, step 300 specifically includes:
1) And acquiring temperature data of the heating cavity at n sampling moments and a preset future time period.
2) And calculating a plurality of predicted temperature data in the preset future time period based on the temperature-power function formula and the temperature data of the heating cavity at n sampling moments.
3) Based on the preset temperature trajectory, a plurality of theoretical temperature data over the preset future time period is determined.
4) And establishing a temperature error objective function according to the plurality of predicted temperature data and the plurality of theoretical temperature data.
5) Establishing the limit value constraint of the output power of the heating element; namely, P is more than or equal to 0 and less than or equal to P m 。
6) And determining a plurality of optimal output powers of the heating element in a preset future time period by taking the minimum value of the temperature error objective function as a target based on the output power limit constraint.
Step 400, determining a plurality of temperature data of the corresponding heating cavity in a preset future time period based on a plurality of optimal output powers of the heating body in the preset future time period; specifically, for the optimal output power of the heating element at n sampling moments, the temperature data of the corresponding heating cavity is the temperature data of the heating cavity acquired at n+1 sampling moments. I.e. the optimal P 'is obtained after the temperature error objective function J is minimized and solved' n ，P′ n+1 …P′ n+m The heating power at the current sampling instant n should be taken as P' n While the power P 'at the sampling instants n+1 to n+m' n+1 …P′ n+m Then no use is made in this step.
Step 500, outputting the optimal output power of the heating body at n sampling moments and the temperature data of the corresponding heating cavity, and exiting temperature tracking when the n sampling moments are preset end moments of the preset temperature track; when the n sampling moments are not the preset end moments of the preset temperature track, updating n to n+1, updating the temperature data set to a plurality of temperature data of the heating cavity in a preset future time period, updating the output power set to a plurality of optimal output powers of the heating body in the preset future time period, and returning to the step 200.
Specifically, the coefficients a and b are iterated. Taking time variability of the system into consideration, a and b are updated in real time by using a least square method according to a sequence of the temperature T and the power P measured at n+1 sampling moments. In the process, the deviation between the actually measured temperature sequence and the target temperature sequence is normal distribution, and if the deviation exceeds 2 times of standard deviation, the corresponding actually measured temperature value is not adopted, so that the anti-interference capability of the system is enhanced. Repeating the steps until the tracking of the preset temperature track is completed.
Preferably, the temperature tracking control method further includes: and displaying the optimal output power of the heating body at a plurality of moments and the temperature data of the corresponding heating cavity in a form of tracking a temperature track curve.
In one embodiment, the heating chamber 1 is a beaker, the working medium 2 is water, and the heating element 3 is a resistive heating element. Wherein the preset temperature trace corresponding to the working medium is shown in fig. 3; the temperature tracking control method of the invention comprises the following steps:
(1) The time lag d is measured. The initial temperature is room temperature, the resistance heater heats water with power of 200W, and samples at a frequency of 5Hz to obtain a temperature data set and an output power meter. According to the time-varying data of the temperature in the temperature data set, the following steps are obtained: after 6s, the thermocouple detects that the temperature starts to rise, and the temperature control time lag d=30.
(2) And acquiring initial coefficients a and b of the temperature control system. From the temperature dataset it can also be known that: after the resistive heater was operated at 200W for 6s, water was continuously heated at 200W, sampled at a frequency of 5Hz for 20s, and 100 sets (T, P) of data were recorded.
Then according to formula T n+1 ＝aT n +bP′ n-d And obtaining an initial coefficient a and an initial coefficient b by using least square fitting.
(3) Taking the time unit number m=3 in a preset future time period for a given temperature track R (T), and measuring the temperature T according to n times of sampling n Calculate T n+1 ，T n+2 And T n+3 According to the step 300, under the constraint condition that P is more than or equal to 0 and less than or equal to 1kW, the minimum value of the objective function J is calculated by adopting a coordinate circulation method, so that the optimal P 'is obtained' n ，P′ n+1 And P' n+2 At this time, the power applied to the resistance type heating element is taken as P' n 。
(4) T to be measured n+1 And P 'corresponding thereto' n And adding the new data into the past input/output sequence to be used as a new group of data, and iteratively updating the coefficient a and the coefficient b in real time.
(5) Let n=n+1, return to step (3) above until the end of the preset target temperature trajectory R (t). Fig. 4 shows an actual tracking temperature curve T (T), and the deviation T (T) -R (T) from the preset temperature trace is small, so that fig. 5 shows that the tracking effect is good.
In summary, the temperature tracking control method of the invention has the following advantages: on the premise of meeting the power input limit of the temperature control system, any one continuous temperature track can be tracked and controlled rapidly and accurately; the time lag of the temperature control system can be effectively solved; constraints of the system can be considered; the time variability of the temperature control system can be effectively solved by updating the system parameters in real time; when the parameters of the temperature control system are updated, sampling data are screened, and the anti-interference capability of the temperature control system is enhanced.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (7)
1. The temperature tracking control method is characterized by being applied to a temperature control system, wherein the temperature control system comprises a heating body and a heating cavity, and a working medium is arranged in the heating cavity;
the temperature tracking control method comprises the following steps:
acquiring a preset temperature track corresponding to the working medium, a temperature data set of the heating cavity in a preset time period and an output power set of the heating body in the preset time period;
determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set;
introducing output power limit constraint of the heating element based on temperature data of the heating element cavity at n sampling moments, the temperature-power function formula and the preset temperature track, and calculating a plurality of optimal output powers of the heating element in a preset future time period by taking the minimum temperature error as a target; the initial time of the preset future time period is n sampling times;
determining a plurality of temperature data of the corresponding heating cavity in a preset future time period based on a plurality of optimal output powers of the heating body in the preset future time period;
outputting the optimal output power of the heating body at n sampling moments and the temperature data of the corresponding heating cavity, and exiting temperature tracking when the n sampling moments are preset end moments of the preset temperature track; when the n sampling moments are not the preset end moments of the preset temperature track, updating n to n+1, updating the temperature data set to a plurality of temperature data of the heating cavity in a preset future time period, updating the output power set to a plurality of optimal output powers of the heating body in the preset future time period, and returning to the step of determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set.
2. The temperature tracking control method according to claim 1, wherein determining a temperature-power function formula corresponding to the temperature control system according to the temperature data set and the output power set specifically includes:
calculating a temperature control time lag according to the temperature data set;
fitting the temperature data set and the output power set by adopting a least square method to obtain a first temperature power correlation coefficient and a second temperature power correlation coefficient;
and determining a temperature-power function formula corresponding to the temperature control system according to the first temperature power correlation coefficient, the second temperature power correlation coefficient and the time lag of the temperature control system.
3. The temperature tracking control method according to claim 2, characterized in that the temperature-power function formula is:
T n+1 ＝aT n +bP′ n-d ；
wherein a represents a first temperature power correlation coefficient, b represents a second temperature power correlation coefficient, T n+1 Representing temperature data in the heating cavity at n+1 sampling moments, T n Representing temperature data in the heating cavity at n sampling moments, P' n-d The output power of the heating element at the sampling time of n-d times is represented, and d represents temperature control time lag.
4. The temperature tracking control method according to claim 1, wherein, based on temperature data of the heating chamber at n sampling times, the temperature-power function formula and the preset temperature trajectory, an output power limit constraint of the heating element is introduced, and a temperature error is targeted at a minimum, a plurality of optimal output powers of the heating element in a preset future time period are calculated, which specifically includes:
acquiring temperature data of the heating cavity at n sampling moments and a preset future time period;
calculating a plurality of predicted temperature data in the preset future time period based on the temperature-power function formula and the temperature data of the heating cavity at n sampling moments;
determining a plurality of theoretical temperature data over the preset future time period based on the preset temperature trajectory;
establishing a temperature error objective function according to the plurality of predicted temperature data and the plurality of theoretical temperature data;
establishing the limit value constraint of the output power of the heating element;
and determining a plurality of optimal output powers of the heating element in a preset future time period by taking the minimum value of the temperature error objective function as a target based on the output power limit constraint.
5. The temperature tracking control method according to claim 4, wherein the temperature error objective function is:
wherein J represents the value of the temperature error objective function, m represents the number of time units within a preset future time period, T n+i Representing predicted temperature data obtained according to a temperature-power function formula at n+i sampling moments, R n+i Representing theoretical temperature data obtained according to a preset temperature track at n+i sampling moments, wherein sigma is a penalty factor, and U=max (0, -P) +max (0, P-P) m ) P represents the power of the heating element at n sampling times, P m Indicating a preset maximum power of the heating element.
6. The temperature tracking control method according to claim 1, characterized in that determining a plurality of temperature data of the corresponding heat generating chamber in a preset future period based on a plurality of optimal output powers of the heat generating body in the preset future period, specifically comprises:
aiming at the optimal output power of the heating body at n sampling moments, the temperature data of the corresponding heating cavity is the temperature data of the heating cavity acquired at n+1 sampling moments.
7. The temperature tracking control method according to claim 1, characterized in that the temperature tracking control method further comprises:
and displaying the optimal output power of the heating body at a plurality of moments and the temperature data of the corresponding heating cavity in a form of tracking a temperature track curve.
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| CN114942659A (en) * | 2022-06-30 | 2022-08-26 | 佛山仙湖实验室 | Kiln temperature control method, system and device and storage medium |
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