The constant temperature accuracy of the constant temperature laboratory is 27 0.2℃. However, due to the uniqueness of the laboratory, there are many internal and external disturbances in the incubator, and the size of some random disturbances is difficult to determine, so it is difficult to achieve the expected results. In order to solve this problem, the transfer function of the controlled object in the greenhouse is obtained by establishing a mathematical model, and then the parameters of PID controller are determined by parameter optimization method. Finally, the influence of indoor and outdoor interference on room temperature is studied by MATLAB simulation method. Through the research, it can be concluded that PID control can ensure the constant temperature accuracy of the incubator when the heat dissipation disturbance of the equipment is 65438 07℃, the supply air temperature disturbance is 0.65438 0℃ and the infiltration air disturbance is not more than 0.3℃.
Keywords: constant temperature room, PID control of infiltration wind disturbance parameters to optimize temperature
1 preface
With the development of science and technology, all kinds of precision products and special scientific experiments need specific working environment, and constant temperature has become one of the essential conditions. At present, the common constant temperature precision of constant temperature greenhouses in China is 1℃ and 0.5℃, and there are also 0. 1℃. However, some high-precision thermostatic chambers, such as the scribing room of optical instrument factory, have reached 0.0056℃. However, in some unconventional scientific laboratories, not only the constant temperature accuracy is very high, but also there are interferences, such as air infiltration, equipment heat dissipation, air supply temperature fluctuation and electric heater power supply voltage fluctuation. However, some disturbances, such as the maximum value of infiltration air, are difficult to determine without taking corresponding measures to control the infiltration air disturbance, which leads to excessive fluctuation of room temperature, and as a result, the constant temperature accuracy of the thermostatic chamber is difficult to meet the requirements. How to make the constant temperature accuracy of these extraordinary scientific laboratories meet the use requirements has also become a huge problem in the design of air conditioning system and control system of thermostatic chamber.
Because the traditional PID control algorithm is simple in operation, convenient in adjustment and strong in robustness, it still plays a very important role in process control, so at present, most air conditioning systems in constant greenhouse adopt PID control. But the effect of PID control depends on the correct setting of controller parameters to a great extent. Therefore, people have proposed various parameter tuning methods, such as minimum error integration, fixed attenuation ratio, pole configuration and so on. These methods mainly use some design methods in classical control theory or rely on field test methods to calculate and tune PID controller parameters. Obviously, this requires operators to have a high theoretical foundation and on-site debugging experience. Moreover, the model parameters of the controlled object are difficult to determine, and the system performance stability is poor, so it is necessary to adjust the parameters frequently, which will definitely affect the normal operation of the system. For the temperature control of these unconventional air-conditioned rooms, because the controlled object has great inertia and time delay, and the transfer function of the object is nonlinear and time-varying, it is difficult to achieve better control effect by using traditional PID control.
In this paper, the simplex method is used to optimize PID parameters, and then the maximum infiltration wind disturbance is determined by MATLAB simulation, so that PID control can ensure the constant temperature accuracy of the thermostatic chamber.
2 Project overview
The thermostatic chamber has a building area of 625m2, a height of 8m, a total air supply of 27,500m3/h, an air supply temperature of 15℃, a room design temperature of 27 0.2℃ and equipment heat dissipation of 135KW. The walls and floors of the thermostatic chamber are made of heat preservation materials, and the infiltration air comes from the outer room with the design temperature of 26 65,438+0℃.
3 Constant temperature greenhouse air conditioning process modeling
1 mathematical model of controlled object of constant temperature greenhouse air conditioning system
In order to control the controlled object of the air conditioning system in a constant temperature greenhouse, a suitable mathematical model must be established. Make some necessary simplifications and assumptions about actual objects with mathematical language;
Because the wall and floor of constant temperature greenhouse are made of thermal insulation materials, the heat transfer between indoor and outdoor wall and floor is ignored.
The ceiling of the thermostatic chamber is composed of cover plates with gaps, so there is a certain infiltration wind, which is ignored in other places such as doors and windows.
If the inertia of the actuator and the transfer lag of the room temperature regulating object are not considered, according to the law of conservation of energy, the energy entering the object per unit time minus the energy flowing out of the object per unit time is equal to the change rate of energy storage in the object. The expression and figure 1 are as follows:
Figure 1 Automatic Room Temperature Adjustment System
The mathematical expression is:
Where: where is the heat capacity of constant temperature room;
C-specific heat of air;
Gs-air supply;
θ0 '- air supply temperature before electric heater;
θ 1- indoor air temperature, return air temperature;
QE heat of electric heater;
QM- heat dissipation of equipment;
Gas-heat brought by infiltration wind;
Through the formula qi = gic it
Where: gi-infiltration air volume;
θit—— air temperature of penetrating wind;
Specific heat of wind penetrating air.
Substitute the formula into the formula and arrange it.
Where: t 1- adjusts the time constant of the object,
t 1 = Chrr/；
K1-Adjust the magnification factor of the object,
k 1 = GSc/；
θE—— the regulating amount of electric heater, which is converted into the change of air supply temperature.
θE = QE/GSC；
θf—— the amount of interference is converted into the change of supply air temperature,
θf '- disturbance of supply air temperature,
θf'=θ0 "
θIf—— the interference amount of infiltration wind,
θIf = homogeneous/GSC;
θMf—— heat dissipation interference of equipment,
θMf=QM/GSC .
Through Laplace transform, we get
If the transfer lag of the controlled object is considered, the transfer function of the air conditioning process in a constant temperature greenhouse is:
2. Transfer function of temperature sensing element and executive regulating mechanism
The temperature sensing element adopts thermal resistance. According to the principle of heat balance, the heat balance equation is:
Where: C2-heat capacity of thermal resistance;
θ 2-thermal resistance temperature;
Q2—— the heat transferred from air to thermal resistance in unit time;
α 2-heat transfer coefficient between indoor air and thermal resistance surface;
F2-surface area of thermal resistance;
θ 1- indoor air temperature, return air temperature.
According to Laplace transform, the transfer function of temperature sensing element can be obtained:
It also performs the transfer function of the adjusting mechanism:
3 Determination of characteristic parameters and other parameters of thermostatic chamber
The characteristics of the constant temperature room, that is, the characteristics of the room, are expressed by three parameters: transfer lag τ, time constant T 1 and amplification coefficient K 1.
Time constant T 1 and amplification factor K 1.
From the formula, η=4, GI=GS×3%, we can get T 1= 18, K 1=0.97 1.
Transfer lag tau
According to the empirical formula τ/T 1=0.07, τ=35 points is calculated.
According to Table 6- in the reference, the time constant and insensitive zone of the temperature sensing element are T3=50 seconds, and 2ε=0.05℃.
The proportional coefficient of the electric heater K2=△θ/△N=0.00009, T2=50 seconds.
Simplex optimization method
Parameter optimization of control system means that the controlled object is known, the structure and form of the controller have been determined, and some parameters of the control system need to be adjusted or found, so that the whole control system can achieve the best under a certain performance index.
The idea of simplex method is very simple. If you need the maximum point of a function, you can first calculate and compare the function values of several points, determine the changing trend of the function as the reference direction according to their size relationship, and then search according to the reference direction until you find the minimum value.
Take four points from different planes in three-dimensional space to form a simplex, as shown in Figure 3.
Fig. 2 Simplex of three-dimensional space
The function values corresponding to these four points X0, X 1, XX3 are F0 and FFF3. By comparison, it can be seen that the largest point is the corresponding point X3, so it can be inferred that the possibility of a better point is the greatest at the symmetrical point XR of almost point XH, and then the function value FR at XR is calculated. If FR≥max, it means that the step from XH is too big, and XR is not necessarily better than XH. So we can compress the step size, find a new point XS between XH and XR, and then take the maximum value of X0, F 1, F2, which shows that the situation has improved, but the forward step size and step size may not be enough, and we can also increase the step size to get a little XE on the extension line of XH and XR. If the function FE corresponding to XE is less than FR, we will take XE as a new point and form a new simplex with X0, X 1, X2. Finally, the function values of each point that constitutes the new simplex are compared. If the relative difference between the maximum value and the minimum value is less than the given number e, it means that the minimum value has been found, otherwise, the above steps are repeated until the minimum value is found.
Simulation of control system of thermostatic chamber
The whole room temperature automatic regulation system includes the regulated object, regulator, temperature sensing element and PID controller. According to the parameter calculation results, the constant temperature control system of the constant temperature greenhouse as shown in Figure 3 is finally obtained.
Fig. 3 simulation block diagram of constant temperature control system in constant temperature greenhouse?
The heat dissipation of experimental equipment in the constant temperature room is quite stable, and it can be concluded from the formula that the disturbance θ MF = 17℃ is a stable disturbance. The disturbance of supply air temperature mainly includes the fluctuation of supply voltage of electric heater, the fluctuation of chilled water temperature of heat exchanger and the change of supply air temperature caused by pipeline temperature rise, and its value is 0. 1℃. The disturbance quantity of infiltration wind is a random disturbance quantity, which changes with the change of outdoor room temperature and infiltration air volume of a constant greenhouse, and is the most important factor affecting the room temperature of the constant greenhouse. The simulation curves of PID control when the infiltration wind disturbance is 0. 1℃, 0.2℃, 0.3℃ and 0.4℃ respectively are shown in Figure 4- Figure 7.
Fig. 4 Simulation curve of PID control when θ if is 0. 1℃
Fig. 5 Simulation curve of PID control when θ if is 0.2℃
Fig. 6 Simulation curve of PID control when θ if is 0.3℃
Fig. 7 Simulation curve of PID control when θ if is 0.4℃
By analyzing Figure 4- Figure, it can be concluded that the indoor temperature fluctuation of constant temperature greenhouse is less than 0.2 when the infiltration wind disturbance θIf is not greater than 0.3℃.
0℃, meet the requirements of constant temperature accuracy of the constant temperature room. However, when the infiltration wind disturbance θIf is 0.4℃, the room temperature fluctuation in the constant temperature chamber is greater than 0.2℃, which is beyond the allowable fluctuation range.
6 conclusion
Through the above simulation and analysis, we can draw the following conclusions:
The constant temperature accuracy of the constant temperature laboratory is 27 0.2℃. However, due to the uniqueness of the laboratory, there are many internal and external interferences in the constant temperature greenhouse. Only when the equipment cooling disturbance is 65438 07℃, the supply air temperature disturbance is 0.65438 0℃, and the infiltration air disturbance is not more than 0.3℃, PID control can ensure the constant temperature accuracy of the constant temperature laboratory and meet the use requirements.
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Room temperature PID control room temperature
The temperature measurement accuracy of a temperature laboratory is 27 0.2℃. However, due to the particularity of the laboratory, it is difficult to determine the volume interference inside and outside the constant temperature room and some random disturbances, which makes it difficult to achieve the expected results. In order to solve this problem, the mathematical model of the controlled object in a constant temperature room is established, and its transfer function is deduced. Then the PID controller parameters are used to determine the optimal parameters. Finally, the disturbance of indoor and outdoor temperatures on the room temperature is studied by MATLAB simulation method. Through research, it can be concluded that when the cooling capacity of the equipment is 65438 07℃, the temperature of disturbance air supply is 0.65438 0℃, and the amount of disturbance air infiltration does not exceed 0.3℃. PID temperature control room is used to ensure the accuracy of the thermostat.
Keywords: thermostatic chamber, PID control parameters, wind disturbance, temperature optimization
1 Introduction
With the development of science and technology, the manufacture of all kinds of precision products and the special requirements of scientific experiments are closely related to the specific working environment. At present, our common room temperature accuracy is 65438 0℃ and 0.5℃, which is 0.65438 0℃. And some, such as high-precision optical instrument factory, have reached the room temperature accuracy of 0.0056℃. However, in some very precise scientific laboratories, not only the temperature is high, but also the disturbances, such as infiltration air volume, equipment cooling, fluctuation of air supply temperature, and electric heaters, such as fluctuation of power supply voltage, and some disturbances, such as wind infiltration, are difficult to determine. If proper measures are not used to control the infiltration of wind interference, the room temperature fluctuates too much, which leads to the difficulty in meeting the requirements of constant temperature accuracy in a constant temperature room. How to make these excellent scientific precision meet the requirements of the constant temperature laboratory has also become a major problem in the design of air conditioning system and control system in the constant temperature room.
Because of the traditional PID control algorithm, the calculation is simple, the adjustment is convenient and the robustness is strong, and this control algorithm still occupies a very important position in process control. Therefore, the current room temperature air conditioning system mostly adopts PID control. However, the effect of PID control depends on the correct controller parameter setting to a great extent. Therefore, many methods of parameter tuning have been proposed, such as minimum error integration, fixed attenuation ratio, pole configuration and so on. These methods mainly use some design methods or test methods in classical control theory, and rely on the field to calculate and set PID control parameters. Obviously, this requires the operator to have a high theoretical foundation and field test experience. Moreover, it is difficult to determine the parameters of the object model, and the system performance is not stable, which requires frequent parameter tuning, which will affect the normal operation of the system. For these unconventional air conditioning room temperature control, because the controlled object has large inertia and time delay, and is influenced by many factors, the transfer function of the object is nonlinear and time-varying, and it is difficult to obtain better control effect by using traditional PID control.
Simplex method is used to optimize PID parameters, and MATLAB is used for simulation to determine the maximum wind disturbance penetration. PID controls the room temperature to ensure the accuracy of constant temperature.
2 Project overview
The thermostatic chamber has a building area of 625m2, a floor height of 8m, a total air volume of 27500m3/h, an air temperature of 65,438 0.5℃, a room design temperature of 27 0.2℃ and a cooling device of 65,438 0.35kW. The walls and floors of the thermostatic chamber are made of heat insulation materials, and the wind permeates to the self-designed outdoor temperature of 26 65,438 0℃.
3 air conditioning room temperature process modeling
A mathematical model of controlled object of air conditioning system in constant temperature room
Taking the air conditioning system of constant temperature room as the control object, a suitable mathematical model is established. Use mathematical language to simplify and assume the number of actual objects;
At room temperature, the heat transfer between indoor and outdoor walls and floors can be ignored because the building walls and floors are made of thermal insulation materials.
The room temperature exists by the gap between flat roofs, and a certain degree of wind penetration is adopted, such as the wind penetration of doors and windows in other places is negligible.
If the actuator does not consider that the transmission of inertia and temperature regulation lags behind the target, according to the law of conservation of energy, the energy entering the target object per unit time is subtracted from the energy flowing out of the target object per unit time and the change rate of the stock of the target object with the same energy, and its expression is as shown in Figure 1:
Figure 1 Automatic Room Temperature Adjustment System
The mathematical expression is:
Where: CHRR-room temperature heat capacity;
C-specific heat of air;
GS-air traffic;
θ0'-air temperature in front of electric heater;
θ 1-indoor air temperature, return air temperature;
QE-thermoelectric heater;
Qm-equipment heat dissipation;
Gas-heat permeates into the wind;
QI = classified by type
Where: GI-infiltration air flow;
θ it-air temperature and wind penetration;
CIt-air permeates hot air.
Skills into style, organize a
Where: T 1-object for adjusting time constant,
t 1 = Chrr/；
K 1-Adjust the magnification factor of the object,
k 1 = GSc/；
θE-Adjust the volume of the electric heater and convert it into the change of air temperature.
θE = QE/GSC；
θ f-converted into the amount that interferes with the change of air supply temperature.
;
θf'-the amount that interferes with the supply air temperature,
θf '= θ0 "
θIf-the volume penetrated by disturbing wind,
θIf = homogeneous/GSC;
θMf-Interference with heat dissipation capacity of equipment,
θMf = QM / GSC。
Laplace transform is also determined by style.
If the controlled object considers the transfer lag, then the process of the room with constant temperature and air conditioning is a transfer function:
2. Transfer function of temperature element and actuator.
The temperature element adopts thermal resistance. According to the thermal balance principle, the thermal balance equation is:
Where: C2-thermal resistance of heat capacity;
θ 2-thermal resistance temperature;
Q2 -- thermal resistance of heat in unit air time;
α2-Surface heat transfer coefficient between indoor air and thermal resistance;
F2-thermal resistance of surface area;
θ 1-indoor air temperature, return air temperature.
Laplace transform is obtained by the following formula, and the heat transfer function component can be used:
The adjusting mechanism realizes the same transfer function:
Determination of room temperature characteristics and other parameters
Room temperature characteristics are the characteristics of the room, which are expressed by three parameters: transfer lag τ, time constant T 1 and amplification coefficient K 1.
Time constant T 1 and amplification factor K 1
From the formula, η = 4, GI = GS × 3%, through the ceremony, we can calculate, T 1 = 18 minutes, K 1 = 0.97 1.
Transmission delay τ
According to the empirical formula, τ/T 1 = 0.07 is τ = 35 minutes.
The reference schedule from the 6-temperature element can be a time constant with a dead time of T3 = 50 seconds and 2ε = 0.05℃.
The ratio of electric heater coefficient K2 = △ θ/△ N = 0.00009, and T2 = 50 seconds.
Simplex optimization method
Parameter optimization of control system means that when the object is known and the control structure and form have been determined, it is necessary to adjust the control system or find some parameters to make the performance index of the whole control system in the best state.
The idea of simplex method is very simple. If the maximum point of a function may be several points for calculating the function value, compare them, and determine the trend of size change according to the functional relationship between them as the reference direction of search, and then search according to the reference direction until the minimum value is found.
Four points in three-dimensional space different from the plane form a simplex, as shown in Figure 3.
Figure 2 Three-dimensional simplex space
The values corresponding to these four points X0, X 1, XX3 are functions of F0 and FFF3, and it can be seen from the comparison that the corresponding point is almost X3, which can well explain that XH is the most likely XR in almost symmetrical points, and then the value function FR of XR is calculated. If FR ≥ max, a big step forward from XH, XR is not necessarily better than XH. In the compression step, we can find a new XS point X0 between XH and XR, where F 1, F2 is the largest. Note that the situation has improved, but the previous step may not be enough. We can gradually add and XR points to expand online XE. If the FE function corresponding to XE is small, it will be used as a new XE point in FR to form a new simplex with X0, X 1, X2. Finally, a new comparison point of simplex function value is constructed. If the maximum and minimum relative difference is less than the given number e, then the minimum value has been found, otherwise, the above steps are repeated until the unique one is found.
5 simulation of room temperature control system
The temperature regulating system includes automatic regulating object, regulator and PID temperature controller. According to the calculation results of the parameters, the room temperature and constant temperature control system as shown in Figure 3 is finally obtained.
Fig. 3 Simulation block diagram of room temperature and constant temperature control system?
The room temperature of laboratory equipment is quite large, and its thermal stability is good. From the calculation of heat dissipation caused by equipment interference, it can be concluded that θMf = 17℃ traffic interference is stable. Interference with air supply temperature, fluctuation of power supply voltage of main electric heater, volume of chilled water heat exchanger, and temperature fluctuation, such as pipeline temperature rise caused by air supply temperature change, has a value of 0.65438 0℃. Interference air permeability is a random disturbance, and indoor temperature changes with the change of outdoor temperature. The change of indoor temperature and permeability is the most important factor affecting indoor temperature. The simulation curve of PID control is shown in Figure 4-7 when the interference of infiltration wind is 0.65438 0℃, 0.2℃, 0.3℃ and 0.4℃ respectively.
Figure 0. Simulation curve of 4θIf for PID control at1℃
Fig. 5θIf is the simulation curve of PID control at 0.2℃
Fig. 6θIf is the simulation curve of PID control at 0.3℃
Fig. 7θIf is the simulation curve of PID control at 0.4℃
By analyzing Figure 4-Figure, it can be concluded that when the permeability θ is less than 0.3℃ if the wind disturbance, the indoor temperature fluctuation is less than 0.2 room.
Temperature, room temperature constant temperature, meet the accuracy requirements. However, when the disturbance amount θ of permeated air is 0.4℃, the temperature fluctuation at room temperature is 0.2℃ higher than that at room temperature, which is beyond the agreed fluctuation range.
6 conclusion
Through the above simulation and analysis, we can draw the following conclusions:
The accuracy of the laboratory temperature is 27 0.2℃, but due to the particularity of the laboratory, the indoor and outdoor temperatures interfere with each other. Only when the air temperature of the cooling equipment interferes with 65,438 0.7℃ and 0.65,438 0℃, the interference of the air volume does not exceed 0.3℃. At this time, PID temperature control can ensure the accuracy of the laboratory temperature and meet the requirements of use.
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