CN109270843A - A kind of water route fuzzy PID control method of critical-cross carbon dioxide system - Google Patents
A kind of water route fuzzy PID control method of critical-cross carbon dioxide system Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The invention discloses a kind of water route fuzzy PID control methods of critical-cross carbon dioxide system, comprise the following steps that the first step, determine variable and its domain;Second step carries out Fuzzy processing to variable, establishes subordinating degree function;Third step establishes fuzzy inference rule table;4th step, fuzzy reasoning and ambiguity solution;5th step, according to Trans-critical cycle CO2The operating condition of heat pump system, corrected Calculation result;Final output is substituted into PID control, executes control by the 6th step.The present invention can be with the adjusting control parameter k of online modification PIDP、kI、kD, have the advantages that control precision is high, control stability is strong, control efficiency is high, control is highly reliable, than common PID control method, be more suitable for Trans-critical cycle CO2Heat pump system heat exchange delay, dynamic change demand for control.Targetedly control strategy can guarantee the stabilization and safety controlled under the extreme operating condition that unit is run.
Description
Technical field
The invention belongs to technical field of heat pumps, in particular to the water route fuzzy control of a kind of critical-cross carbon dioxide system
Method processed.
Background technique
In recent years, with the continuous aggravation of greenhouse effects, research institution and government department's increasingly concern for the environment friendly
Good refrigerant.Therefore natural refrigerant refrigerant receives more and more attention, CO2It is latent as natural refrigerant depletion of the ozone layer
Can value ODP be 0, global warming potential index GWP be 1, have superior environmental-friendly performance.Early in the eighties in 19th century, CO2
Just it is introduced into field of Refrigeration and Air-conditioning, CO2As naturally occurring inorganic compound, there is good safety and chemical stabilization
Property, it is safe and non-toxic, it is non-combustible, it is gaseous state (risk of explosion without phase-change) either to produce, transport or use under normal temperature and pressure,
Equal no pollution to the environment.CO simultaneously2Refrigerating effect per unit swept volume be 3~5 times of conventional refrigerants, it means that identical heat is provided
Compressor displacement required for pump capacity is smaller, and unit charging amount is less, reduces unit volume.CO simultaneously2Adiabatic exponent compared with
The compression of height, Trans-critical cycle refrigeration cycle is smaller, and compressor efficiency is high.Preceding International Institute or Refrigeration chairman G.Lorentzen is proposed
Standard Trans-critical cycle CO2The circulatory system, CO2It revert to the research of mainstream again in refrigeration subject.
Modern Family is 20%~30% for meeting the energy consumed by hot water demand and having reached life total energy consumption,
It includes that combustion heat energy (fossil fuel, bio-fuel) directly heats, electric heating is converted, solar energy that traditional domestic hot-water, which produces mode,
The modes such as thermal-arrest.These traditional hot water produce mode, and not only energy utilization rate is low but also to will cause environment to a certain extent dirty
Dye.Using Trans-critical cycle CO2Heat pump techniques directly can disposably provide the hot water higher than 65 DEG C or more.At the same time it can also utilize
Waste heat supplied heat source, largely saves primary energy consumption, and reduce environmental pollution index.Utilize Trans-critical cycle CO2Heat pump provides 65 DEG C
Hot water, annual system can save at least 64% energy consumption.Therefore, either civilian or in commercial kitchen area, across facing
Boundary CO2Heat pump system all has the energy conservation and environment-friendly advantage that other heating modes can not compare.
In Trans-critical cycle CO2In Teat pump boiler, water circuit system is very important a part in entire unit, not only and
The production hot water demand of unit is related, while also affecting the normal work of system.Trans-critical cycle CO2The water route of heat pump system is general
By pipeline, water pump, waterway electromagnetic valve, flow control valve (or frequency converter), the components composition such as target stream switch, wherein flow control valve
It is the critical component that control water flow is played in water circuit system.Because of Trans-critical cycle CO2Heat pump system is different from conventional heat pump system
Supercritical region exothermic temperature sliding phenomenon, outlet water temperature range greatly increases compared with conventional heat pump water heater, may be implemented 55
DEG C~90 DEG C of a wide range of water outlet, therefore the selection to target leaving water temperature may be implemented, this just proposes water route control and wants
It asks.Moreover, because the flow velocity in water route, flow directly affect the heat exchange situation of the gas cooler side of system, further will affect
The pressure at expulsion of system, as Ruo Shui Road control is bad, it will lead to system high side pressure fluctuation acutely, pressure at expulsion is excessively high
Security risk, this just also proposed requirement to the speed and stability of water route control.
From the foregoing, it can be seen that for Trans-critical cycle CO2Water route control in heat pump system proposes that precision is high, stability is good, efficiency
High, highly reliable control method is of great significance to the operation of its highly effective and safe.
Summary of the invention
The purpose of the present invention is to provide a kind of water route fuzzy PID control methods of critical-cross carbon dioxide system, with solution
The problem of certainly existing CO 2 trans-critical heat pump system controls;The present invention can efficiently control critical-cross carbon dioxide
The water route flow of heat pump system, outlet water temperature range is big and can be realized that precision is high, stability is good, high-efficient, highly reliable
Water route control.
In order to achieve the above objectives, the present invention adopts the following technical scheme:
A kind of water route fuzzy PID control method of critical-cross carbon dioxide system, comprising the following steps:
The first step determines variable and its domain: in PID controller, input parameter is gas cooler leaving water temperature
Tw,outWith setting leaving water temperature Tw,oDifference DELTA T and its rate d Δ T/dt that changes with time;Output variable is pid parameter
Correction value Δ kp, Δ kI, Δ kD;After determining variable, the domain of variable is given;
Second step carries out Fuzzy processing to the variable that the first step determines: the domain for outputting and inputting variable is defined as
Seven fuzzy subsets: PB, PM, PS, ZO, NS, NM, NB;Establish the linear subordinating degree function of each subset;Input variable Δ T and d
Δ T/dt is fuzzy to turn to T and TC, output variable Δ kp, Δ kI, Δ kDIt is fuzzy to turn to KP, KI and KD;PB, PM, PS, ZO, NS, NM,
NB is respectively honest, center, just small, and nearly zero, it bears small, bears, bear big;
Third step establishes fuzzy inference rule table;
4th step, fuzzy reasoning and ambiguity solution: acquisition gas cooler leaving water temperature Tw,out, and according to setting leaving water temperature
Tw,oInput variable Δ T and d Δ T/dt is calculated, input variable is calculated on each fuzzy subset according to subordinating degree function first
Secondly degree of membership is calculated the degree of membership of all fuzzy rules according to fuzzy inference rule meter, is carried out finally by weighted mean method
Ambiguity solution operation;
5th step, according to Trans-critical cycle CO2Corrected Calculation result: the operating condition of heat pump system acquires real-time environment temperature
Spend Tair, gas cooler inflow temperature Tw,inWith gas cooler leaving water temperature Tw,out, the gain of PID control is modified;
6th step substitutes into final output in PID control, controls Trans-critical cycle CO by PID controller2Heat pump system
The aperture of water route flow control valve in unit.
Further, the domain that parameter, Δ T is inputted in the first step is [- 10,10], and the domain of d Δ T/dt is [- 5,5], when
Δ T is taken as -10 when being less than -10, is taken as 10 when Δ T is greater than 10, -5 is taken as when d Δ T/dt is less than -5, when d Δ T/dt is greater than
5 are taken as when 5;In fuzzy controller, the pid parameter in k-th of sampling time is respectively as follows: kp(k)=kp0+Δkp(k), kI
(k)=kI0+ΔkI(k), kD(k)=kD0+ΔkD(k);In formula, kp0, kI0, kD0The respectively initial ginseng of classical PID controller
Number;The output variable of fuzzy controller is Δ kp, Δ kI, Δ kD;Their domain is respectively as follows: Δ kpFor [- 10,10], Δ kI
For [- 10,10], Δ kDFor [- 5,5].
Further, fuzzy inference rule table described in third step are as follows:
Further, in the 4th step, degree of membership of the T and TC on each fuzzy subset is calculated, m is usedi(T) and mi(TC)
It indicates, i=NB, NM, NS, ZO, PS, PM, PB;
The degree of membership of first fuzzy rule of KP are as follows: mKP,1=mNB(T)*mNB(TC), wherein * expression take it is small;Successively class
It pushes away, calculates KP for the degree of membership of all fuzzy rules, totally 49 fuzzy rules;Defuzzification uses weighted mean method, calculates
Formula is as follows:
In formula, Δ kPTo be weighted the gain correction value that method of average ambiguity solution is obtained and exported;mKP,jIt is pushed away for each item is fuzzy
Manage the degree of membership of rule;KPjFor fuzzy subset's value that each fuzzy inference rule obtains, for example, in fuzzy inference rule table
A line first row KP1For PB, the first row the 7th arranges KP7For ZO, the third line the 4th arranges KP18For PS;ΔkPDomain be [- 10,
10], the fuzzy set after blurring is { PB, PM, PS, ZO, NS, NM, NB }, that is, gather 10,20/3,10/3,0, -10/3, -
20/3, -10 }.According to Δ kpCalculation method, calculate Δ kIWith Δ kDOutput result.
Further, in the 5th step, environment temperature T is establishedair, gas cooler inflow temperature Tw,inAnd gas cooler
Leaving water temperature Tw,outRelational expression between water flow is as follows:
In formula, q is the calculated value of water flow, unit m3/h;qmaxFor Trans-critical cycle CO2The maximum flow of water of heat pump system unit
Amount, unit m3/h;
Based on water flow calculated value, to kpIt is modified, to reduce overshoot, the calculating formula of gain is as follows after amendment,
Middle x=q/qmax:
In formula, kpIt (k) is the yield value in finally obtained k-th of sampling time, kp0For the initial increasing of classical PID controller
Benefit value, Δ kpIt (k) is the gain correction value of fuzzy controller output.
Further, in the 6th step, PID is controlled using calculus of finite differences:
Wherein n is operation times.
Compared to the prior art, the invention has the following advantages that
1, present invention employs the methods of fuzzy-adaptation PID control to control Trans-critical cycle CO2The water route of heat pump system, in different machines
Under the conditions of group operating condition, the adjusting control parameter k of online modification PIDP、kI、kD, there is control precision height, control stability
By force, the advantage that control efficiency is high, control is highly reliable.Control method of the invention than common PID control method, be more suitable for across
Critical CO2Heat pump system heat exchange delay, dynamic change demand for control.
2, the present invention is according to Trans-critical cycle CO2The actual operating mode parameter of heat pump repairs the PID gain of final output
Just, the demand for control in heat pump actual motion is preferably embodied.Targetedly control strategy can guarantee in unit operation
Extreme operating condition reduces the overshoot on control boundary under low ambient temperature, high leaving water temperature, to guarantee the stabilization and peace of control
Entirely.
Detailed description of the invention
Fig. 1 is the Trans-critical cycle CO that water route control method of the invention is applicable in2Heat pump system flow chart.
Fig. 2 is fuzzy controller input/output variable subordinating degree function schematic diagram of the invention;Wherein Fig. 2 (a) is input
The subordinating degree function schematic diagram of variable T and output variable KP, KI, Fig. 2 (b) are input variable TC and output variable KD degree of membership letter
Number schematic diagram.
Fig. 3 is water route fuzzy PID control method schematic diagram of the invention.
Fig. 4 is CO 2 trans-critical heat pump system water route fuzzy-adaptation PID control workflow of the invention.
Fig. 5 is the effect contrast figure of control method of the present invention and existing control method.
Specific embodiment
It please refers to shown in Fig. 3, a kind of water route fuzzy PID control method of critical-cross carbon dioxide system of the present invention is applicable in
In Trans-critical cycle CO shown in FIG. 12Heat pump system, Trans-critical cycle CO2Heat pump system includes compressor 1, the outlet of compressor 1 and is entered
Gas cooler 6, electric expansion valve 5, evaporator 3 and gas-liquid separator 2 are sequentially connected between mouthful;Evaporator 3 is equipped with blower
4;The entrance of the outlet connection gas-liquid separator 2 of evaporator 3, the entrance of the gas vent connect compressor 1 of gas-liquid separator 2.
The outlet of water pump 8 connects the water inlet of gas cooler 6 by Water flow adjusting valve 7, and the water outlet of gas cooler 6, which connects, to be used
Family hot water pipeline.The sender property outlet of the outlet of the working medium entrances connect compressor 1 of gas cooler 6, gas cooler 6 connects electricity
Sub- expansion valve 5.Working medium and water exchange heat in gas cooler 6, are thermally formed the hot water of user demand.Control method of the present invention
Input is gas cooler inflow temperature, gas cooler leaving water temperature, environment temperature and the setting leaving water temperature of heat pump, control
The output of method is gain coefficient, integral coefficient and differential coefficient needed for PID control, final control water route flow control valve
Aperture, control method the following steps are included:
The first step determines variable and its domain: in PID controller, input parameter is gas cooler leaving water temperature
Tw,outWith setting leaving water temperature Tw,oDifference DELTA T and difference change with time rate d Δ T/dt;Input the opinion of parameter, Δ T
Domain is [- 10,10], and the domain of d Δ T/dt is [- 5,5], is taken as -10 when Δ T is less than -10, is taken as 10 when Δ T is greater than 10,
- 5 are taken as when d Δ T/dt is less than -5, is taken as 5 when d Δ T/dt is greater than 5.
In fuzzy controller, the pid parameter in k-th of sampling time is respectively as follows: kp(k)=kp0+Δkp(k), kI(k)
=kI0+ΔkI(k), kD(k)=kD0+ΔkD(k).In formula, kp0, kI0, kD0The respectively initial parameter of classical PID controller, can
It is adjusted according to the methods of critical proportional band law, attenuation curve method.The output variable of fuzzy controller is Δ kp, Δ kI,
ΔkD.Their domain is respectively as follows: Δ kpFor [- 10,10], Δ kIFor [- 10,10], Δ kDFor [- 5,5].
Second step carries out Fuzzy processing to the variable that the first step determines: the domain for outputting and inputting variable is all defined
For seven fuzzy subsets, be respectively as follows: honest (PB), hit exactly (PM), just small (PS), nearly zero (ZO) bears small (NS), bear in (NM),
Negative big (NB);The subordinating degree function of the corresponding fuzzy subset of the domain of each parameter uses linear function.Input variable Δ T and d Δ
T/dt is fuzzy to turn to T and TC, output variable Δ kp, Δ kI, Δ kDIt is fuzzy to turn to KP, KI and KD;Each subordinating degree function schematic diagram is such as
Shown in attached drawing 2.
Third step establishes fuzzy inference rule table: adjusting principle according to experiment experience and pid parameter, obtains fuzzy control
The inference rule table of device processed.The fuzzy inference rule table of foundation is as shown in table 1.
1 fuzzy inference rule table of table
4th step, fuzzy reasoning and ambiguity solution: acquisition gas cooler leaving water temperature Tw,out, and according to setting leaving water temperature
Tw,oCalculate input variable Δ T and d Δ T/dt, according to fig. 2 in subordinating degree function curve, calculate T and TC in each fuzzy son
Degree of membership on collection, uses mi(T) and mi(TC) it indicates, i=NB, NM, NS, ZO, PS, PM, PB.For example, as Δ T=5, mNB
(T)=mNM(T)=mNS(T)=mZO(T)=mPB(T)=0, mPS(T)=mPS(T)=0.5;As d Δ T/dt=5, mNB(T)=
mNM(T)=mNS(T)=mZO(T)=mPS(T)=mPM(T)=0, mPB(T)=1.
The degree of membership of first fuzzy rule of KP are as follows: mKP,1=mNB(T)*mNB(TC), wherein " * " expression take it is small.Successively
Analogize, calculate KP for the degree of membership of all fuzzy rules, totally 49 fuzzy rules.Defuzzification uses weighted mean method, meter
Formula is as follows:
In formula, Δ kPTo be weighted the gain correction value that method of average ambiguity solution is obtained and exported;mKP,jIt is pushed away for each item is fuzzy
Manage the degree of membership of rule;KPjFor fuzzy subset's value that each fuzzy inference rule obtains, for example, in fuzzy inference rule table
A line first row KP1For PB, the first row the 7th arranges KP7For ZO, the third line the 4th arranges KP18For PS;ΔkPDomain be [- 10,
10], the fuzzy set after blurring is { PB, PM, PS, ZO, NS, NM, NB }, that is, gather 10,20/3,10/3,0, -10/3, -
20/3, -10 }.
Similar, it can accordingly calculate Δ kIWith Δ kDOutput result.
5th step, according to Trans-critical cycle CO2Corrected Calculation result: the operating condition of heat pump system is obtained based on many experiments
Data, establish environment temperature Tair, gas cooler inflow temperature Tw,inWith gas cooler leaving water temperature Tw,outWith water flow
Between relational expression, it is as follows:
In formula, q is the calculated value of water flow, unit m3/h;qmaxFor Trans-critical cycle CO2The maximum flow of water of heat pump system unit
Amount, unit m3/h。
According to Trans-critical cycle CO2The operating condition of heat pump unit, when water flow is smaller, the disengaging water temperature difference of gas cooler
Larger, often leaving water temperature is higher, at this moment, needs the overshoot controlled leaving water temperature to limit, otherwise will lead to machine
Group pressure at expulsion transfinite, alarm shut down the problems such as.Based on water flow calculated value, to kpIt is modified, to reduce overshoot, corrects
The calculating formula of gain is as follows afterwards, wherein x=q/qmax:
In formula, kpIt (k) is the yield value in finally obtained k-th of sampling time, kp0For the initial increasing of classical PID controller
Benefit value, Δ kpIt (k) is the gain correction value of fuzzy controller output.
6th step substitutes into final output in PID controller, controls Trans-critical cycle CO by PID controller2Heat pump system
The aperture of water route flow control valve, executes control in system unit.
The part PID calculation formula:
F (t) is the aperture of water route flow control valve, and Δ T is gas cooler leaving water temperature and the difference for setting leaving water temperature
Value.In view of the retardance of system heat exchange, PID is controlled using calculus of finite differences in practice.
Wherein n is operation times.When F (t) is continuous
Between on calculating;F (k) is using the calculated result on the discrete instants after calculus of finite differences.
Trans-critical cycle CO2The bad working environments of heat pump system unit operation include that environment temperature is lower or leaving water temperature is higher, because
This, by water route control method application heat pump system of the invention, is tested under the operating condition of the high leaving water temperature of low ambient temperature
The result arrived is as shown in Figure 5.10 DEG C, which are fixed as, in inflow temperature sets leaving water temperature to be switched on and being adjusted in the case where 90 DEG C
Section, there is 2 recurrent fluctuations of effluent temperature curve in traditional PID adjusting method and 3 overshoot of effluent temperature curve causes row pressure and surpasses
The case where limit alarm, the influence this is because the PID adjusting and the row pressure of unit in water route, row's temperature control system intercouple.Leaving water temperature
Curve 1 is being rapidly heated after applying control method of the invention as a result, realizing, safe and reliable and high-precision control.
Claims (7)
1. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system, which comprises the following steps:
The first step determines variable and its domain: in PID controller, input parameter is gas cooler leaving water temperature Tw,outWith
Set leaving water temperature Tw,oDifference DELTA T and its rate d Δ T/dt that changes with time;Output variable is the amendment of pid parameter
It is worth Δ kp, Δ kI, Δ kD;After determining variable, the domain of variable is given;
Second step carries out Fuzzy processing to the variable that the first step determines: the domain for outputting and inputting variable is defined as seven
Fuzzy subset: PB, PM, PS, ZO, NS, NM, NB;Establish the linear subordinating degree function of each subset;Input variable Δ T and d Δ T/
Dt is fuzzy to turn to T and TC, output variable Δ kp, Δ kI, Δ kDIt is fuzzy to turn to KP, KI and KD;PB, PM, PS, ZO, NS, NM, NB points
Wei not be honest, center is just small, and nearly zero, it bears small, bears, bear big;
Third step establishes fuzzy inference rule table;
4th step, fuzzy reasoning and ambiguity solution: acquisition gas cooler leaving water temperature Tw,out, and according to setting leaving water temperature Tw,o
Input variable Δ T and d Δ T/dt is calculated, input variable being subordinate on each fuzzy subset is calculated according to subordinating degree function first
Secondly degree calculates the degree of membership of all fuzzy rules according to fuzzy inference rule meter, carries out solution mould finally by weighted mean method
Paste operation;
5th step, according to Trans-critical cycle CO2Corrected Calculation result: the operating condition of system acquires real-time environment temperature Tair, gas
Cooler inflow temperature Tw,inWith gas cooler leaving water temperature Tw,out, calculating amendment is carried out to the gain of PID control;
6th step substitutes into final output in PID control, controls Trans-critical cycle CO by PID controller2Water in system unit
The aperture of road flow control valve.
2. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system according to claim 1, feature exist
In the domain for inputting parameter, Δ T in the first step is [- 10,10], and the domain of d Δ T/dt is [- 5,5], is taken when Δ T is less than -10
It is -10, is taken as 10 when Δ T is greater than 10, be taken as -5 when d Δ T/dt is less than -5, is taken as 5 when d Δ T/dt is greater than 5;In mould
It pastes in PID controller, the pid parameter in k-th of sampling time is respectively as follows: kp(k)=kp0+Δkp(k), kI(k)=kI0+ΔkI
(k), kD(k)=kD0+ΔkD(k);In formula, kp0, kI0, kD0The respectively initial parameter of classical PID controller;Fuzzy-adaptation PID control
The output variable of device is Δ kp, Δ kI, Δ kD;Their domain is respectively as follows: Δ kpFor [- 10,10], Δ kIFor [- 10,10], Δ
kDFor [- 5,5].
3. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system according to claim 1, feature exist
In fuzzy inference rule table described in third step are as follows:
4. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system according to claim 1, feature exist
In in the 4th step, degree of membership of the calculating T and TC on each fuzzy subset uses mi(T) and mi(TC) it indicates, i=NB, NM,
NS, ZO, PS, PM, PB;
The degree of membership of first fuzzy rule of KP are as follows: mKP,1=mNB(T)*mNB(TC), wherein * expression take it is small;And so on, meter
KP is calculated for the degree of membership of all fuzzy rules, totally 49 fuzzy rules;Defuzzification uses weighted mean method, and calculating formula is such as
Under:
In formula, Δ kPTo be weighted the gain correction value that method of average ambiguity solution is obtained and exported;mKP,jIt is advised for each fuzzy reasoning
Degree of membership then;KPjThe fuzzy subset's value obtained for each fuzzy inference rule;
According to Δ kpCalculation method, calculate Δ kIWith Δ kDOutput result.
5. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system according to claim 1, feature exist
In establishing environment temperature T in the 5th stepair, gas cooler inflow temperature Tw,inWith gas cooler leaving water temperature Tw,outWith
Relational expression between water flow is as follows:
In formula, q is the calculated value of water flow, unit m3/h;qmaxFor Trans-critical cycle CO2The maximum flow of water amount of heat pump system unit, it is single
Position m3/h;
Based on water flow calculated value, to kpIt is modified, to reduce overshoot, the calculating formula of gain is as follows after amendment, wherein x=
q/qmax:
In formula, kpIt (k) is the yield value in finally obtained k-th of sampling time, kp0For the initial gain of classical PID controller
Value, Δ kpIt (k) is the gain correction value of fuzzy controller output.
6. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system according to claim 1, feature exist
In in the 6th step, PID is controlled using calculus of finite differences:
Wherein n is operation times.
7. a kind of water route fuzzy PID control method of critical-cross carbon dioxide system according to claim 1, feature exist
In, in second step, kp0, kI0, kD0It is adjusted according to critical proportional band law or attenuation curve method.
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CN111595021A (en) * | 2020-04-22 | 2020-08-28 | 青岛海信日立空调系统有限公司 | Heat pump water heater |
CN117366800A (en) * | 2023-10-16 | 2024-01-09 | 北京绿卡科技有限公司 | Transcritical carbon dioxide refrigerating system based on fuzzy PID control |
CN117742426A (en) * | 2024-02-20 | 2024-03-22 | 北京金博众科技有限公司 | Intelligent control method and system for constant-temperature and constant-pressure water supply unit |
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