JP2713660B2 - Control method of air conditioner - Google Patents

Control method of air conditioner

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Publication number
JP2713660B2
JP2713660B2 JP2305476A JP30547690A JP2713660B2 JP 2713660 B2 JP2713660 B2 JP 2713660B2 JP 2305476 A JP2305476 A JP 2305476A JP 30547690 A JP30547690 A JP 30547690A JP 2713660 B2 JP2713660 B2 JP 2713660B2
Authority
JP
Japan
Prior art keywords
wind speed
rule
δfan
wind direction
thfn
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
JP2305476A
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Japanese (ja)
Other versions
JPH04177041A (en
Inventor
直弥 城所
忠司 藤崎
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Mitsubishi Heavy Industries Ltd
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Mitsubishi Heavy Industries Ltd
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Priority to JP2305476A priority Critical patent/JP2713660B2/en
Publication of JPH04177041A publication Critical patent/JPH04177041A/en
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Description

【発明の詳細な説明】 (産業上の利用分野) 本発明は空気調和機の制御方法に関する。The present invention relates to a method for controlling an air conditioner.

(従来の技術) 従来の空気調和機においては、室温とその設定温度と
の偏差をPID演算することによってインバータ駆動圧縮
機の運転周波数を算出し、この運転周波数に応じて室内
に吹き出される冷風の風速を複数段階に切り換えてい
た。また、冷風の吹出方向は一定で変更することができ
なかった。
(Prior Art) In a conventional air conditioner, an operation frequency of an inverter-driven compressor is calculated by performing a PID operation on a deviation between a room temperature and a set temperature, and cold air blown into a room according to the operation frequency. Had been switched to multiple stages. Further, the blowing direction of the cold air was constant and could not be changed.

(発明が解決しようとする課題) 第8図に示すように、冷房中の室内における在室者が
快適と感じる範囲、即ち、快適ゾーンは室温と冷風の風
速によって変化する。
(Problems to be Solved by the Invention) As shown in FIG. 8, the range in which the occupant feels comfortable in the room being cooled, that is, the comfort zone changes according to the room temperature and the wind speed of the cool air.

また、在室者の快適度指数、即ち、PMV値は第9図に
示すように、冷房の立上り運転時、長袖シャツを着て輻
射温度が高い場合のそれ(曲線イ)と半袖シャツを着て
輻射温度が低い場合のそれ(曲線ロ)とは大きく異な
り、かつ、これら快適度指数は室温の低下に応じて低く
なる。
As shown in FIG. 9, the comfort index of the occupants, that is, the PMV value, is as shown in FIG. Thus, the radiation index is significantly different from that when the radiation temperature is low (curve b), and these comfort indexes decrease as the room temperature decreases.

しかるに、従来の制御方法では冷房の立上り運転時、
室温を設定温度に早急に到達させるように制御するの
で、在室者の快適感を阻害するのみならず、第8図に示
すように、冷房の立上がり運転時、室温を快適ゾーンに
到達させるのに時間がかかる(約15分)という問題があ
った。
However, in the conventional control method, at the time of the start-up operation of cooling,
Since the room temperature is controlled so as to quickly reach the set temperature, not only does the comfort of the occupants be hindered, but also the room temperature reaches the comfort zone during the start-up operation of the cooling as shown in FIG. It took a long time (about 15 minutes).

(課題を解決するための手段) 本発明は上記課題を解決するために発明されたもので
あって、その要旨とするところは、室内空気の温度、平
均輻射温度、水蒸気圧、風速並びに在室者の衣服抵抗、
体射量、作業量に基づいて快適度指数を算出し、この快
適度指数とこの時間的変化率に基づいてファジィ論理演
算により室内に吹き出される冷風の風向及び風速を算出
することを特徴とする空気調和機の制御方法にある。
(Means for Solving the Problems) The present invention was invented to solve the above problems, and the gist of the present invention is that the temperature of the indoor air, the average radiant temperature, the water vapor pressure, the wind speed, and the occupancy of the room Clothing resistance,
Calculating a comfort index based on the amount of body radiation and the amount of work, and calculating a wind direction and a wind speed of the cool air blown into the room by fuzzy logic operation based on the comfort index and the temporal change rate. To control the air conditioner.

(実施例) 本発明の1実施例を第1図ないし第7図を参照しなが
ら具体的に説明する。
(Embodiment) An embodiment of the present invention will be specifically described with reference to FIG. 1 to FIG.

第1図には制御ブロックが示されている。 FIG. 1 shows a control block.

衣服抵抗設定手段1によって設定された在室者の衣服
抵抗CLO(m2℃/w)、体射量設定手段2によって設定さ
れた在室者の体射量M(w/m2)、作業量設定手段3によ
って設定された在室者の作業量W(w/m2)、室温検出手
段4によって検出された室温Ta(℃)、平均輻射温度検
出手段5によって検出された室内の平均輻射温度Tr
(℃)、風速検出手段5によって検出された室内の風速
Var(m/sec)、水蒸気圧検出手段7によって検出された
室内の水蒸気圧Pa(Pa)はPMV値計算手段8に入力さ
れ、ここで公知のPMV理論から快適度指数、即ち、PMV値
Pが算出される。算出されたPMV値PはPMV値記憶手段9
に入力されて、ここに記憶されると同時に減算器10に入
力される。減算器10ではPMV値記憶手段9から入力され
た先のサンプリング時に記憶されたPMV値と比較される
ことによりPMV値の時間的変化率ΔPが算出される。こ
の時間的変化率ΔP及びPMV値Pはファジィ演算手段11
に入力され、ここで制御ルール記憶手段12から入力され
る制御ルールに基づいて公知のファジィ論理演算するこ
とにより室内に吹き出される冷風の風向及び風速の増分
のファジィ分布Δfanが算出される。
The clothing resistance CLO (m 2 ° C / w) of the occupant set by the clothing resistance setting means 1, the body radiation M (w / m 2 ) of the occupant set by the body radiation setting means 2, work The work amount W (w / m 2 ) of the occupant set by the amount setting means 3, the room temperature Ta (° C.) detected by the room temperature detecting means 4, and the average radiation in the room detected by the average radiation temperature detecting means 5 Temperature Tr
(° C.), the indoor wind speed detected by the wind speed detecting means 5
Var (m / sec) and the water vapor pressure Pa (Pa) in the room detected by the water vapor pressure detecting means 7 are input to the PMV value calculating means 8, where the comfort index, that is, the PMV value P Is calculated. The calculated PMV value P is stored in the PMV value storage means 9
, And stored here, and at the same time, to the subtractor 10. The subtracter 10 calculates the temporal change rate ΔP of the PMV value by comparing the PMV value stored in the previous sampling and inputted from the PMV value storage means 9 with the PMV value. The temporal change rate ΔP and the PMV value P are calculated by the fuzzy operation means 11.
, Where a known fuzzy logic operation is performed based on the control rule input from the control rule storage means 12 to calculate the fuzzy distribution Δfan of the wind direction and the increment of the wind speed of the cool air blown into the room.

このファジィ分布Δfanは非ファジィ化手段13に入力
されてここで量子化することによって風向・風速の設定
変数FANの増分ΔFANが得られる。この増分ΔFANは加算
器14に入力され、ここでFAN記憶手段15から入力された
先のサンプリング時に求められた風向・風速の設定変数
FANと加算されることにより今回の風向・風速の設定変
数FANが算出され、この設定変数FANはFAN記憶手段15に
入力されてここに記憶されると同時に風向・風速指令手
段16を経て冷風の風向を規制する図示しないルーバの回
転モータ及び冷風の風速を規制する図示しないファンの
回転モータに出力される。
The fuzzy distribution Δfan is input to the defuzzification means 13 and is quantized to obtain an increment ΔFAN of the setting variable FAN of the wind direction / speed. This increment ΔFAN is input to the adder 14, where the wind direction / wind speed setting variables obtained from the previous sampling, input from the FAN storage means 15, are set.
The setting variable FAN of the current wind direction / wind speed is calculated by being added to the FAN, and this setting variable FAN is input to the FAN storage means 15 and stored therein, and at the same time, is passed through the wind direction / wind speed It is output to a louver rotation motor (not shown) that regulates the wind direction and a fan rotation motor (not shown) that regulates the wind speed of the cool air.

制御ルール記憶手段12には第1表に示す制御ルールが
記憶されている。
The control rule storage means 12 stores the control rules shown in Table 1.

第1表 ルール1 IF P=NB,ΔP=NB THFN ΔFAN=NB ルール2 IF P=NB,ΔP=ZO THFN ΔFAN=NB ルール3 IF P=NS,ΔP=PS THFN ΔFAN=ZO ルール4 IF P=NS,ΔP=ZO THFN ΔFAN=NS ルール5 IF P=NS,ΔP=NS THFN ΔFAN=NS ルール6 IF P=ZO,ΔP=PB THFN ΔFAN=PB ルール7 IF P=ZO,ΔP=PS THFN ΔFAN=PS ルール8 IF P=ZO,ΔP=ZO THFN ΔFAN=ZO ルール9 IF P=ZO,ΔP=NS THFN ΔFAN=NS ルール10 IF P=ZO,ΔP=NB THFN ΔFAN=NB ルール11 IF P=PS,ΔP=PS THFN ΔFAN=PS ルール12 IF P=PS,ΔP=ZO THFN ΔFAN=PS ルール13 IF P=PS,ΔP=NS THFN ΔFAN=ZO ルール14 IF P=PB,ΔP=ZO THFN ΔFAN=PB ルール15 IF P=PB,ΔP=PB THFN ΔFAN=PB PMV値Pに対応するファジィ変数のメンバーシップ関
数が第2図に、時間的変化率ΔPに対応するファジィ変
数のメンバーシップ関数が第3図に、ΔFANに対応する
ファジィ変数のメンバーシップ関数が第4図に示されて
いる。これら第1表及び第2図ないし第4図において、
NBは負方向に大、NSは負方向に小、ZOは零、PSは正方向
に小、PBは正方向に大を意味している。
Table 1 Rule 1 IF P = NB, ΔP = NB THFN ΔFAN = NB Rule 2 IF P = NB, ΔP = ZO THFN ΔFAN = NB Rule 3 IF P = NS, ΔP = PS THFN ΔFAN = ZO Rule 4 IF P = NS, ΔP = ZO THFN ΔFAN = NS Rule 5 IF P = NS, ΔP = NS THFN ΔFAN = NS Rule 6 IF P = ZO, ΔP = PB THFN ΔFAN = PB Rule 7 IF P = ZO, ΔP = PS THFN ΔFAN = PS Rule 8 IF P = ZO, ΔP = ZO THFN ΔFAN = ZO Rule 9 IF P = ZO, ΔP = NS THFN ΔFAN = NS Rule 10 IF P = ZO, ΔP = NB THFN ΔFAN = NB Rule 11 IF P = PS, ΔP = PS THFN ΔFAN = PS Rule 12 IF P = PS, ΔP = ZO THFN ΔFAN = PS Rule 13 IF P = PS, ΔP = NS THFN ΔFAN = ZO Rule 14 IF P = PB, ΔP = ZO THFN ΔFAN = PB Rule 15 IF P = PB, ΔP = PB THFN ΔFAN = PB The membership function of the fuzzy variable corresponding to the PMV value P is shown in FIG. 2, and the membership function of the fuzzy variable corresponding to the temporal change rate ΔP is shown in FIG. Fuzzy variables corresponding to ΔFAN Membership function is shown in Figure 4. In Table 1 and FIGS. 2 to 4,
NB means large in the negative direction, NS means small in the negative direction, ZO means zero, PS means small in the positive direction, and PB means large in the positive direction.

また、風向・風速の設定変数FANと風向・風速との関
係が第5図に示されている。
FIG. 5 shows the relationship between the wind direction / wind speed setting variable FAN and the wind direction / wind speed.

ファジィ演算手段11におけるファジィ論理演算につい
て説明する。
The fuzzy logic operation in the fuzzy operation means 11 will be described.

算出されたPMV値をP1、時間的変化率ΔP1とする。ル
ールiに関するPMV値Pのメンバーシップ関数Ai1、時間
的変化率ΔPのメンバーシップ関数をそれぞれAi2とす
ると、各ルールの適合度Wiは次の(1)式で表される Wi=Ai1(P1)∧Ai2(Δp1)……………………(1) (但し、∧はminとする。) ルールiに関する風向・風速の設定変数FANの増分ΔF
ANのメンバーシップ関数をBiとすると、PMV値P1と時間
変化率ΔP1による増分ΔFAN1は、(2)式で計算される
Δfan1の重心の値として計算される。
The calculated PMV value is defined as P1, and the temporal change rate ΔP1. Assuming that the membership function Ai1 of the PMV value P and the membership function of the temporal change rate ΔP for the rule i are Ai2, the fitness Wi of each rule is expressed by the following equation (1): Wi = Ai1 (P1) ∧Ai2 (Δp1) ………………………………………………………………………………………………………………………………………………………………………………………… (1) where min is the increment.
Assuming that the membership function of AN is Bi, the increment ΔFAN1 due to the PMV value P1 and the time change rate ΔP1 is calculated as the value of the center of gravity of Δfan1 calculated by the equation (2).

風向・風速の設定変数FANはΔFAN1と前のサンプリン
グ時の風向・風速の設定変数FANとの和によって与えら
れる。
The wind direction / wind speed setting variable FAN is given by the sum of ΔFAN1 and the wind direction / wind speed setting variable FAN at the time of the previous sampling.

冷房運転の開始時等、PMV値PがP2、時間的変化率Δ
PがΔP2の場合の制御量演算過程を第6図を参照して説
明する。この場合に用いられるルールは11、12、14でこ
れらルールの適合度W11、W12、W14は(1)式より W11=0.5∧0.4=0.4 W12=0.6∧0.5=0.5 W14=0.6∧0.5=0.5 となる。
When the cooling operation is started, the PMV value P is P2, and the temporal change rate Δ
The control variable calculation process when P is ΔP2 will be described with reference to FIG. The rules used in this case are 11 , 12 , and 14 , and the degrees of conformity W 11 , W 12 , and W 14 of these rules are obtained from equation (1) as W 11 = 0.5∧0.4 = 0.4 W 12 = 0.6∧0.5 = 0.5 W 14 = 0.6∧0.5 = 0.5.

出力分布Δfan2は(2)式より Δfan2=〔W11B11〕∨〔W12B12〕∨〔W14B14〕 で求められる。The output distribution Δfan2 is obtained from the equation (2) as Δfan2 = [W 11 B 11 ] 11 [W 12 B 12 ] ∨ [W 14 B 14 ].

ルール11についてのΔFANのメンバーシップ関数B11
PS、ルール12についてのそれB12はPS、ルール14につい
てのそれB14はPBである。よって、 Δfan2の出力分布は第6図の右端に示すようになり、
風向・風速の設定変数FANの増分ΔFAN2は出力分布Δfan
2の重心となる。
Membership function B 11 of ΔFAN of the rules 11
PS, it B 12 of the rules 12 PS, it B 14 of the rules 14 is PB. Therefore, the output distribution of Δfan2 is as shown at the right end of FIG.
Increment ΔFAN2 of wind direction and wind speed setting variable FAN is output distribution Δfan
It becomes the center of gravity of 2.

なお、第6図において、上段はルール11の流れ、中段
はルール12の流れ、下段はルール14の流れを示し、ま
た、山は左からP、ΔP、ΔFANの評価関数を、ΔFANの
山の内側の山は各ルールの適合度で評価されたΔFAN
を、右端の山は各ルールの出力分布を合成したものをそ
れぞれ示している。
In FIG. 6, the upper part shows the flow of rule 11, the middle part shows the flow of rule 12, and the lower part shows the flow of rule 14. Further, the peaks indicate the evaluation functions of P, ΔP, and ΔFAN from the left, and the peaks of ΔFAN The inner mountain is ΔFAN evaluated by the conformity of each rule.
, And the mountain at the right end shows a composite of the output distribution of each rule.

しかして、冷房運転開始時には、風速を大きくし、か
つ、風向を居住空間に向けることにより第8図に実線に
示すように、素早くPMV値Pを快適ゾーンに入れること
ができる。そして、室温の低下に合わせて風速を小さく
し、かつ、風向を拡散させることによって快適ゾーンに
入ったまま室温を設定温度にすることができる。
Thus, at the start of the cooling operation, the PMV value P can be quickly entered into the comfort zone as shown by the solid line in FIG. 8 by increasing the wind speed and directing the wind direction to the living space. Then, by lowering the wind speed in accordance with the decrease in the room temperature and diffusing the wind direction, the room temperature can be set to the set temperature while entering the comfort zone.

次に、通常の冷房運転時等PMV値PがP3、時間的変化
率ΔPがΔP3の場合の制御量演算過程を第7図を参照し
て説明する。この状態に対応するルールはルール8と12
である。
Next, a control amount calculation process when the PMV value P is P 3 and the temporal change rate ΔP is ΔP 3 during normal cooling operation will be described with reference to FIG. Rules corresponding to this condition are rules 8 and 12.
It is.

ルール8及び12の適合度W8及びW12は次式で表され
る。
The fitness levels W 8 and W 12 of the rules 8 and 12 are represented by the following equations.

W8=0.8∧1.0=0.8 W12=0.2∧1.0=0.2 出力分布Δfan3は次式で求められる。W 8 = 0.8∧1.0 = 0.8 W 12 = 0.2∧1.0 = 0.2 The output distribution Δfan3 is obtained by the following equation.

Δfan3=〔W8B8〕∨〔W12B12〕 ルール8についてのΔFANのメンバーシップ関数B8はZ
O、ルール12についてのそれB12はPSである。よって、Δ
fan3の出力分布は第7図の右端を示すようになる。そし
て、風向・風速の設定変数FANの増分ΔFAN3は出力分布
Δfan3の重心となる。
Δfan3 = [W 8 B 8 ] ∨ [W 12 B 12 ] The membership function B 8 of ΔFAN for rule 8 is Z
O, it about rule 12, B 12 is PS. Therefore, Δ
The output distribution of fan3 is as shown at the right end of FIG. Then, the increment ΔFAN3 of the setting variable FAN of the wind direction / wind speed becomes the center of gravity of the output distribution Δfan3.

このようにして、PMV値Pが殆ど零の快適な状態に達
していれば、風向・風速の設定変数FANは殆ど変化せ
ず、このPMV値Pを零に保とうとする。
In this way, if the PMV value P has reached a comfortable state of almost zero, the setting variable FAN of the wind direction / wind speed hardly changes, and the PMV value P is to be kept at zero.

(発明の効果) 本発明においては、室内空気の温度、平均輻射温度、
水蒸気圧、風速並びに在室者の衣服抵抗、体射量、作業
量に基づいて快適度指数を算出し、この快適度指数とこ
の時間的変化率に基づいてファジィ論理演算により室内
に吹き出される冷風の風向及び風速を算出するため、室
内に吹き出される冷風の風向及び風速を変化させること
によって、室内空気の温度、平均輻射温度、水蒸気圧、
風速並びに在室者の衣服抵抗、体射量、作業量の如何に
拘らず快適度を良好に維持できる。
(Effect of the Invention) In the present invention, the temperature of the indoor air, the average radiant temperature,
A comfort index is calculated based on the water vapor pressure, the wind speed, the clothes resistance, the amount of body radiation, and the amount of work of the occupants, and the room is blown into the room by fuzzy logic operation based on the comfort index and the temporal change rate. In order to calculate the wind direction and wind speed of the cold air, by changing the wind direction and wind speed of the cold air blown into the room, the temperature of the indoor air, the average radiant temperature, the water vapor pressure,
The comfort level can be maintained satisfactorily irrespective of the wind speed and the occupant's clothing resistance, the amount of body radiation, and the amount of work.

また、室温を設定温度に維持しながら在室者の衣服抵
抗、体射量、作業量に対応した快適度にすることができ
る。また、冷房運転の開始時等には素早く快適ゾーンに
入れることができる。
In addition, while maintaining the room temperature at the set temperature, it is possible to achieve a comfort level corresponding to the clothes resistance, the amount of body radiation, and the amount of work of the occupants. In addition, at the start of the cooling operation or the like, it is possible to quickly enter the comfort zone.

【図面の簡単な説明】[Brief description of the drawings]

第1図ないし第7図は本発明の1実施例を示し、第1図
は制御ブロック図、第2図は快適度のメンバーシップ関
数を示す線図、第3図は時間的変化率のメンバーシップ
関数を示す線図、第4図は風向・風速の設定変数の増分
についてのメンバーシップ関数を示す線図、第5図は風
向・風速の設定変数と風向・風速との関係を示す線図、
第6図は冷房開始時における制御量の演算過程を示す説
明図、第7図は通常の冷房運転時における制御量の演算
過程を示す説明図、第8図は冷房運転時における室温と
風速との関係を示す線図、第9図は冷房開始時における
快適度及び室温の時間的変化を示す線図である。 室温検出手段……4、平均輻射温度検出手段……5、水
蒸気圧検出手段……7、風速検出手段……6、衣服抵抗
設定手段……1、体射量設定手段……2、作業量設定手
段……3、快適度の演算手段……8、時間的変化率の演
算手段……10、ファジィ演算手段……11、制御ルール記
憶手段……12、風向・風速演算手段……14
1 to 7 show an embodiment of the present invention, FIG. 1 is a control block diagram, FIG. 2 is a diagram showing a membership function of comfort, and FIG. 3 is a member of a temporal change rate. FIG. 4 is a diagram showing a membership function for increment of wind direction / wind speed setting variables, and FIG. 5 is a diagram showing a relationship between wind direction / wind speed setting variables and wind direction / wind speed. ,
FIG. 6 is an explanatory diagram showing the process of calculating the control amount at the start of cooling, FIG. 7 is an explanatory diagram showing the process of calculating the control amount at the time of normal cooling operation, and FIG. FIG. 9 is a diagram showing a temporal change of the comfort level and the room temperature at the start of cooling. Room temperature detecting means ... 4, average radiation temperature detecting means ... 5, water vapor pressure detecting means ... 7, wind speed detecting means ... 6, clothing resistance setting means ... 1, body radiation amount setting means ... 2, work amount Setting means ... 3, means for calculating comfort level ... 8, means for calculating temporal change rate ... 10, fuzzy calculating means ... 11, control rule storage means ... 12, wind direction / wind speed calculating means ... 14

Claims (1)

(57)【特許請求の範囲】(57) [Claims] 【請求項1】室内空気の温度、平均輻射温度、水蒸気
圧、風速並びに在室者の衣服抵抗、体射量、作業量に基
づいて快適度指数を算出し、この快適度指数とこの時間
的変化率に基づいてファジィ論理演算により室内に吹き
出される冷風の風向及び風速を算出することを特徴とす
る空気調和機の制御方法。
1. A comfort index is calculated based on the indoor air temperature, average radiant temperature, water vapor pressure, wind speed and the occupant's clothing resistance, body radiation, and work load. A method for controlling an air conditioner, comprising calculating a wind direction and a wind speed of cold air blown into a room by fuzzy logic operation based on a change rate.
JP2305476A 1990-11-09 1990-11-09 Control method of air conditioner Expired - Lifetime JP2713660B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP2305476A JP2713660B2 (en) 1990-11-09 1990-11-09 Control method of air conditioner

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP2305476A JP2713660B2 (en) 1990-11-09 1990-11-09 Control method of air conditioner

Publications (2)

Publication Number Publication Date
JPH04177041A JPH04177041A (en) 1992-06-24
JP2713660B2 true JP2713660B2 (en) 1998-02-16

Family

ID=17945618

Family Applications (1)

Application Number Title Priority Date Filing Date
JP2305476A Expired - Lifetime JP2713660B2 (en) 1990-11-09 1990-11-09 Control method of air conditioner

Country Status (1)

Country Link
JP (1) JP2713660B2 (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2011015132A1 (en) * 2009-08-05 2011-02-10 Yu Jundong System and method for controlling blower device of underfloor air-distribution air-conditioner in machine room

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2762425B2 (en) * 1991-11-13 1998-06-04 松下冷機株式会社 Air conditioner

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2011015132A1 (en) * 2009-08-05 2011-02-10 Yu Jundong System and method for controlling blower device of underfloor air-distribution air-conditioner in machine room

Also Published As

Publication number Publication date
JPH04177041A (en) 1992-06-24

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