Patent Publication Number: US-9841204-B2

Title: Air conditioning control system and air conditioning control method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2014-37024, filed on Feb. 27, 2014, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiment discussed herein is related to an air conditioning control system and an air conditioning control method. 
     BACKGROUND 
     In datacenters, jobs are distributed to a plurality of electronic apparatuses such as servers, and each electronic apparatus executes its jobs. Each electronic apparatus is provided with a heat generating component such as a central processing unit (CPU). When processing a large amount of jobs, the CPU temperature rises, which may result in failure of the electronic apparatus or deterioration in the performance thereof. 
     To prevent such rise in CPU temperature, datacenters are provided with mechanisms to cool their electronic apparatuses. Among them, module-type datacenters configured to take in external air as cooling air are effective in terms of energy saving since they have no heat exchanger for cooling the external air. 
     In such a module-type datacenter, warm cooling air discharged from the exhaust surface of each electronic apparatus is sent back to the intake surface of each electronic apparatus. In this way, it is possible to prevent excessive cooling of the electronic apparatus during the winter season, for example. Moreover, by supplying the warm cooling air to the intake surface of the electronic apparatus in this manner, the humidity around the intake surface can be adjusted as well. 
     However, there is still room for improvement in module-type datacenters for further energy saving. 
     Note that a technology related to this application is disclosed in Japanese Laid-open Patent Publication No. 2013-92298. 
     SUMMARY 
     According to one aspect discussed herein, there is provided an air conditioning control system, including an electronic apparatus having an intake surface from which cooling air is taken in and an exhaust surface from which the cooling air is discharged, a flow path through which the cooling air discharged from the exhaust surface is returned to the intake surface, a damper which is provided in the flow path, an opening extent of the damper being adjustable, a temperature measuring unit that measures a real temperature of the cooling air at the intake surface, a humidity measuring unit that measures a real humidity of the cooling air at the intake surface, a target value changing unit that changes a target temperature of the real temperature in accordance with a value of the real temperature, and also changes a target humidity of the real humidity in accordance with a value of the real humidity, and a controlling unit that predicts a predicted temperature of the real temperature in a future and a predicted humidity of the real humidity in the future, where the controlling unit controlling the opening extent of the damper such that the predicted temperature becomes close to the target temperature and a predicted humidity becomes close to the target humidity, wherein the target value changing unit sets the target temperature and the target humidity such that the real temperature and the real humidity are raised and lowered in opposite directions. 
     According to another aspect discussed herein, there is provided an air conditioning control method, the method including measuring, by a temperature measuring unit, a real temperature of cooling air that is taken into an electronic apparatus from an intake surface of the electronic apparatus, measuring, by a humidity measuring unit, a real humidity of the cooling air, changing, by a target value changing unit, a target temperature of the real temperature in accordance with a value of the real temperature, and changing a target humidity of the real humidity in accordance with a value of the real humidity, and adjusting, by a control unit, an opening extent of a damper provided in a flow path through which the cooling air discharged from an exhaust surface of the electronic apparatus is returned to the intake surface, where the opening extent being adjusted, by predicting a predicted temperature of the real temperature in a future and a predicted humidity of the real humidity in the future, such that the predicted temperature becomes close to the target temperature and the predicted humidity becomes close to the target humidity, wherein in the changing the target temperature and the target humidity, the target value changing unit sets the target temperature and the target humidity such that the real temperature and the real humidity are raised and lowered in opposite directions. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claim. 
     It is to be understood that both the forgoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic top view of a datacenter used for consideration; 
         FIG. 2  is a schematic side view of the datacenter used for the consideration; 
         FIG. 3A  is a graph obtained by studying the relationship between the time elapsed after start of control on damper, and real humidity in the datacenter in  FIG. 1 ; 
         FIG. 3B  is a graph obtained by studying the relationship between the time elapsed after start of the control on the damper, and the opening extent of the damper in the datacenter in  FIG. 1 ; 
         FIG. 4  is a functional block diagram of an air conditioning control system according to an embodiment; 
         FIG. 5  is a flowchart illustrating an air conditioning control method according to this embodiment; 
         FIG. 6A  is a graph illustrating the relationship between the time elapsed after start of control, and the opening extent of damper according to this embodiment; 
         FIG. 6B  is a graph illustrating the relationship between the elapsed time and the real temperature of cooling air at an intake surface according to this embodiment; 
         FIG. 6C  is a graph illustrating the relationship between the elapsed time and the real humidity of the cooling air at the intake surface according to this embodiment; 
         FIG. 7  is a flowchart illustrating a method of changing a target temperature and a target humidity with a target value changing unit according to this embodiment (part 1); 
         FIG. 8  is a flowchart illustrating the method of changing the target temperature and the target humidity with the target value changing unit according to this embodiment (part 2); 
         FIG. 9  is a flowchart illustrating the method of changing the target temperature and the target humidity with the target value changing unit according to this embodiment (part 3); 
         FIG. 10A  is a graph obtained by studying the relationship between the time elapsed after start of the control on the damper, and the real temperature of the cooling air at the intake surface in this embodiment; 
         FIG. 10B  is a graph obtained by studying the relationship between the elapsed time and the real humidity of the cooling air at the intake surface in this embodiment; 
         FIG. 10C  is a graph obtained by studying the relationship between the elapsed time and the opening extent of the damper in this embodiment; 
         FIG. 11A  is a graph obtained by studying the relationship between the time elapsed after start of the control on the damper, and the real humidity of the cooling air at the intake surface in this embodiment; and 
         FIG. 11B  is a graph obtained by studying the relationship between the elapsed time and the opening extent of the damper. 
     
    
    
     DESCRIPTION OF EMBODIMENT 
     Prior to describing an embodiment, matters that the inventor of this application considered will be described. 
       FIG. 1  is a schematic top view of a datacenter used for that consideration. 
     This datacenter  1  is a module-type datacenter configured to taken in external air as cooling air, and includes a cuboidal container  10 . 
     In the container  10 , there are provided a fan unit  12  and a plurality of racks  13  housing electronic apparatuses  14  such as servers. 
     Among the two opposite faces of the container  10 , an air intake opening  10   a  is provided at one face, while an air exhaust opening  10   b  is provided at the other face. 
     The fan unit  12  includes a plurality of fans  12   a . By rotating the fans  12   a , the fans  12   a  take external air into the container  10  from the air intake opening  10   a  and generate cooling air C from the external air. 
     The cooling air C cools the electronic apparatuses  14 . After that, the cooling air C is discharged from the air exhaust opening  10   b.    
     Further, evaporative cooler  16  are provided between the fan unit  12  and the air intake opening  10   a.    
     The evaporative cooler  16  are configured to bring external air into contact with an unillustrated element containing moisture to thereby generate air D lower in temperature than the external air, and supply the air D to the fan unit  12 . Moreover, the humidity of the air D is made higher than that of the external air by the moisture of the element. 
     By using the air D which differs from the external air in temperature and humidity in this manner, it is possible to widen the ranges of adjustment of the temperature and humidity of the cooling air C. 
     Note that the evaporative cooler  16  may be omitted in some cases. 
       FIG. 2  is a schematic side view of the datacenter  1 . 
     Note that the same elements in  FIG. 2  as those described with reference to  FIG. 1  are denoted by the same reference numerals as those in  FIG. 1 , and description thereof is omitted below. 
     As illustrated in  FIG. 2 , each electronic apparatus  14  has an intake surface  14   x  and an exhaust surface  14   y . The cooling air C is taken into each electronic apparatus  14  from the intake surface  14   x  and then discharged from the exhaust surface  14   y.    
     Moreover, the space between the fan unit  12  and the racks  13  serves as a cold isle  22 , while the space between the racks  13  and the air exhaust opening  10   b  serves as a hot isle  23 . 
     A partition plate  15  is provided above the cold isle  22 . Moreover, this partition plate  15 , the upper faces of the racks  13 , and the ceiling surface of the container  10  define a flow path  24 . 
     In this way, part of the warm cooling air C discharged from each electronic apparatus  14  flows through the flow path  24  and returns to the intake surface  14   y  of the electronic apparatus  14 . 
     Provided at an end of the flow path  24  is damper  17  whose opening extent is adjustable. The definition of the opening extent is not particularly limited. Let 0°-θ max  be the range in which an inclination angle θ of each damper  17  can be laid. Note that the angle θ is measured form the vertical direction. Then, by making correspondence between the range 0°-θ max  and the range 0%-100% of the opening extent u, the opening extent u is associated with the angle θ in the following. 
     By adjusting the opening extent u of the damper  17 , it is possible to adjust the flow rate of the warm cooling air C passing through the flow path  24 , and thereby adjust the temperature and humidity of the cooling air C to be supplied to the intake surface  14   x.    
     For example, by increasing the opening extent u of the damper  17 , the warm cooling air C is supplied more to the intake surface  14   x  from the flow path  24 . Thus, the temperature of the cooling air C at the intake surface  14   x  can be raised. 
     Moreover, since temperature and humidity have a negative correlation with each other, the humidity of the cooling air C at the intake surface  14   x  can be lowered as well. 
     On the other hand, in order to lower the temperature of the cooling air C at the intake surface  14   x  and to raise the humidity of the cooling air C at the intake surface  14   x , the opening extent u of the damper  17  may be reduced instead. 
     Next, a method of adjusting the opening extent u of the damper  17  is discussed. 
     For each electronic apparatus  14 , allowable ranges are sometimes set for a real temperature T ca  and a real humidity H ca  of the cooling air C to be taken from the intake surface  14   x.    
     In the following, the upper and lower limits in the allowable temperature range will be described as T max0  and T min0 , respectively. Also, the upper and lower limits in the allowable humidity range will be described as H max0  and H min0 , respectively. 
     In order to keep the real temperature T ca  and the real humidity H ca  within the above-mentioned allowable ranges, it is required to adjust the opening extent u of the damper  17  in such a manner that the relations T min0 &lt;T ca &lt;T max0  and H min0 &lt;H ca &lt;H max0  hold. 
     In this example, the opening extent u of the damper  17  is adjusted by switching between two modes. One of the modes is a temperature control mode for controlling only the real temperature T ca , and the other mode is a humidity control mode for controlling only the real humidity H ca . 
     Here, the temperature control mode is a mode for controlling the opening extent u of the damper  17  such that the real temperature T ca  satisfies the relation T min0 &lt;T ca &lt;T max0 . In this mode, a PID controller controls the opening extent u of the damper  17  such that the real temperature T ca  becomes equal to a target temperature, and the PID controller does not control the real humidity H ca . 
     On the other hand, the humidity control mode is a mode for adjusting the opening extent u of the damper  17  such that the real humidity H ca  satisfies the relation H min0 &lt;H ca &lt;H max0 . In this mode, the PID controller controls the opening extent u of the damper  17  such that the real humidity H ca  becomes equal to a target humidity, and the PID controller does not control the real temperature T ca . 
     Which modes is to be selected is determined based on the real temperature T ca  and the real humidity H ca . For example, if the real temperature T ca  is about to be out of the allowable range, the temperature control mode is selected in order to place priority on controlling the real temperature T ca . On the other hand, if the real humidity H ca  is about to be out of the allowable range, the humidity control mode is selected in order to place priority on controlling the real humidity H ca . 
     By selecting between the temperature control mode and the humidity control mode in this manner, it is possible to the keep the real temperature T ca  and the real humidity H ca  within their allowable ranges. 
     However, according to an examination conducted by the inventor of this application, this method is found to have the following problem. 
       FIG. 3A  is a graph obtained by studying the relationship between the time elapsed after starting the control on the damper  17 , and the real humidity H ca  of the cooling air C at the intake surface  14   x.    
     Moreover,  FIG. 3B  is a graph obtained by studying the relationship between the time elapsed after starting the control on the damper  17 , and the opening extent u of the damper  17 . 
     As illustrated in  FIG. 3B , in this control method, the opening extent u of the damper  17  fluctuates greatly. Due to this fluctuation, a hunting phenomenon is occurring in which the real humidity H ca  greatly swings as illustrated in  FIG. 3A . 
     The cause of this hunting phenomenon is considered that the opening extent u is adjusted by switching between the temperature control mode and the humidity control mode. 
     When the opening extent u of the damper  17  greatly changes due to the hunting phenomenon in this manner, the power for driving the damper  17  is wasted, thereby making it difficult to achieve energy saving of the datacenter  1 . 
     (First Embodiment) 
     In this embodiment, the datacenter  1  illustrated in  FIG. 1  and  FIG. 2  is controlled as follows. 
       FIG. 4  is a functional block diagram of an air conditioning control system according to this embodiment for controlling the air conditioning of the datacenter  1 . 
     Note that the same elements in  FIG. 4  as those described with reference to  FIG. 1  and  FIG. 2  are denoted by the same reference numerals as those in  FIG. 1  and  FIG. 2 , and description thereof is omitted below. 
     As illustrated in  FIG. 4 , an air conditioning control system  100  includes a parameter setting unit  31 , a humidity measuring unit  32 , a temperature measuring unit  33 , and a controlling unit  30 . 
     The parameter setting unit  31  is configured to store various control parameters to be used to control the opening extent of the damper  17 . 
     The humidity measuring unit  32  is configured to measure the real humidity H ca  of the cooling air C at the intake surface  14   x  (see  FIG. 2 ) of each electronic apparatus  14  and transfer the measurement result to the controlling unit  30 . 
     Moreover, the temperature measuring unit  33  is configured to measure the real temperature T ca  of the cooling air C at the intake surface  14   x  of each electronic apparatus  14  and transfer the measurement result to the controlling unit  30 . 
     The number of humidity measuring units  32  is not particularly limited. The largest value of the humidity measured by a plurality of humidity measuring units  32  may be transferred as the real humidity H ca  to the controlling unit  30 . Likewise, the largest value of the temperature measured by a plurality of temperature measuring units  33  may be transferred as the real temperature T ca  to the controlling unit  30 . 
     On the other hand, the controlling unit  30  is, any one of a microcomputer, a field programmable gate array (FPGA), and a programmable logic controller (PLC) for example, and includes a target value changing unit  34  and a model predicting unit  35 . 
     Note that a specific electronic apparatus  14  in a rack  13  may be used as the controlling unit  30  by loading a dedicated program onto that electronic apparatus  14 . 
     The target value changing unit  34  is configured to set a target temperature r 1  and a target humidity r 2  of the cooling air C at the intake surface  14   x . Moreover, the target value changing unit  34  changes the target temperature r 1  and the target humidity r 2  in accordance with the values of the real temperature T ca  and the real humidity H ca  respectively, and outputs these values r 1  and r 2  to the model predicting unit  35 . How to change the target temperature r 1  and the target humidity r 2  will be described later. 
     Note that the target temperature r 1  and the target humidity r 2  will also be described below in a vector notation as in the equation (1) given below: 
     
       
         
           
             
               
                 
                   r 
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               r 
                               1 
                             
                           
                         
                         
                           
                             
                               r 
                               2 
                             
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Moreover, the model predicting unit  35  includes a prediction model  44 , a correcting unit  45 , a cost function  46 , an optimizing unit  47 , and a control signal storing unit  48 . 
     Among them, the prediction model  44  is configured to predict a predicted temperature {tilde over (y)} 1  of the real temperature T ca  and a predicted humidity {tilde over (y)} 2  of the real humidity H ca  in a future based on the opening extent u of the damper  17 . 
     Note that the above predicted temperature and the predicted humidity will also be described below in a vector notation as in the equation (2) given below: 
     
       
         
           
             
               
                 
                   
                     y 
                     ~ 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               ~ 
                             
                             1 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               ~ 
                             
                             2 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Moreover, the correcting unit  45  is configured to correct this predicted value {tilde over (y)} so as to bring it close to the real temperature and humidity of the cooling air C at the intake surface  14   x.    
     Further, the cost function  46  is a function which weights the difference between the predicted value {tilde over (y)} and the target value r, and its form will be described later. 
     Furthermore, the optimizing unit  47  is configured to calculate, in a predetermined period of time from the present to a future, a manipulation amount Δu that minimizes the value J of the cost function  46  and satisfies later-described constraint conditions. The manipulation amount Δu thus calculated is output to the control signal storing unit  48  and the damper  17  by the optimizing unit  47 . 
     Moreover, the control signal storing unit  48  is configured to store the past manipulation amount Δu of the opening extent of the damper  17  and output the manipulation amount Δu to the prediction model  44 . 
     Next, an air conditioning control method according to this embodiment will be described. 
       FIG. 5  is a flowchart illustrating the air conditioning control method according to this embodiment. 
     This flowchart is carried out by the controlling unit  30  in a predetermined control cycle Δt. The control cycle Δt is an integer representing the cycle in which this flowchart is carried out, and is 1 second, for example. 
     First, in step S 11 , the controlling unit  30  acquires the real temperature T ca  and the real humidity H ca  of the cooling air C at the intake surface  14   x . Among them, the real temperature T ca  is acquired from the temperature measuring unit  33  by the controlling unit  30 . Then, the real humidity H ca  is acquired from the humidity measuring unit  32  by the controlling unit  30 . 
     Next, the method proceeds to step S 12 , in which the controlling unit  30  acquires various control parameters from the parameter setting unit  31 . 
     The control parameters include the allowable ranges of each of the real temperature T ca  and the real humidity H ca , for example. The allowable ranges are not particularly limited. In the following, the lower limit temperature T min0  of the real temperature T ca  is 10° C., and the upper limit temperature T max0  of the real temperature T ca  is 35° C. Moreover, the lower limit humidity H min0  of the real humidity H ca  is 10%, and the upper limit humidity H max0  of the real humidity H ca  is 85%. 
     Next, the method proceeds to step S 13 , in which the target value changing unit  34  changes the target temperature r 1  and the target humidity r 2  in accordance with the values of the real temperature T ca  and the real humidity H ca , respectively. How to makes the changes will be described later in detail. 
     Then, the method proceeds to step S 14 . 
     In step S 14 , the model predicting unit  35  predicts the future predicted temperature {tilde over (y)} 1  of the real temperature T ca  and the future predicted humidity {tilde over (y)} 2  of the real humidity H ca , and controls the opening extent of the damper  17  such that the real temperature T ca  becomes close to the target temperature r 1  and the real humidity H ca  becomes close to the target humidity r 2 . This control is performed by using a prediction model as follows. 
     The general equations of this prediction model are described bt the equations (3) and (4) given below:
 
 {tilde over (y)}   1 ( k+ 1)= f   1 ( u ( k ))  (3)
 
 {tilde over (y)}   2 ( k+ 1)= f   2 ( u ( k ))  (4).
 
     The equation (3) is a temperature prediction model, and the equation (4) is a humidity prediction model. A time point k is included in both prediction models (3) and (4). The time point k is an integer indicating the number of times that the controlling unit  30  carries out the flowchart in  FIG. 5 . Thus, the equations (3) and (4) are interpreted as the equations to find a temperature y 1  and a humidity y 2  at a future time point k+1 based on an opening extent u(k) of the damper at the time point k. 
     Note that the equation (3) and the equation (4) are described together in a vector notation as in the equation (5) given below: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 y 
                                 ~ 
                               
                               1 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 y 
                                 ~ 
                               
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 f 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   u 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 f 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   u 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Further, by collecting the functions f 1  and f 2  into a function f, the equation (5) can be described as the equation (6) given below:
 
 {tilde over (y)} ( k+ 1)= f ( u ( k ))  (6).
 
     In this embodiment, the general equation (6) is specialized as in the equations (7) and (8) given below:
 
 x ( k+ 1)= Ax ( k )+ B   u   u ( k )  (7)
 
 {tilde over (y)} ( k )= C·x ( k )  (8).
 
     Note that x(k) in the equations (7) and (8) is a state variable at the time point k and is a n-dimensional (n is a natural number) vector. Moreover, A is an n×n matrix, B u  is an n-dimensional vector, and C is an n-dimensional vector. 
     Note also that the each components of A, B u , and C can be found by system identification based on test data such that a predicted value {tilde over (y)} of the future real temperature and real humidity of the cooling air C can be best approximated. Examples of the system identification include, for example, a prediction error method or a subspace identification method. 
     Moreover, when it is possible to derive a differential equation of a physics model which expresses the dynamic characteristics of the real temperature and real humidity of the cooling air C, the components of A, B u , and C can be found by linearizing the differential equation through the Taylor expansion. 
     Further, it is known that n is determined by an order n d1  of the temperature prediction model, dead times d t1 , d t2 , and an order n d2  of the humidity prediction model, and is expressed as n=n d1 +d t1 +n d2 +d t2 . The reason for this will be explained in a later-described reference example. 
     Note that the dead time d t1  is a dead time of the temperature of the cooling air C at the intake surface  14   x  with respect to the opening extent of the damper  17 . The dead time d t2  is a dead time of the humidity of the cooling air C at the intake surface  14   x  with respect to the opening extent of the damper  17 . In this embodiment, the dead times d t1  and d t2  are rounded off to integer values, and the dead times d t1  and d t2  are set to 1 second. 
     Meanwhile, although a state-space model is used in the above case, the model may be expressed as a multiple regression model or data such as a map function. 
     Next, the correcting unit  45  corrects the predicted value {tilde over (y)}(k+1) of the temperature and humidity at the time point k+1 based on the equation (9) given below to calculate a corrected predicted value y(k+1|k):
 
 y ( k+ 1| k )= {tilde over (y)} ( k+ 1| k )+( y   real ( k )− y ( k|k− 1))  (9).
 
     Here, 
                     y   =     [           y   1               y   2           ]       ,           (   10   )               
where y 1  represents the temperature after the correction, and y 2  represents the humidity after the correction.
 
     Further, 
                         y   real     ⁡     (   k   )       =     [             T   ca     ⁡     (   k   )                   H   ca     ⁡     (   k   )             ]       ,           (   11   )               
where T ca (k) and H ca (k) are the temperature and the humidity at the time point k acquired in step S 11 , respectively.
 
     In the equation (9) and the subsequent equations, when a variable α at a time point p is to be calculated from information at a time point q, the variable α will be described as α(p|q). 
     The first term of the right-hand side of the equation (9), {tilde over (y)}(k+1|k), is the uncorrected predicted value of the temperature and humidity of the cooling air C at the time point k+1. 
     Moreover, the second term of the right-hand side of the equation (9) is a correction term. y(k|k−1) appearing in the correction term is the predicted value of the temperature and humidity of the cooling air C at the intake surface  14   x  at the time point k. 
     At the time point k, the real value is deviated from the predicted value by y real (k)−y(k|k−1). Therefore, by adding y real (k)−y(k|k−1) to the right-hand side of the equation (9), it is possible to prevent the predicted value at the time point k+1 from deviating from the real value. 
     Note that the above correction may be omitted in some cases. 
     Here, a future period p is introduced. The future period p is an integer indicating a period of time from the present to a future at which the temperature and humidity of the cooling air C is to be predicted. In the following, the future period p is 100, for example. 
     Then, the change amount Δu of the opening extent of the damper  17  is defined as in the equation (12) given below:
 
 u ( k+i|k )= u ( k+i− 1| k )+Δ u ( k+i|k )
 
( i= 0,1, . . . , p− 1)  (12).
 
     In the equation (12), i is an index which equally divides the future period p into p parts. 
     As can be understood from the equation (12), a change amount Δu(k+i|k) is defined by an opening extent u(k+i|k) of the damper  17  at a time point k+i, and an opening extent u(k+i−1|k) of the damper  17  at a time point k+i−1, which is the antecedent time point of k+i by one step. 
     Moreover, as each opening extent u(k) in the equation (12), those stored in the control signal storing unit  48  can be used. 
     Note that since the opening extent of the damper  17  is manipulated by the controlling unit  30 , the change amount Δu will also be called the manipulation amount Δu in the following. 
     By using the index i in the equation (12), the equations (7) to (9) mentioned above can be expressed as the equations (13) to (15) given below, respectively:
 
 x ( k+i+ 1| k )= Ax ( k+i|k )+ B   u   u ( k+i|k )  (13),
 
 {tilde over (y)} ( k+i+ 1| k )= C·x ( k+i+ 1| k )  (14),
 
 y ( k+i+ 1| k )= {tilde over (y)} ( k+i+ 1| k )+( y   real ( k )− y ( k|k− 1))  (15).
 
     Further, the allowable ranges of the parameters are defined as in the equations (16) to (19) given below:
 
 T   min   ≦y   1 ( k+i+ 1| k )≦ T   max   (16),
 
 H   min   ≦y   2 ( k+i+ 1| k )≦ H   max   (17),
 
Δ u   min   ≦Δu ( k+i|k )≦Δ u   max   (18),
 
 u   min   ≦u ( k+i|k )≦ u   max   (19).
 
     The equation (16) defines the allowable range of the temperature y 1  of the cooling air C at the intake surface  14   x.    
     Similarly, the equation (17) defines the allowable range of the humidity y 2  of the cooling air C at the intake surface  14   x.    
     The equation (18) defines the allowable range of the manipulation amount Δu of the damper  17 . A minimum value Δu min  and a maximum value Δu max  of this allowable range are limit values that the opening extent of the damper  17  can be changed in one manipulation. 
     Moreover, the equation (19) defines the allowable range of the opening extent u of the damper  17 . U min  and U max  represent the lower limit value and upper limit value of that allowable range, respectively. 
     The parameters y 1 , y 2 , Δu, and u are subjected to the constraint conditions of the equations (16) to (19), respectively. 
     Moreover, in this embodiment, besides the above constraint conditions, the equation (20) given below is provided as another constraint condition on the manipulation amount Δu:
 
Δ u ( k+h|k )=0
 
( h=m, . . . ,p− 1)  (20).
 
     The equation (20) indicates that the manipulation amount Δu becomes 0 at and after a time point k+m. This is based on an idea that the manipulation amount Δu should gradually approach 0 toward the end of the future period, instead of shifting the manipulation amount Δu suddenly to 0 at the end of the future period. 
     Meanwhile, the value of m is not particularly limited. In this example, m is set to 1. 
     Next, the optimizing unit  47  calls the cost function  46  which is described as in the equation (21) given below: 
     
       
         
           
             
               
                 
                   
                     J 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         
                           p 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             [ 
                             
                               
                                 y 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       k 
                                       + 
                                       i 
                                       + 
                                       1 
                                     
                                     | 
                                     k 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 r 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     i 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                           T 
                         
                         ⁢ 
                         
                           Q 
                           ⁡ 
                           
                             [ 
                             
                               
                                 y 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       k 
                                       + 
                                       i 
                                       + 
                                       1 
                                     
                                     | 
                                     k 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 r 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     i 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         u 
                         ⁡ 
                         
                           ( 
                           
                             
                               k 
                               + 
                               i 
                             
                             | 
                             k 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         R 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           u 
                         
                       
                       ⁢ 
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         u 
                         ⁡ 
                         
                           ( 
                           
                             
                               k 
                               + 
                               i 
                             
                             | 
                             k 
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         [ 
                         
                             
                         
                         ⁢ 
                         
                           
                             u 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   k 
                                   + 
                                   i 
                                 
                                 | 
                                 k 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               u 
                               target 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 + 
                                 i 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             R 
                             u 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 u 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       k 
                                       + 
                                       i 
                                     
                                     | 
                                     k 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   u 
                                   target 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     In the equation (21), Q is a 2×2 matrix representing a weight, and RΔ u  and R u  are scalars representing weights. 
     In the first term of the right-hand side of the equation (21), the difference (y 1 −r 1 ) between the predicted temperature y 1  and the target temperature r 1 , and the difference (y 2 −r 2 ) between the predicted humidity y 2  and the target humidity r 2  are weighted. This first term represents an operation to bring the temperature y 1  and the humidity y 2 , which are control targets, close to their respective target values r 1  and r 2 , and the matrix Q is a weight for the operation, i.e. a target value following parameter. 
     The second term of the right-hand side of the equation (21) represents an operation to bring the change amount Δu of the manipulation amount u close to 0, and RΔ u  is a weight for this operation, i.e. a manipulation amount reducing parameter. The smaller the RΔ u , the larger the change amount Δu, and the larger the RΔ u , the smaller the change amount Δu. 
     The third term of the right-hand side of the equation (21) represents an operation to bring the opening extent u of the damper  17  close to a target opening extent U target . In this embodiment, u target  is set to 0. R u  is a weight for the operation to bring the opening extent close to the target opening extent u target , i.e. a manipulation amount shift width parameter. 
     These control parameters Q, RΔ u , and R u  are stored in the parameter setting unit  31  mentioned above, and are acquired by the model predicting unit  35  in step S 12  in advance. 
     Then, the optimizing unit  47  calculates an input sequence of the manipulation amounts Δu which minimize the value J of the cost function  46 , based on the equation (22) given below: 
     
       
         
           
             
               
                 
                   
                     { 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             u 
                             opt 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               | 
                               k 
                             
                             ) 
                           
                         
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             u 
                             opt 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 m 
                                 - 
                                 1 
                                 + 
                                 k 
                               
                               | 
                               k 
                             
                             ) 
                           
                         
                       
                     
                     } 
                   
                   ⁢ 
                   arg 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       min 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             u 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 | 
                                 k 
                               
                               ) 
                             
                           
                         
                         , 
                         … 
                         ⁢ 
                         
                             
                         
                         , 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             u 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   m 
                                   - 
                                   1 
                                   + 
                                   k 
                                 
                                 | 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         J 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Then, the optimizing unit  47  extracts the first element Δu opt (k|k) in the optimum input sequence {Δu opt (k|k), . . . , Δu opt (m−1+k|k)} calculated from the equation (22). 
     Further, the optimizing unit  47  calculates the opening extent u(k) of the damper  17  at the time point k from the equation (23) given below:
 
 u ( k )= u ( k− 1)+Δ u   opt ( k|k )  (23).
 
     The optimizing solver which minimizes the cost function  46  may use a metaheuristic numerical solution which searches for an approximate solution such as an genetic algorithm (GA) or particle swarm optimization (PSO). Note that sequential quadratic programming (SQP) is used in this example to solve a quadratic programming problem. 
     By the above operation, step S 14  ends. 
     Thereafter, the method proceeds to step S 15 , in which the controlling unit  30  generates a control signal for controlling the opening extent of the damper  17  and changes the opening extent of the damper  17  to u(k) appearing in the equation (23). 
     By the above operation, the basic steps of the air conditioning control method according to this embodiment ends. 
       FIGS. 6A to 6C  are graphs illustrating one exemplary result that are obtained by controlling the datacenter  1  using the above-described air conditioning control method. 
       FIG. 6A  is a graph illustrating the relationship between the time elapsed after start of the control, and the opening extent of the damper  17 . 
     Further,  FIG. 6B  is a graph illustrating the relationship between the above elapsed time and the real temperature T ca  of the cooling air at the intake surface  14   x.    
     Furthermore,  FIG. 6C  is a graph illustrating the relationship between the above elapsed time and the real humidity H ca  of the cooling air at the intake surface  14   x.    
     As illustrated in  FIGS. 6B and 6C , the real temperature T ca  and the real humidity H ca  substantially match their predicted values. 
     Next, a method of changing the target temperature r 1  and the target humidity r 2  in the target value changing unit  34  will be described. 
     In this embodiment, the target temperature r 1  and the target humidity r 2  are not fixed at certain values but are dynamically changed in the following way in accordance with the values of the real temperature T ca  and the real humidity H ca , respectively. 
       FIGS. 7 to 9  are flowcharts illustrating the method of changing the target temperature r 1  and the target humidity r 2  in the target value changing unit  34 . 
     Here, the definitions of the symbols used in this example are listed below again. 
     r 1 : target temperature 
     r 2 : target humidity 
     T max0 : upper limit temperature 
     T min0 : lower limit temperature 
     H max0 : upper limit humidity 
     H min0 : lower limit humidity 
     If the real temperature is too close to the limit value T max0  or T min0 , the real temperature may exceed or fall below the limit value. To deal with this problem, margins are provided to each of the limit values T max0  and T min0  in this example, and the limit values T max0  and T min0  thus provided with the margins are employed as new limit values T max  and T min  as follows:
 
 T   max   =T   max0   −m   T  
 
 T   min   =T   min0   +m   T ,
 
where m T  is a positive value determined in view of the margin, and m T =1 in this example.
 
     For the same reason, the following new limit values H max  and H min  are employed for the humidity:
 
 H   max   =H   max0   −m   H  
 
 H   min   =H   min0   +m   H ,
 
where m H  is a positive value determined in view of the margin, and m H =1 in this example.
 
     Moreover, the smallest unit of change for the target temperature r 1  by the target value changing unit  34  is defined as dT, and the target temperature r 1  is raised or lowered by the unit dT. 
     Likewise, the smallest unit of change for the target humidity r 2  by the target value changing unit  34  is defined as dH, and the target humidity r 2  is raised or lowered by the unit dH. 
     In this example, dT=dH=5. 
     First, in step S 21  in  FIG. 7 , it is determined whether or not the real temperature T ca  is higher than the upper limit temperature T max . 
     When it is determined that the real temperature T ca  is higher than the upper limit temperature T max  (YES), the method proceeds to step S 22 , in which the real temperature T ca  is lowered. 
     To lower the real temperature T ca , it is only required to change the target temperature r 1  to a lower temperature than the real temperature T ca . In this example, the target temperature r 1  is changed such that r 1 =T max . 
     Meanwhile, as opposed to the lowering the real temperature T ca , the target humidity r 2  is changed so as to raise the real humidity H ca . In this example, the real humidity H ca  is raised by changing the target humidity r 2  such that r 2 =H ca +dH. 
     The real temperature T ca  and the real humidity H ca  have a negative correlation with each other. Therefore, when the real temperature T ca  is desired to be lowered, the target humidity r 2  is changed in the opposite way, i.e. raised. As a result, as the real temperature T ca  is lowered, the real humidity H ca  is automatically brought close to the target humidity r 2 . In this way, the real temperature T ca  and the real humidity H ca  can be easily brought close to their respective target temperature r 1  and target humidity r 2  through the adjustment of the opening extent of the damper  17 . 
     Then, in order to check whether the target humidity r 2  changed in step S 22  is within the allowable range, the method proceeds to step S 23 , in which it is determined whether or not the target humidity r 2  is higher than the upper limit humidity H max . 
     Here, when it is determined that the target humidity r 2  is higher than the upper limit humidity H max  (YES), the method proceeds to step S 24 . 
     In step S 24 , the target humidity r 2  is changed such that r 2 =H max , to thereby bring the target humidity r 2  within the allowable range. 
     On the other hand, when it is determined in step S 23  that the target humidity r 2  is not higher than the upper limit humidity H max  (NO), the method is ended. 
     Next, the case where it is determined in step S 21  that the real temperature T ca  is not higher than the upper limit temperature T max  (NO) will be described. 
     In this case, the method proceeds to step S 25 , in which it is determined whether or not the real temperature T ca  is lower than the lower limit temperature T min . 
     Here, when it is determined that the real temperature T ca  is lower than the lower limit temperature T min  (YES), the method proceeds to step S 26 , in which the real temperature T ca  is raised. 
     To raise the real temperature T ca , it is only required to change the target temperature r 1  to a higher temperature than the real temperature T ca . In this example, the target temperature r 1  is changed such that r 1 =T min . 
     Moreover, as opposed to raising the real temperature T ca  in this manner, the target humidity r 2  is changed so as to lower the real humidity H ca . In this example, the real humidity H ca  is lowered by changing the target humidity r 2  such that r 2 =H ca −dH. 
     By raising and lowering the real temperature T ca  and the real humidity H ca  in the opposite directions in this manner, the real temperature T ca  and the real humidity H ca  can be easily brought close to their respective target temperature r 1  and target humidity r 2  through the adjustment of the opening extent of the damper  17  for the same reason as that for step S 22  mentioned above. 
     Next, to check whether the target humidity r 2  changed in step S 26  is within the allowable range, the method proceeds to step S 27 , in which it is determined whether or not the target humidity r 2  is lower than the lower limit humidity H min . 
     Here, when it is determined that the target humidity r 2  is lower than the lower limit humidity H min  (YES), the method proceeds to step S 28 . 
     In step S 28 , the target humidity r 2  is changed such that r 2 =H min , to thereby bring the target humidity r 2  within the allowable range. 
     On the other hand, when it is determined in step S 27  that the target humidity r 2  is not lower than the lower limit humidity H min  (NO), the method is ended. 
     Next, the case where it is determined in step S 25  that the real temperature T ca  is not lower than the lower limit temperature T min  (NO) will be described. 
     In this case, the method proceeds to a subroutine A of step S 29 . 
       FIG. 8  is a flowchart illustrating the content of processing in the subroutine A. 
     First, in step S 31 , it is determined whether or not the real humidity H ca  is higher than the upper limit humidity H max . 
     Here, when it is determined that the real humidity H ca  is higher than the upper limit humidity H max  (YES), the method proceeds to step S 32 , in which the real humidity H ca  is lowered. 
     To lower the real humidity H ca , it is only required to change the target humidity r 2  to a lower humidity than the real humidity H ca . In this example, the target humidity r 2  is changed such that r 2 =H max . 
     Moreover, as opposed to lowering the real humidity H ca  in this manner, the target temperature r 1  is changed so as to raise the real temperature T ca . In this example, the real temperature T ma  is raised by changing the target temperature r 1  such that r 1 =T ca +dH. 
     As mentioned above, the real temperature T ca  and the real humidity H ca  have a negative correlation with each other. For this reason, when the real humidity H ca  is desired to be lowered, the target temperature r 1  is changed in the opposite way, i.e. raised. Thus, as the real humidity H ca  is lowered, the real temperature T ca  is automatically brought close to the target temperature r 1 . In this way, the real temperature T ca  and the real humidity H ca  can be easily brought close to their respective target temperature r 1  and target humidity r 2  through the adjustment of the opening extent of the damper  17 . 
     Next, to check whether the target temperature r 1  changed in step S 32  is within the allowable range, the method proceeds to step S 33 , in which it is determined whether or not the target temperature r 1  is higher than the upper limit temperature T max    
     Here, when it is determined that the target temperature r 1  is higher than the upper limit temperature T max  (YES), the method proceeds to step S 34 . 
     In step S 34 , the target temperature r 1  is changed such that r 1 =T max , to thereby bring the target temperature r 1  within the allowable range. 
     On the other hand, when it is determined in step S 33  that the target temperature r 1  is not higher than the upper limit temperature T max  (NO), the method is ended. 
     Next, the case where it is determined in step S 31  described above that the real humidity H ca  is not higher than the upper limit humidity H max  (NO) will be described. 
     In this case, the method proceeds to step S 35 , in which it is determined whether or not the real humidity H ca  is lower than the lower limit humidity H min . 
     Here, when it is determined that the real humidity H ca  is lower than the lower limit humidity H min  (YES), the method proceeds to step S 36 , in which the real humidity H ca  is raised. 
     To raise the real humidity H ca , it is only required to change the target humidity r 2  to a higher humidity than the real humidity H ca . In this example, the target humidity r 2  is changed such that r 2 =H min . 
     Moreover, as opposed to raising the real humidity H ca  in this manner, the target temperature r 1  is changed so as to lower the real temperature T ca . In this example, the real temperature T ca  is lowered by changing the target temperature r 1  such that r 1 =T ca −dT. 
     By raising and lowering the real temperature T ca  and the real humidity H ca  in the opposite directions in this manner, the real temperature T ca  and the real humidity H ca  can be easily brought close to their respective target temperature r 1  and target humidity r 2  through the adjustment of the opening extent of the damper  17  as in the case of step S 32  mentioned above. 
     Then, to check whether the target temperature r 1  changed in step S 36  is within the allowable range, the method proceeds to step S 37 , in which it is determined whether or not the target temperature r 1  is lower than the lower limit temperature T min . 
     Here, when it is determined that the target temperature r 1  is lower than the lower limit temperature T min  (YES), the method proceeds to step S 38 . 
     In step S 38 , the target temperature r 1  is changed such that r 1 =T min , to thereby bring the target temperature r 1  within the allowable range. 
     On the other hand, if it is determined in step S 37  that the target temperature r 1  is not lower than the lower limit temperature T min  (NO), the method is ended. 
     Next, the case where it is determined in step S 35  that the real humidity H ca  is not lower than the lower limit humidity H min  (NO) will be described. 
     In this case, the method proceeds to a subroutine B of step S 39 . 
       FIG. 9  is a flowchart illustrating the content of processing in the subroutine B. 
     In the subroutine B, the target temperature r 1  is lowered as much as possible within the allowable range in the following way. 
     First, in step S 41 , it is determined whether or not there is still room to further lower the real temperature T ca  in the allowable range. 
     As mentioned above, the smallest unit of lowering the temperature is dT. Therefore, in this step, decision is made on whether or not there is still room to lower the real temperature T ca , by determining whether or not T ca −dT is larger than the lower limit temperature T min . 
     Here, when it is determined that T ca −dT is larger than the lower limit temperature T min  (YES), it is decided that there is still room to lower the real temperature T ca , and the method proceeds to step S 42 . 
     In step S 42 , the target temperature r 1  is lowered by changing the target temperature r 1  to T ca −dT. 
     Then, the method proceeds to step S 43 , in which it is decided whether there is still room to further raise the real humidity H ca  in the allowable range. 
     As mentioned above, the smallest unit of raising the humidity is dH. Therefore, in this step, decision is made on whether or not there is still room to raise the real humidity H ca , by determining whether or not H ca +dH is smaller than the upper limit humidity H max . 
     Here, when it is determined that H ca +dH is smaller than the upper limit humidity H max  (YES), it is decided that there is still room to raise the real humidity H ca , and the method proceeds to step S 44 . 
     In step S 44 , the target humidity r 2  is changed to H ca +dH. 
     On the other hand, when it is determined in step S 43  that H ca +dH is not smaller than the upper limit humidity H max  (NO), there is no room to raise the real humidity H ca . 
     Therefore, in this case, the method proceeds to step S 45 , in which the target humidity r 2  is set to the upper limit humidity H max  so as to raise the humidity as much as possible within the allowable range. 
     Further, when it is determined in step S 41  that T ca −dT is not larger than the lower limit temperature T min  (NO), the method proceeds to step S 46 . 
     In this case, there is no room to lower the real temperature T ca . Therefore, the target temperature r 1  and the target humidity r 2  are changed such that r 1 =T ca  and r 2 =H ca , so as to maintain the real temperature T ca  and the real humidity H ca  at their current values. 
     By the above operation, the basic steps of the method of changing the target temperature r 1  and the target humidity r 2  in the target value changing unit  34  end. 
     After that, the flowcharts in  FIGS. 7 to 9  are repeated in the predetermined control cycle. Thus, each time step S 42  in  FIG. 9  is performed, the target temperature r 1  is lowered by dT, and hence the target temperature r 1  is changed to a temperature closer to the lower limit temperature T min  than to the upper limit temperature T max . 
     By lowering the target temperature r 1  as much as possible within a range within which the target temperature r 1  does not lower than the lower limit temperature T min  in this manner, it is possible to efficiently cool the electronic apparatuses  14  with the cooling air C of the real temperature T ca  which is low and close to the lower limit temperature T min . 
     The inventor of this application conducted an examination to check whether the real temperature T ca  of the cooling air C could be maintained at and around the lower limit temperature T min . As a result, graphs in  FIGS. 10A to 10C  were obtained. 
       FIG. 10A  is a graph obtained by studying the relationship between the time elapsed after start of the control of the damper  17 , and the real temperature T ca  of the cooling air C at the intake surface  14   x.    
     Moreover,  FIG. 10B  is a graph obtained by studying the relationship between the time elapsed after the start of the control of the damper  17 , and the real humidity H ca  of the cooling air C at the intake surface  14   x.    
     Furthermore,  FIG. 10C  is a graph obtained by studying the relationship between the time elapsed after the start of the control of the damper  17 , and the opening extent of the damper  17 . 
     In this examination, parameters were set as follows:
         T max0 =35° C.   T min0 =10° C.   H max0 =85%   H min0 =10%   dT=dH=1   T max =T max0 −dT=34° C.   T min =T min0 +dT=11° C.   H max =H max0 −dH=84%   H min =H min0 +dH=11%.       

     As illustrated in  FIG. 10A , the real temperature T ca  was maintained at the lower limit temperature T min  (11° C.). From this result, it was confirmed that the real temperature T ca  of the cooling air C could be maintained at and around the lower limit temperature T min  by following the flowchart in  FIG. 9 . 
     Moreover, in step S 42  and step S 44  mentioned above, the target temperature r 1  and the target humidity r 2  are changed such that the target temperature and the target humidity are raised and lowered in opposite directions each other. Since temperature and humidity have a negative correlation with each other, both the real temperature T ca  and the real humidity H ca  can be easily brought close to their target values r 1  and r 2  by raising and lowering these target values in the opposite directions in this manner. 
     According to this embodiment described above, in step S 22  in  FIG. 7 , the target value changing unit  34  sets the target temperature r 1  and the target humidity r 2  such that the real temperature T ca  and the real humidity H ca  can be raised and lowered in the opposite directions. This is also the case in step S 26 , step S 32 , and step S 36 . 
     Thus, both the real temperature T ca  and the real humidity H ca  can be easily brought close to their target values as mentioned above. 
     Next, the inventor of this application conducted an examination on advantageous effects obtained by setting the target temperature r 1  and the target humidity r 2  such that the real temperature T ca  and the real humidity H ca  can be raised and lowered in the opposite directions as described above. As a result, graphs in  FIGS. 11A and 11B  were obtained. 
       FIG. 11A  is a graph obtained by studying the relationship between the time elapsed after the start of the control of the damper  17 , and the real humidity H ca  of the cooling air C at the intake surface  14   x.    
     Moreover,  FIG. 11B  is a graph obtained by studying the relationship between the time elapsed after the start of the control of the damper  17 , and the opening extent of the damper  17 . 
     As illustrated in  FIG. 11A , the real humidity H remained stable and did not largely fluctuate as in the case of  FIG. 3A . 
     Moreover, as illustrated in  FIG. 11B , no large fluctuations were observed in the opening extent of the damper  17 , which indicates that any noticeable hunting phenomenon as that in  FIG. 3B  did not occur. 
     From these results, it was confirmed that the hunting phenomenon could be effectively suppressed by setting the target temperature r 1  and the target humidity r 2  such that the real temperature T ca  and the real humidity H ca  could be raised and lowered in the opposite directions as in this embodiment. 
     The reason for this is considered that, unlike the example of  FIGS. 3A and 3B  in which the switching between the temperature control mode and the humidity control mode is performed, the target temperature r 1  and the target humidity r 2  are changed as a whole in the present embodiment. Namely, in the present embodiment, the target temperature r 1  and the target humidity r 2  are raised and lowered in opposite directions each other in accordance with their negative correlation. 
     Since the hunting phenomenon of the damper  17  can be suppressed as described above, the power consumption of the damper  17  can be reduced, thereby making it possible to achieve energy saving of the datacenter  1 . 
     Although the present embodiment is described above in detail, the present embodiment is not limited to the above. 
     For example, although the air conditioning control method for the datacenter  1  is described above, this embodiment may be applied to the air conditioning of facilities including heat generating parts. 
     REFERENCE EXAMPLE 
     In step S 14  (see  FIG. 5 ) of this embodiment, it is mentioned that the dimension n of the state variable x(k), the order n d1  of the temperature prediction model, the dead times d t1  and d t2 , and the order n d2  of the humidity prediction model satisfy the relation n=n d1 +d t1 +n d2 +d t2 . The reason for this will be described below. 
     First, consider the state-space model of discrete time represented by the following equation (24). Note that the number of the input parameter and the output parameter of this model is one, and dimension of this model is one.
 
 x ( k+ 1)= Ax ( k )+ Bu ( k )
 
 y ( k )= Cx ( k )
 
 A =[ a ]
 
 B =[ b ]
 
 C =[ c ]
 
 x (0)= x   1 (0)  (24)
 
     Here, in the case where the dead time of an input u is 1 second and the cycle of k is 1 second, the model can be expressed such that, like the equation (25) given below, the value of the input u is stored in the second component of the state variable and shifted to the first row in the next cycle. 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           + 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         Ax 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       + 
                       
                         Bu 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       Cx 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         x 
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       = 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       A 
                       = 
                       
                         [ 
                         
                           
                             
                               a 
                             
                             
                               b 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       B 
                       = 
                       
                         [ 
                         
                           
                             
                               0 
                             
                           
                           
                             
                               1 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       C 
                       = 
                       
                         
                           [ 
                           c 
                           ] 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     In the example of the equation (25), the order of the state variable is 2, which is the sum of 1 as the model order and 1 as a value taking into consideration of the dead time. 
     Moreover, in the case where the dead time of the input u is 2 seconds, the model can be expressed such that, like the equation (26) given below, the second component and the third component of the state variable and the value of the input u are shifted, as in the above case. 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           + 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         Ax 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       + 
                       
                         Bu 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       Cx 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         x 
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       = 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       A 
                       = 
                       
                         [ 
                         
                           
                             
                               a 
                             
                             
                               0 
                             
                             
                               b 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       B 
                       = 
                       
                         [ 
                         
                           
                             
                               0 
                             
                           
                           
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       C 
                       = 
                       
                         [ 
                         
                           c 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     In the example of the equation (26), the order of the state variable is 3, which is the sum of 1 as the model order and 2 as a value taking into consideration the dead time. 
     In the case where the dead time of the input u is 3 seconds, the model can be expressed such that, like the equation (27) given below, the second component, the third component, and the fourth component of the state variable and the value of the input u are shifted, as in the above cases. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         x 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         
                           Ax 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         + 
                         
                           Bu 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         y 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       = 
                       
                         Cx 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           x 
                           ⁡ 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         = 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     x 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     0 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                       , 
                       
                         A 
                         = 
                         
                           [ 
                           
                             
                               
                                 a 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 b 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                       , 
                       
                         B 
                         = 
                         
                           [ 
                           
                             
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                       , 
                       
                         C 
                         = 
                         
                           [ 
                           
                             c 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     In the example of the equation (27), the order of the state variable is 4, which is the sum of 1 as the model order and 3 as a value taking into consideration the dead time. 
     Next, consider the state-space model of discrete time represented by the following equation (28). Note that the number of the input parameter and the output parameter of this model is one, and dimension of this model is two. 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           + 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         Ax 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       + 
                       
                         Bu 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       Cx 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     A 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               a 
                               11 
                             
                           
                           
                             
                               a 
                               12 
                             
                           
                         
                         
                           
                             
                               a 
                               21 
                             
                           
                           
                             
                               a 
                               22 
                             
                           
                         
                       
                       ] 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     B 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               b 
                               1 
                             
                           
                         
                         
                           
                             
                               b 
                               2 
                             
                           
                         
                       
                       ] 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     C 
                     = 
                     
                       [ 
                       
                         
                           c 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                       ] 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       x 
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               
                                 x 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 x 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     Here, in the case where the dead time of the input u is 1 second and the cycle of k is 1 second, the model can be expressed such that, like the equation (29) given below, the value of the input u is stored in the third component of the state variable and shifted to the first row and the second row in the next cycle. 
     
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         
                           Ax 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         + 
                         
                           Bu 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       = 
                       
                         Cx 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       x 
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               
                                 x 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 x 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                         
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     A 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               a 
                               11 
                             
                           
                           
                             
                               a 
                               12 
                             
                           
                           
                             
                               b 
                               1 
                             
                           
                         
                         
                           
                             
                               a 
                               21 
                             
                           
                           
                             
                               a 
                               22 
                             
                           
                           
                             
                               b 
                               2 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     B 
                     = 
                     
                       [ 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     C 
                     = 
                     
                       [ 
                       
                         
                           c 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     Thus, the order of the state variable is 3, which is the sum of 2 as the model order and 1 as a value taking into consideration the dead time. 
     Moreover, in the case where the dead time of the input u is 2 seconds and the cycle of k is 1 second, the model can be expressed such that, like the equation (30) given below, the value of the input u is stored in the third component of the state variable, and further stored in the fourth component in the next cycle and then shifted to the first row and the second row. 
     
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         
                           Ax 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         + 
                         
                           Bu 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       = 
                       
                         Cx 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       x 
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               
                                 x 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 x 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     A 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               a 
                               11 
                             
                           
                           
                             
                               a 
                               12 
                             
                           
                           
                             0 
                           
                           
                             
                               b 
                               1 
                             
                           
                         
                         
                           
                             
                               a 
                               21 
                             
                           
                           
                             
                               a 
                               22 
                             
                           
                           
                             0 
                           
                           
                             
                               b 
                               2 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     B 
                     = 
                     
                       [ 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             
                               
                                 
                                   1 
                                 
                               
                               
                                 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     C 
                     = 
                     
                       [ 
                       
                         
                           c 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     In the example of the equation (30), the order of the state variable is 4, which is the sum of 2 as the model order, and 2 as a value taking into consideration the dead time. 
     By the analogy with the above discussion, it is understood that the relation n=n d1 +d t1 +n d2 +d t2  holds in the present embodiment. 
     All examples and conditional language provided herein are intended for the pedagogical purpose of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention has been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.