209

Chapter 9

Computer Control of Air Conditioning The purpose of computer control of an air conditioning system is to minimise energy consumption for air conditioning of occupied spaces within an appropriate comfort range, to achieve safe operation and to make an easier maintenance of air conditioning components with an economically justifiable installation. Compared with conventional automatic control, computer control brings higher reliability and versatility, makes it possible to predict future conditions for better control and keeps extensive records to expedite supervision of complicated systems.

It is important, however, to remember that the optimum design of an air conditioning system should be made in combination with the optimum control of system operation. In other words, the total system should be designed so that the comfortable environmental spaces can be realised by operating the smallest system at the highest efficiency with the lowest consumption of energy.

Instead of describing the hardware of a computer control system, this chapter refers briefly to the conceptual background of software used in the computer control of air conditioning.

9.1. A SYSTEM MODEL FOR COMPUTER CONTROL OF AIR CONDITIONING

In a general sense, the computer referred to is a digital computer. It is necessary for engineers to set up system models of air conditioning components and various circuits as discussed in Chapter 8 System Simulation of Air Conditioning. The system model for computer control is, however, naturally different from the system model for simulation. Whereas the system simulation requires the mathematical expression of characteristics of subsystems to be as accurate as possible, the computer used for control programs is generally of mini size for which simpler equations are considered more suitable.

Suppose that the control system for a cooling coil as shown in Fig. 9.1 has an electronic controller which controls the flow rate of the inlet water to the coil by regulating the motorised valve with a signal given by the thermostat located at the exit of coil. The system model for simulating the situation around the coil may be set up by attempting to express the relationships between the inlet and outlet air temperature, inlet and outlet water temperature and flow rates of water and air. Figure 9.2 represents the control system replaced by computer control, where the

210

Fig. 9.1. Electronic control of flow rate of coil.

computer calculates the necessary water flow rate to the coil by a signal transmitted from the temperature sensor and delivers a command to the motorised valve so that the opening ratio can be adjusted to allow for the necessary water flow rate. This calculation routine must be simple, preferably expressed by a linear relationship. For example, suppose that the necessary water flow rate at time n, Lw(n) (kgs-1), may be expressed by the linear form as:

)()()()()()( a2w21w12a21a1w ncLnθbnθbnθanθanL ++++= (9.1)

where La(n) = air flow rate through coil (kgs-1); θa1(n), θa2(n) = inlet and outlet air temperature respectively (°C); θw1(n), θw2(n) = inlet and outlet water temperature (°C) and a1, a2, b1, b2, c are constants.

Fig. 9.2. Computer control of flow rate of coil.

211

The constants in eqn. (9.1) can be determined from the past operation data stored in the file of the computer. Then, the opening ratio of the motorised valve to give the necessary water flow rate can be computed with a predetermined relationship as:

)(f wLp = (9.2)

where p =the opening ratio of valve. The final operation to move the valve is made by converting a digital signal into an analog signal at the converter.

In general eqn. (9.2) is not linear. In the case of actual control, however, the incremental change in the opening ratio against the incremental change in the outlet air temperature is important. Then eqns. (9.1) and (9.2) may be combined to give:

)]()1([)()1( 2a2a2 nθnθanpnp −+=−+ (9.3)

When θw1, θw2, θa1, La do not change from time n to n + 1, the linear relationship as expressed by eqn. (9.3) may be valid with reasonable accuracy.

Receiving a command to set outlet air temperature θa2(n + 1) from elsewhere, the computer only ought to be executed to calculate eqn. (9.3) for regulating the water flow rate.

9.2. METHOD OF OPTIMISATION IN THE CONTROL

For optimisation in the control of an air conditioning system one must define the evaluation functions which ensure optimisation. The evaluation functions may be expressed as:

),,(f 21 xxE ii = (9.4)

where Ei = variables of evaluation, x1, x2,... = parameters to be optimised. Then to achieve optimisation, it is necessary to find out the values of x1, x2,...for optimising the value of Ei.

For example, E1 may be taken as energy consumption for a day, E2 room air temperature at any time of occupancy and so on. Since there are several variables to be evaluated overall, it is not so easy to find out the values of parameters to be optimised.

There are also many constraints which confine the parameters to be varied within a certain range. In this sense the parameters themselves may be considered as evaluation variables of higher priority in terms of the computation algorithm.

Nakahara et al. [9.1] stated that to minimise energy consumption was a primary variable of evaluation and the effective temperature of room air was a primary constraint in their design of an air conditioning system with computer control. It may be understood that the effective temperature of a space resulted from the

212

control can be considered as a variable for evaluation of higher priority than minimisation of energy consumption. It is always important to define the evaluation functions for planning effective computer control of air conditioning systems.

9.3. CONTROL OF START AND STOP OF AIR CONDITIONING COMPONENTS

If the perimeter zone of the room space is heated or cooled by fan-coil units, the question arises as to when the fan-coil units must be started prior to the time of

Fig. 9.3. The performance characteristics of fan-coil start-up optimisation for

pre-heating [9.1].

213

occupancy. This is an especially important problem in the control of air conditioning on intermittent operation if energy consumption is to be minimised.

Nakahara et al. used the following equation to determine the optimum starting time ts of fan-coil units:

)]1()([ L0s −+−= jPjEktt (9.5)

where t0 = time when occupancy starts, E(j) = predicted heat load from tc to 11a.m., P(j − 1) = penalty function, parameter j identifies the day in question and (j − 1) the previous day, kL = constant.

)](30[)](30[)](30[{),()( F2r2a1

11

c

nθknθknθknjCjE

tn−+−+−=

= (9.6)

where tc = starting time of recording the trend of outside air temperature θa(n), room air temperature θr(n) and floor slab temperature θF(n), C(j, n) = coefficient determined from the learning process based on the past data associated with the difference between predicted and real heat load of the previous day, k1, k2, k3 = constants determined from learning process. The so-called learning process may be defined as the process by which the computer acquires data, uses the data for prediction, modifies the data if the data used was inadequate and finds the correct data for control. Essentially it is a repetition of iteration and generally refers to finding the constant values in hypothetical formulas.

An example of the performance data taken at the Osaka Obayashi Building is shown in Fig. 9.3.

9.4. CONTROL OF OUTSIDE AIR INTAKE

Since heating and cooling loads associated with outside air intake are so great in air conditioning it is well worthwhile attempting to control the amount of outside air intake on a reasonable basis. Introduced here is a very effective example of controlling outside air intake achieved by Nakahara et al. [9.1] in a large office building as cited previously. There are two different criteria to be considered in controlling outside air intake; one is to let in outside air as a heat source when the room requires cooling in winter or intermediate seasons and the other is to reduce the rate of outside air intake as much as possible to the limit that CO2 concentration in the room would not exceed the threshold value. The former is rather easy to do and the latter is quite unique and interesting.

214

Fig. 9.4. Prediction of carbon dioxide gas concentration and outside air damper action

at sampling time n [9.1].

The equation for predicting the CO2 concentration of room air is given as:

)1()(Δ)1(exp1)()( a −

−−−+=

nQnkt

VnQnCnC

[ ])1()1(Δ)1(exp a −−−

−−+ nCnCt

VnQ

　 (9.7)

where C(n), Ca(n) = CO2 concentration of room air and outside air respectively at time n (ppm), Q(n – 1) = rate of outside air intake (m3h-1), V = air volume in the interior space (m3), k(n) = generation rate of CO2 within the building (cm3h-1) and ∆t = sampling time interval ( = 5min).

Control of outside air intake is made in such a way that when CO2 concentration is lower than 1000 ppm (warning value), the outside air (OA) damper is set at the position corresponding to the predicted C(n) from eqn. (9.7) and when the predicted C(n) might exceed 3000 ppm (threshold value), the OA damper is wide open immediately to dilute the room air. The characteristics of the OA damper opening are shown in Fig. 9.4.

215

9.5. PREDICTION CONTROL

Prediction control of air conditioning is different from real-time control. In real-time control used in the field of process industries, the computer acquires the process data in real time, processes the data using the predefined procedures, issues various kinds of commands to the object process and then controls it. For example, the target of maintaining a constant temperature of a space may be realised by a control command to make rise or fall of the temperature continuously given in real time to the object process when the actual temperature is going down or up to the target temperature.

This concept, so-called feedback control or real-time control, is often used in computer control of air conditioning systems. There are, however, those cases where a satisfactory control command for a future point of time may not be obtained only with the information at the concurrent time. In other words, it is likely to occur when the control command of real-time control fails to act fast enough for satisfactory operation, or where real-time control requires large-scale devices if it is to act in time. It may be called prediction control when the heat load of tomorrow is predicted and control is simultaneously made by using various data obtained today. As the state of the process in the future is generally unknown at the time of control, it must be predicted by executing some calculations and then issuing a control command on line based on the prediction. For using computerised prediction control, the following factors must be predetermined [9.2].

1. What is to be predicted? ... Object of prediction. 2. How far in future to be predicted? ... Range of prediction. 3. When is it to be predicted? ... Time of prediction. 4. What data can be used? ... Inputs for prediction. 5. For what control is the prediction to be made? ... Control target. 6. What accuracy is required? ... Accuracy of prediction. 7. To what degree does an operator take part in control? ... Control level.

In addition, the learning process is important for prediction control. The deeper the operation experience, the clearer the operation characteristics of various devices and the thermal response characteristics of building structure will become. These characteristics can be theoretically analysed to some degree, but theoretical strictness tends to make complication of models. It may be considered more practical, therefore, to have some appropriate constants substituted into certain simplified equations for setting up control models. The learning process mainly aims at obtaining these appropriate constants during the period of trial operation.

Besides these data and algorithms directly required for actual control, some fundamental studies for the above must be made and always referred to as off-line information. Figures 9.5 and 9.6 show the points of the above description.

216

Fig. 9.5. Profiles of load and disturbance [9.2]

Fig. 9.6. General flow chart of prediction control [9.2].

217

Prediction control is considered effective in minimising energy consumption in a heat recovery system combined with a heat storage tank. Especially in winter, it is necessary to predict the future heating load profile of 24 or 48 hours in advance and to store the optimum amount of heat within the storage tanks. If this predicted amount of heat storage is equal to the shaded area as shown in Fig. 9.7, this amount is considered optimum. There are several computation methods for load prediction and a regression model is suggested in this scheme. Briefly, this method is such that the heating and cooling loads are regressively analysed with parameters of inside and outside conditions to be specified in the preceding period and then a prediction model for heating and cooling loads can be made.

Fig. 9.7. Total heating and cooling loads in winter [9.2]. Time in day hours.

The measurable variables for this model are defined as follows: y(n) = hourly

mean value of heating load from time t = (n − 1) ∆t to n ∆t, x1(n), x2(n), x3(n),... = hourly mean values of outside air temperature, outside air humidity, solar radiation, electric power consumption by illumination, electric power consumption by business machines and heat generated by occupant persons per unit area and other parameters from time t = (n−1) ∆t to n ∆t respectively.

Here, new variables as hourly increments of the above variables are introduced, viz.:

for k =1, 2, 3, … (9.8)

An unmeasurable variable β0 must be defined to express the amount of stored energy in the building structure.

Incremental heating load Y(n) may be considered linear in relation to the variables, Xk(n) and β0, to be expressed as:

)1()()()1()()(−−=

−−=nxnxnX

nynynY

kkk

218

)()()()()( 3322110 nenXβnXβnXββnY +++++= (9.9)

where β1, β2, β3,... are regression coefficients. A variable e(n) means an error term to be added because the objective variable

Y(n) cannot be explained exactly by the measured variables X1(n), X2(n),.... The values of these variables measured every hour from the beginning to the end of the air-conditioning period are substituted into eqn. (9.9) and then the following relations are obtained:

)()()()()(

)2()2()2()2()2()1()1()1()1()1(

)()()()()(

3322110

3322110

3322110

3322110

jnejnXβjnXβjnXββjnY

nenXβnXβnXββnYnenXβnXβnXββnY

nenXβnXβnXββnY

−++−+−+−+=−

−++−+−+−+=−−++−+−+−+=−

+++++=

(9.10)

Equation (9.10) can be rewritten with vector matrix notation as follows:

e . XY += β (9.11)

Where

−

−−

=

)(

)2()1(

)(

jnY

nYnYnY

Y

−−−

−−−−−−

=

)()()(

)2()2()2()1()1()1(

)()()(

21

21

21

21

jnXjnXjnY

nXnXnYnXnXnYnXnXnY

X

=

jβ βββ

2

1

0

β

−

−−

=

)(

)2()1(

)(

jne

nenene

e

The square error matrix et･e can be derived from eqn. (9.11) as:

ββββ

ββtttt

t

. X.XYXXYY Y.] . X[XY . ] X.[Ye .e+−−=

−−=

2t

t

(9.12)

Differentiating eqn. (9.12) with respect to the matrix [β] and equating it to zero, the optimum coefficient [ β

] of the prediction model can be obtained as:

219

Y] . [X . X].[X -1 ttβ =

(9.13)

Substituting eqn. (9.13) into eqn. (9.9), the following prediction model is established:

+++= )(X)(X)( 22110 nβnββnY (9.14)

Substituting the incremental values of predicted weather data and the present data of inside conditions into eqn. (9.14), the incremental values of heating and cooling loads can be obtained. Then the load profile for the next day can be predicted on line for making control commands. The optimal coefficients may vary among four seasons and they must be frequently reviewed and updated.

220

Appendix Solution of the problem in page 208. Calculation Sequence for n=8 Total step Calc Sequence θ r (n) θ w1 (n) H c (n) H s (n) θ s (n) θ H1 (n) θ H2 (n) H H (n) H A (n)

1 Initial guess 18.0 27.0 1,900 02 Step 1 eq.(8.67) 18.0 27.0 459 1,900 03 Step 2 eq.(8.68) 18.0 27.0 459 1,900 25.8 04 Assumption: θH1 (n ) = θ s (n ) 18.0 27.0 459 1,900 25.8 25.8 05 Step 3 eq.(8.69) 18.0 27.0 459 1,900 25.8 25.8 20.3 06 Step 4 eq.(8.70) 18.0 27.0 459 1,092 25.8 25.8 20.3 07 Step 5 Iteration 18.0 25.8 1,092 0

8~1819 Step 5 converged ( θw1 (n ) ≈ θ s (n ) ) 18.0 26.4 483 1,177 26.4 26.4 20.5 020 Step 6 eq.(8.71) 16.4 26.4 483 1,177 26.4 26.4 20.5 021 Step 8 Use auxiliary heater eq.(8.72) 16.4 26.4 483 1,177 26.4 26.4 20.5 1,960 022 Step 9 eq.(8.73) 16.4 26.4 483 1,177 26.4 26.4 20.5 1,960 78323 Step 10 eq.(8.74) 16.4 26.4 483 1,177 26.4 30.3 20.5 1,960 78324 Step 3 eq.(8.69) 16.4 26.4 483 1,177 26.4 30.3 20.6 1,960 78325 Step 4 eq.(8.70) 16.4 26.4 483 1,944 26.4 30.3 20.6 1,960 78326 Step 6 eq.(8.71) 18.0 26.4 483 1,944 26.4 30.3 20.6 1,960 783

27~4950 Step 6 eq.(8.71) 18.0 26.4 483 1,956 26.4 31.9 22.1 1,960 1,088

iterate the calculation until θw1(n ) converges

iterate the calculation until θ r(n ) converges

Summary of Otput Data

n θ r (n) θ w1 (n) H c (n) H s (n) θ s (n) θ H1 (n) θ H2 (n) H H (n) H A (n)

8 18.0 - - 1,900 27.0 - - - -9 18.0 26.4 483 1,956 26.4 31.9 22.1 1,960 1,08810 18.3 26.1 1,368 1,706 26.1 26.1 20.4 1,560 011 18.1 27.0 2,303 1,224 27.0 27.0 20.9 1,166 012 19.4 28.6 3,387 1,473 28.6 28.6 21.3 762 0

1,956 1,706 1,224 1,4731,960

1,560 1,166 762

18.0 18.3 18.1 19.4

26.4 26.1 27.0 28.6

05001,0001,5002,0002,5003,0003,5004,000

048

121620242832

9 10 11 12

Tem

pera

ture

[ºC]

Storage tank water temperature θs Room temperature θr

Collected solar energy Hc Space heating load HH

n =

Colle

cted

sola

r ene

rgy

[W]

Spac

e he

atin

g lo

ad [W

]