*4.3. Fuzzy Control Scheme*

A two-dimensional fuzzy controller is established based on the fuzzy logic theory [34] and applied to the HVAC automatic control system. The signal obtained by the sensor is compared with the set value to obtain the deviation e and the deviation change rate ec, and then the deviation e and deviation change rate *ec* are taken as two inputs of the fuzzy controller. The fuzzy quantization process is performed to obtain the fuzzy variables *E* and *EC*. According to fuzzy rules, the fuzzy decision is made to obtain a fuzzy control quantity *U*. Finally, the actual control output is obtained through the defuzzification and the proportional transformation. For the LFF control strategy, the input of fuzzy control is the cooling load demand. The difference between the input load and the set load is the deviation *e*. The change rate of the load versus time is the deviation change rate *ec*. *e* and *ec* are the double inputs of the fuzzy control system and the output value *u* is the pump speed control value.

The sub-fuzzy system was selected to represent the control level. As shown in Equations (11)–(13).

$$E(\varepsilon) \in \{\text{NB, NM, NS, ZO, PS, PM, PB}\} \tag{11}$$

$$EC(cc) \in \{NB, NM, NS, ZO, PS, PM, PB\} \tag{12}$$

#### *U(u)*∈*{NB, NM, NS, ZO, PS, PM, PB}* (13)

*E*: The universe of *E* is {−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6}. The minimum value of the load is 0 kW and the maximum value is 68.6 kW. In order to convert *e* into the domain of *E*, we need to multiply the coefficient ke. The value of ke is determined to be 0.175.

*EC*: The universe of *EC* is {−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6}. The minimum value of load change rate is −27.2 and the maximum value is 27.2. The universe [−6,6] that converts *ec* to *EC* needs to be multiplied by the coefficient kec, the value of kec is determined to be 0.221.

*U*: The universe of *u* and *U* are both [0,1].

Fuzzy sets: Each input parameter is represented by a fuzzy set Ak with a membership function μ, see Equations (14) and (15). The most commonly used triangular membership function was used in this study [35].

$$Ak = \langle (i, \,\mu(i)) \rangle \tag{14}$$

$$\mu(i) \in [0, 1] \tag{15}$$

#### *4.4. Optimization of Pumps and Units Control*

The control strategy of the pump is as follows: when the required flow of the system is less than or equal to half of the maximum flow, one pump is individually frequency-controlled and the other is not operated. If the required flow is greater than half of the maximum flow, one pump provides half the flow at full load and the other pump provides the remaining flow by frequency conversion. Specific control strategies for pumps is shown in Table 2. The fuzzy control output value *u* is between 0 and 1. The pump operates at a frequency and the operating frequency is proportional to the control signal.


**Table 2.** Pump control strategy.

In order to ensure the normal operation of the system, one unit is always running and the other unit is controlled by the set start-stop time. The start and stop time means that the unit is turned on within the set time, while the unit is turned o ff outside the set time. For example, a start-stop time of 0.5 means that the unit's on-time and o ff-time are each half of the total operating time. The specific operation control strategy of the unit is shown in Table 3.

**Table 3.** Heat units control strategy.

