In this paper, a typical zone is chosen. Its volume is 36 m³. Two people with 150 W

load and two lamps with load 500 W are considered. Based on energy and mass balance governing equations of the zone, the equation [5] can be obtained

ρ a C p a V d T z d t = m a C p a ( T s − T z ) + K F ( T o − T z ) + q ( t ) (1)

where its parameters is showed in Table 1.

The Laplace transform of the Equation (1) is:

T z ( s ) = G z ( s ) [ λ T ( s ) + γ T o ( s ) + q ( s ) ] (2)

where G z ( s ) = 1 ρ a C p a V s + m a C p a + K F = 1 45.23 s + 60.24 , λ = m a C p a , γ = K F ,

the diagram of the zone is showed in Figure 2.

Heat transfer from the fan motor to air is considered, and causes air temperature to increase about 1˚C - 2˚C normally. The transfer function of the fan is a first

order function: G F ( s ) = 1 s + 1 . The sensor measure the actual temperature of

the zone, and transfer to the controller for the control of the temperature, its

transfer function is written as G S ( s ) = 1 s + 1 .

In this study, the winter operation season is chosen. Heating coil is water to air heat exchanger, which provides conditioned air for ventilation purposes in buildings. In order to build the simplified model of the heat coil, it has been assumed that the mass flow rate of the water inside the coil and the temperature of the air out from the coil are constants, the balance equation can be obtained:

C a h d T c o d t = f s w ρ w C p w ( T w i − T w o ) + ( U A ) a h ( T o − T c o ) + f s a ρ a C p a ( T m − T c o ) (3)

where the information of the parameters is described in Table 2.

The Laplace transform of the Equation (3) is expressed by

T c o ( s ) = G A ( s ) [ α T w i ( s ) + ( U A ) a h T o ( s ) + β T m ( s ) ] (4)

where G A ( s ) = 1 C a h s + [ ( U A ) a h + β ] = 1 4.5 s + 0.28 .

Similarly, the transfer function of the humidifier can be expressed by

G p ( s ) = 1 0.63 s + 0.21 .

In this paper, the values of the parameters in the HVAC system are showed in Table 3.

In the temperature control of the zone, a first order ESO and second order controller of the LADRC are chosen, ESO is expressed by

{ z ˙ 1 = z 2 + β 1 ( − z 1 + y ) + b 0 u z ˙ 2 = β 2 ( − z 1 + y ) (5)

where u and y are the input and output respectively, β 1 and β 2 are the gains of the observer, z 1 and z 2 are the estimators of the output y and the whole disturbances, second order controller is expressed by

{ u = ( − z 2 + u 0 ) / b 0 u 0 = k p ( T r − z 1 ) (6)

The diagram of the LADRC is showed in Figure 3 and Figure 4.

In practice, fuzzy control [17] is adopted in many process controls. The steady-state error of the output is a problem in traditional fuzzy controller. Hence, the error integral is added to the fuzzy controller in this study, the fuzzy controller is called integral-fuzzy controller.

1) Design of the fuzzy controller

The inputs in the integral-fuzzy controller of the HVAC system are the error e and its change-in-error d e / d t of return air temperature T_z and the set point of the temperature in the zone. The scale of the error e ∈ [ − 2 , 2 ] (˚C), the linguistic value of e is expressed by {neglarge, negsmall, zero, possmall, poslarge} = {NB, NS, ZE, PS, PB}, membership function of the e is triangle; the scale of d e / d t ∈ [ − 0.5 , 0.5 ] , the linguistic values of the d e / d t is expressed by {neglarge, negsmall, zero, possmall, poslarge} = {NB, NS, ZE, PS, PB}, membership function of the d e / d t is triangle, the linguistic value of the output u is the following {close, minor-open, half-open, small-open, big-open} = {CB, CS, M, OS, OB}, membership function of the u is trapezoid, the membership functions are drew in Table 4.

Rule base of the fuzzy controller is showed in Table 5.

2) Integral of the error

In order to eliminate the steady-state error in the control of the HVAC system, the integral of the error is chosen as a part of the controller, the diagram of the integral-fuzzy controller is showed in Figure 5.

Supposed that the temperature outside is 0˚C, set point of the temperature of the zone is 20˚C, simulation modules are established in Matlab/Simulink environment, include the traditional PID controller, integral-fuzzy controller and LADRC. When the HVAC system approaches steady state, there are disturbances outside, such as open the door and windows, and so on. A step disturbance is added to the system in t = 500 s in order to check the rejection disturbance capabilities. The tuning parameters of the controllers based on the experience is adapted, the values of the parameters is showed in Table 6.

Simulation result is showed in Figure 6, comparisons in overshot. Rising time and the rising time in step disturbance are showed in Table 7.