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Heating, ventilation, and air conditioning (HVAC) system is significant to the energy efficiency in buildings. In this paper, temperature control of HVAC system is studied in winter operation season. The physical model of the zone, the fan, the heating coil and sensor are built. HVAC is a non-linear, strong disturbance and coupling system. Linear active-rejection-disturbance-control is an appreciate control algorithm which can adapt to less information, strong-disturbance influence, and has relative-fixed structure and simple tuning process of the controller parameters. Active-rejection-disturbance-control of the HVAC system is proposed. Simulation in Matlab/Simulink was done. Simulation results show that linear active-rejection-disturbance-control was prior to PID and integral-fuzzy controllers in rising time, overshoot and response time of step disturbance. The study can provide fundamental basis for the control of the air-condition system with strong-disturbance and high-precision needed.

HVAC (heating, ventilation, and air conditioning, HVAC) is a typical complex system with non-linear, strong coupling and strong disturbance influence. The study on HVAC system is significant for the energy efficiency in buildings, and its control strategies are the major concern [

Active-rejection-disturbance-control (ADRC) algorithm was proposed by Han Jingqing in 1998 [

Original ADRC consists of non-linear ESO and non-linear controller, and has strong robustness and disturbance rejection capabilities. However, the development of ADRC is limited by the complicated structure and difficult parameters tuning. In 2001, non-linear ADRC is simplified to linear active rejection disturbance control (LADRC) by Gao [

In the paper, the physical model of HVAC system is built, including the zone, fan, heating coil, duct and sensor. LADRC with strong disturbance rejection capabilities, self-decoupling and simple structure is applied in temperature control of the HVAC system. The design of LADRC in the system is proposed. Simulation in Matlab/Simulink is done. Simulation results are compared with PID and Integral-Fuzzy control. Simulation results show that LADRC has priority to PID and integral-Fuzzy control in rising time, overshooting and rejecting the step disturbance. The study can provide fundamental basis for high-precision requirement, rejection strong disturbance and reduce energy consumption of HVAC system.

In this paper, the temperature control of the HVAC system in winter operation season is chosen, when the disturbances of the system appear, in order to keep the temperature of the zone in 20˚C, actuator adjusts the water supply of internal coil of air handling unit. HVAC model is composed of zone, fan, heating coil and temperature sensor, the structural diagram is showed in

In this paper, a typical zone is chosen. Its volume is 36 m^{3}. 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 [

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

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

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

Parameters | Unit |
---|---|

r_{a} density of air | kg/m^{3} |

C_{pa} specific heat of air | kJ/(kg・˚C) |

V volume of the zone | m^{3} |

T_{z} Temperature of the zone | ˚C |

m_{a} mass flow rate of the air stream | kg/s |

T_{s} supply temperature | ˚C |

K heat transfer coefficient in the ambient | W/(m^{2}・˚C) |

F contact area of the wall and zone | m^{2} |

T_{o} temperature outside | ˚C |

q(t) heat gains from occupants, and light | W |

Parameters | Unit |
---|---|

C_{ah} overall thermal capacitance of the air handling unit | kJ/C |

T_{co} temperature of the air out from the coil | ˚C |

f_{sw} water flow rate in coil | m^{3}/s |

ρ_{w} density of water | kg/m^{3} |

C_{pw} specific heat of water | kJ/(kg・˚C) |

T_{wi} supply water temperature | ˚C |

(UA)_{ah} overall transmittance area factor of the air handling unit | kJ/(s・C) |

f_{sa} volume flow rate of the supply air | m^{3}/s |

T_{m} temperature in to the coil | ˚C |

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

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

In practice, fuzzy control [

C_{ah} = 4.5 kJ/C | C_{pa} = 1.005 kJ/(kg・˚C) | F=30 m^{2} |
---|---|---|

f_{sa}=0.192m^{3}/s | C_{pw} = 4.1868 kJ/kg・˚C | ρ_{w} = 988 kg/m^{3} |

m_{a} = 0.24 kg/s | K = 2 W/(m^{2}・˚C) | ρ_{a} = 1.25 kg/m^{3} |

V = 36 m^{3} | (UA)_{ah} = 0.04 kJ/(s・C) |

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

Rule base of the fuzzy controller is showed in

Variables | Membership functions |
---|---|

e | |

de/dt | |

u |

u | e | |||||
---|---|---|---|---|---|---|

NB | NS | ZE | PS | PB | ||

de/dt | NB | OB | OB | OB | OS | CB |

NS | OB | OS | OS | M | CB | |

ZE | OB | OS | M | CS | CB | |

PS | OB | M | CS | CS | CB | |

PB | OB | CS | CS | CS | CB |

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

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

Simulation result is showed in

Controller | Parameters | |||
---|---|---|---|---|

PID | k_{p} | k_{i} | k_{d} | |

2.3 | 0.15 | 6 | ||

LADRC | b_{0} | k_{p} | β_{1} | β_{2 } |

2.8 | 0.053 | 15 | 380 | |

Integral-Fuzzy controller | f_{kp} | f_{kd} | f_{ki} | f_{p} |

2.20 | 0.70 | 0.20 | 0.5 |

Controller | Rising time (s) | Overshot (˚C) | Rising time of the step disturbance (s) |
---|---|---|---|

PID | 240 | 1.04 | 180 |

Integral-Fuzzy controller | 340 | 0.27 | 235 |

LADRC | 150 | 0 | 80 |

In the temperature control of the HVAC system, three approaches, including PID control, integral-fuzzy control and LADRC, are designed. Simulation results show that the LADRC obtains a good performance in the rising time and no overshooting; when the step disturbance is added to the system in t = 500 s, the LADRC can quickly and smoothly reach the steady state in 80 s and shows good disturbance rejection capability. In the temperature control of the HVAC system, the LADRC represents in rising time, strong disturbance rejection and high precision. The study provides fundamental basis for the control of the HVAC system and energy conservation.

The project is supported by the Science & Technology Program of Beijing Municipal Commission of Education (No. KM201611417007) and the National Natural Science Foundation of China (No. 51578065).

Huang, C.-E., Li, C.W. and Ma, X.J. (2018) Active-Disturbance- Rejection-Control for Temperature Control of the HVAC System. Intelligent Control and Automation, 9, 1-9. https://doi.org/10.4236/ica.2018.91001