Design of Fuzzy-PI Decoupling Controller for the Temperature and Humidity Process in HVAC System

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Design of Fuzzy-PI Decoupling Controller for the Temperature and Humidity Process in HVAC System

Trinh Luong Mien

University of Transport and Communications Falculty of Electrical and Electronic Engineering Hanoi, Vietnam

Abstract: Ensuring the comfortable air quality for people, using the heating, ventilation and air conditioning (HVAC) system, in the commercial center buildings or underground infrastructures is extremely important. This is directly related to the design of the controllers for two channels of the air conditioning: temperature and humidity of the indoor air. Firstly, the analysis and building an interactive nonlinear mathematical model of the indoor air is presented in this paper. Then, the article refers to methods of design the traditional PI controller, PI controller combined with decoupled controller and PI controller with self-tuning parameter based on fuzzy logic principle combined with decoupled controller for the heating and humidifying processes of the indoor air. Finally, the proposed controlles for temperature and humidity process is simulatated and tested on Matlab.

Keywords: Temperature And Humidity; Fuzzy Logic Control; Decoupling Control; PID; Self-Tunning Fuzzy PID; HVAC.


Symbol Unit Description

a kg/m3 Air density

Cp J/kgoC Heat capacity of air

Vi m3 Volume of the room

Tp ,Tq ,To oC Temp. after heating/cooling coil, temp.

after humidifier, and outdoor temperature

s Time

Fp m3/s Flowrate of hot/cold water

Aw m2 Area of the wall

Uw W/m2. oC Overall heat transfer coefficient Kb W/moC Thermal conductivity of the brick dw m Thickness of the wall

ha W/moC Convection heat transfer coefficient of air

Ep kJ/kg Vapour enthalpy

fa m3/s Flow rate of the supplied air

Fq m3/s Flowrate of steam

Hp , Hq , Ho % Humidity after heating/cooling coil, humi.

after humidifier, and outdoor humidity

Gij , i,j=1,2 Laplace transfer function

h , t Channel coupling coefficient

It , Ih mA Controlled current for temp., hum. valves

T*, H* Setpoint temperature, humidity

ij Delay time


HVAC Heating, ventilating, air conditioning PI, PID Propotinal, integral, derivative control NL Negative large

NS Negative small

ZE Zero

PS Positive small

PL Positive large

SM Small,

ME Medium

LA Large

QL Quite large

VL Very large

ET,DET Error and derivative error of temperature EH,DEH Error and derivative error of humidity

PT,IT Fuzzy output for tunning-parameters of PI temperature PH,IH Fuzzy output for tunning-parameters of PI humidity


    The strong growth in the civil indutrial construction and transport infrastructure leading to the introduction of more high buildings, commercial centers, many tunnels, undergrounds … where are required to be equiped with the HVAC system [1]. HVAC systems ensure to supply and maintain the comfortable indoor air for occupants with the desired air temperature, humidity and quality. The comfortable air inside these buidlings depends on the acurate temperature and relative humidity process control in HVAC system [2-4]. The comfortable temperature and humidity range are changing following on seasons and different countries [3]. Moreover, conventional HVAC systems consume approximate half of the total electric energy that is largely depend upon fossil fuel in modern cities [5]. This causes polluted atmophere and increasing in greenhouse gases emissions from HVAC applications. Therefore, the demand for the comfortable indoor air is in conflict with the call for reduction of energy consumption and environmental protection. Besides the problem of energy consumption, sometimes the incorrect operation of the HVAC systems may not help to improve indoor air [6-7]. Hence, it is a necessary to design control temperature and humidity strategies in order to improve the performance of HVAC systems. The control systems for indoor building air can be mainly classified into two categories according to the approaches employed: the conventional controllers and computational intelligence techniques. The proportional integrate derivative (PID) controller is employed the popular in conventional HVAC systems, because of the simpleness, easy installation and use [8-9]. However, PID is not solved completely nonlinear plant, resisting noise weakly, and not satifying demand about the indoor air quality. Intelligent controller, fuzzy logic or neural networks have

    recently become practical as a fast, accurate and flexible tool to HVAC control strategy modeling, simulation and design [10- 14]. With the designed controller, the performance of a HVAC system can be significantly improved [4,15]. Moreover, there are several disadvantages that limit the performance of current control technologies, such as: the on/off control causes the system switching working state too frequently; and neural

      1. Mathematical model of the indoor air temperature

        The indoor air temperature is affected by the outside air temperature, initial indoor air temperature, volume of the room, heat loss from the wall, hot/cold water flowrate and steam flowrate as presented in Fig. 1. Thus, the indoor air temperature can be expressed as follow:

        networks are hard to put into application; controller is so

        complex. The results of applying the seft-tuning intelligent

        T ( ) Tp ( ) Tq ( )


        PID, fuzzy adaptive PID, adaptive predictive decoupling control, fuzzy control combined with neural network for the HVAC system, in papers [16-21], are to impove performance

        The main temperature Tp is supplied by the hot/cold water flowrate through the heating/cooling coil. Hence, it can be expressed as follows based on energy conservation principle:

        of the HVAC system. But the nonlinear model and the


        r C V = a

        F (t )- U A [T (t )- T (t )]


        interaction between temperature and humidity process were not

        a p i dt p p

        w w p o

        regarded completly. Hence, it is worth developing temperature and humidity process controllers of HVAC system for the purpose of impoving the indoor air quality and energy

        The overall heat transfer coefficient for the wall Uw when the individual convection heat transfer coefficients for fluid on each side of the wall is equal, can be calculated as [3,6-7]:


        In this paper, by combining advantages of the self-turing parameters fuzzy PI control and decoupling control mothod,

        U = ( 2 + dw )- 1



        ha Kb


        new temperature and humidity controller are developed and their performances as well as their potentials in HVAC control

        By using Laplace transform, after changing equation (2)

        can be described as follows:

        systems are discussed. The proposed control system is finally

        r aCpVi

        [ s + 1]T (s) =

        a p

        F (s) + T (s)


        tested and evaluated by the simulation on Matlab.

        U A p

        U A p o


    w w w w

    Assume To=0 and consider effect of the time delay of the heat transfer process in the room, such as tp, then (5) can be simply transferred as follows:

    We study a room, equiped with the base HVAC system

    which has the heater by hot/cold water and the humidifier by

    G = Tp



    – qtps

    k e

    k e


    ; t =

    r aCpVi , k =

    a p


    steam, suc as Fig.1. Depend on the mixed air temperature

    11 F (s)

    t s + 1

    tp U A tp U A

    p tp w w w w

    after the filter, the outside air is heating or cooling by the heating/cooling coil. Then, the outside air can be humidified by the steam humidifier, and then it is supplied into the room by the supply fan. The exhaust air is conducted out the room

    The indoor air temperature is also affected by the steam humidifier. Calculating the same as the main temperature, the temperature Tq causes by the steam humidifier, is expressed as

    T (s) k e- qtqs V a a

    by the return fan. The heating/cooling coil gives the indoor air

    G = q =

    tq ; t

    = i , k

    = q t


    a thermal-humid energy P by changing the hot/cold water

    12 F (s)

    t s + 1

    tq f tq

    f r E

    flowrate Fp through the HWR/CHR control valve. The steam

    q tq

    a a a p

    humidifier also gives the indoor air a thermal-humid energy Q by varying the steam flowrate Fq through the control steam valve. This system uses the temperature & humidity controller to adjusting the position of hot/cold water, steam valves, and

      1. Mathematical model of the indoor air humidity

        The indoor air humidity is directly affected by the steam humidifier, initial indoor air humidity, heating/cooling coil as in Fig.1. The indoor air humidity can be expressed as follows:

        then can change flowrate Fp, Fq following equation:

        H ( ) Hp ( ) Hq ( )


        P = p.Fp; Q = q.Fq (1)

        The main indoor air humidity Hq is produced by adjusting the position of the steam valve. So that it can be described as follows based on the energy conservation principle:

        r V E

        dHq = a

        F (t )- r

        f E (H

        – H )


        a i p dt

        q q a a p q o

        Assume Ho=0 and consider the time delay of the humidity spread process in the room, such as hq, then (9) can be simply transferred in Laplace – domain, as follows:

        H (s)

        k e- qhqs V a q

        G = q =

        hq ; t hq = i , khq = (10)

        22 F (s)

        t s + 1

        fa far a Ep

        q hq

        The indoor air humidity is also affected by the heating/cooling coil. So that humidity Hp can be presented as:

        G = H p (s)


        – qhps

        k e

        k e


        ; t hp =

        r aCpVi

        , k = a pah (11)



        21 F (s)

        t s + 1

        Uw Aw

        Uw Aw

        Fig. 1. Schematic diagram of the indoor air temperature & humidity

        control processes in HVAC system

        p hp

      2. Dynamic model of control valve

    Most of the control valves are usually designed so that the flowrate through the valve is a nearly linear function of the signal to the valve actuator. Therefore, a first-order transfer function is an adequate model [8,14] for the dynamic characteristic of the electric-pneumatic valve in this project:

    3.1. The PI controllers design

    The purpose of this PI controllers design is determined the initial paramaters for Fuzzy-PI controllers (kP0, kI0) for two temperature & humidity feedback control loop. If neglecting interaction between temperature and humidity, the transfer function of the temperature control loop object as:

    Fp (s)

    kvt e- qvt s

    Fq (s)

    kvhe- qvhs

    0.42e- 6.2s

    Gvt =


    I (s) t

    ; Gvh =

    s + 1


    I (s) t

    s + 1


    GT = Gvt G11 =

    (562.24s + 1)(1.5s + 1)


    t vt h vh

    2.4. The mathematical model of the control object in the indoor air temperature and humidity control system

    The transfer function of the humidity control loop object:

    0.52e- 17.2s

    When considering interaction between temperature and

    GH = GvhG22 =

    (1600s + 1)(2.5s + 1)


    humidity, the indoor air temperature and humidity processes is

    Applied Skogestads approximation method, we have:

    a two-input two-output model. The matrix transfer of control object in the indoor air temperature and humidity control

    0.42e- 6.95s

    GT = =



    system, when adding the model of the control valve, is given 562.99s + 1 (562.99s + 1)(6.95s + 1)

    as follows:

    0.52e- 18.45s


    T Gvt G11

    GvhG12 Fp

    GH = 1601.25s + 1 = (1601.25s + 1)(18.45s + 1)


    H Gvt G21

    GvhG22 Fq


    Arcoding to the optimal module principle [22], the

    In this paper, we assume that the length of the testing room is 4m, width is 2m, heigh is 3m; the thickness of the brick wall

    parameters kP0, kI0 can be determined as follows:

    kT k H

    R0 (s) = kT + I 0 , R0 (s) = k H + I 0


    is 0.3m; and the desired indoor temperature is 20oC. Therefore

    Vi=24m3, Aw=36m2, dw=0.3m, fa=0.015m3/s. From [3-4] we recieve values as follows: Ep=2538kJ/kg, Cp=1005J/kg.oC,

    T P0 s H P0 s

    kT = 562.99 = 96.44, kT = 1 = 0.17

    Kb=0.6W/m.oC, a=1.2kg/m3, ha=10W/m.oC. And then we can calculate: Uw=1.43, ktp=0.019, tp=562.24, ktq=0.009,


    k H =



    I 0

    = 83.45, k H =



    = 0.05

    =1600, k =0.006, =562.24, k =0.022,

    =1600, We

    P0 2×0.52×18.45

    I 0 2×0.52×18.45

    tq hp hp hq hq

    assume: t=0.4, h=0.3,tp=5.6, tq=6.4, hp=1.7, hq=16, kvt=22, vt=1.5, vt=0.6, kvh=23.75, vh=2.5, vh=1.2


    The temperature and humidity processes in the room are complicated: when making change the humidity then the temperature is also changing and on contrary while adjusting the temperature then humidity is also affected. So that , it is necessary to adding decoupling controllers in order to remove the relations between these two channels.

    In HVAC system, it is common traditional PID controllers. However, the parameters of PID controllers is offten fixed in all operating time. This reduces the quality of control system when the process requires operating in different modes, or when the object parameters change, or impact noise. Meanwhile, the fuzzy logic has advantages in controlling uncertain objects and lets take advantage of experience operating the system.

    Therefore, two PI controllers with seft-tunning parameters based on fuzzy logic calculations is proposed for two feedback control loop of the temperature & humidity processes. The structure of the Fuzzy-PI controllers decoupling controller for the temperature and humidity control in HVAC system is proposed as in Fig.2. The RT, RH are Fuzzy-PI controllers

    Fig. 2. Structure of Fuzzy-PI decoupling controller for HVAC system

      1. The decoupling controllers design

        Arcoding to the decoupling control principle, the decoupler RTH is designed to cancel H21 arising from process interaction between UT and H, and the decoupler RHT is designed to cancel T12 arising from process interaction between UH and T. In order to cancelling the influence between temperature and humidity chanels, output U21 & U12 need to satisfy conditions:

        (FPI); kP0, kI0 are initial parameters of PI controller; kP, kI are

        Gvt G21U11 + GvhG22U21 = 0, GvhG12U22 + GvtG11U12 = 0


        seft-tunning parameters based on fuzzy logic calculations

        Hence we obtain the transfer function of the decouplers:

        (FC). The RTH, RHT are the decoupling controllers, designed

        G (s)G (s)

        G (s)G (s)

        based on the decoupling control principle.

        R (s) = – vn 21 , R

        (s) = – va 12






        va (s)G22

        (s) HT




        Using Skogestads approximation [22], the decoupling controllers have the following form:


    The simulation is carried out to analyse the performance of


    (s) = – 0.25(1601.25s + 1)(18.45s + 1) (562.99s + 1)(3.0s + 1)

    0.51(562.99s + 1)(6.95s + 1)


    three controllers for the humidity and temperature control loops in HVAC system: (1)- PI controller (PI), (2)- PI decoupling controller (PIdcp); (3)- fuzzy-PID decoupling

    RHT (s) = –

    (1601.25s + 1)(8.85s + 1)


    controller (FPIDdcp). The PI controller was designed in 3.1, The PI decoupling controller is composed of the decoupler in

      1. The fuzzy logic calculation blocks design

    Fuzzy logic calculations blocks (FC) have: two inputs – temperature/humidity error (ET or EH), derivative of temperature error (DET or DEH); two output is PT (or PH), IT (or IH) corresponding to the output value kPT, kIT (or kPH, kIH).

    Using membership functions are shaped triangular for all variables, fuzzied for all input variables by 5 fuzzy sets {NL (Negative Large), NS (Negative Small), ZE (ZEro), PS (Positive Small), PL (Positive Large)}, fuzzied for all output variables by 5 fuzzy sets {SM (SMall), ME (MEdium), LA (LArge), QL (Quite Large), VL (Very Large)}. The physical domain of the input & output variables are determined as: ET[-50,50], DET[-5,5], PT[0,100], IT[0,0.5];

    PH[0,95], IH[0,0.5], EH[-95,95], DEH[-10,10].

    Depending on the characteristics of the indoor air temperature (or humidity) control process and the PID control principle in order to improve quality control for system (see Tab.1), we define the 25 base fuzzy rules as Tab.2.

    Tab.1. The effect of kP, kI tunning

    Closed- loop respond

    Rise time

    Settling time

    Over- shoot

    Steady state error






    Small increase





    Small decrease



    Large decrease


    Tab.2. The base fuzzy rule of kPT, kIT (or kPH, kIH)

    PT (or PH) IT (or IH)

    ET (or EH)







    (or DEH)































    Using the Max-Min composition rule and the cetroid defuzzification method, we can obtain the clear output value of FCs: kPT, kIT for temperature loop and kPH, kIH for humidity loop. Then, the self-tuning parameters of PI controllers can be calculated by equations:

    3.2 and the PI controller in 3.1. The fuzzy-PID decoupling controller consists of the decoupler in 3.2 and the PI controller with seft-tunning parameters (the fuzzy logic calculation block was designed in 3.3, the PI initial parameters in 3.1). The simulations have been taken on the platform of Matlab as describled in Fig.3. The simulating results are used to indicate the controllers performance including several indexes: overshoot, steady time, steady error, coupling effect.

    The simulation was tested with initial indoor air situations: 150C, 10% and assume required humidity & temperature

    Fig. 3. Simulating the temperature & humidity control processes in Matlab

    The simulation was tested with initial indoor air situations: 150C, 10%; Assume required indoor air temperature increased from 35oC up 55oC at 200 seconds, and humidity varied from 90% down to 70% at 400 seconds (Fig.4). The response curves of the indoor air temperature & humidity control

    k*T = kT kT , k*T = kT kT


    processes with 3 controllers is presented in Fig.4.

    P P0 P I I 0 I

    k*H = k H k H , k*H = k H k H


    P P0 P I I 0 I



    60 T [oC]

    50 1 4

    45 2

    40 3









    The simulation results have proved the proposed fuzzy-PI decoupling controller has excellent performance on efficient auto tuning of the PI parameters only when needed: fast

    6 response speed; small overshoot; small steady error; and stability and adaptability response to uncertain factors. In other words the fuzzy-PI decoupling controller suitbles for controlling simultaneously the indoor air temperatue and humidity processes in HVAC system. The fuzzy-PI decoupling controller can improve the indoor air quality, increase the process efficiency and bring economic benefits to the user.



    0 100 200 300 400 500 600



    80 H [%]

    70 1 3 7

    60 5






    0 100 200 300 400 500 600

    Fig. 4. Response curves of temperature & humidity control with 3 cotrollers: 4-T*, 4-H*, 1-PI, 2-Pidcp, 3-FPIdcp, 6-varying H* affect the temperature response, 7-varying T* effect the humidity response.

    The performance of the proposed controllers (PI, PIdcp, FPIdcp) is presented in Tab.3.

    Tab.3. The proposed controllers performance

    Control process

    Control- ler

    Over- shoot (%)

    Steady time (s)

    Steady error

    Coupling effect (%)

    Temp- erature












    ~ 0
















    ~ 0




    The simulating results of the proposed temperature and humidity controllers show that the FPIdcp has the best control quality: no overshoot, eliminating steady error, the smallest steady time and eliminating neraly the effect of the coupling channels disturbaces when it was compared to other controllers: PI, PIdcp.

    Therefore, with the proposed FPIdcp controller, the indoor air quality can be well control since: PI controller is suitable for various control object including indoor climate factors control; the fuzzy logic calculation block for optimal PI parameters tuning to ensure adaptability to different situations; better PI control parameters selection can ensure the desired system output; the decoupling controllers eliminate the interaction between temperature & humidity processes.


The indoor air temperature and humidity control process was studied and presented in this paper. Based on the nonlinear model of the indoor air temperature and himidity, considering the influence of the coupling channels, three controllers (PI controller, PI decoupling controller, fuzzy-PI decoupling controller) were designed, simulated on Matlab.

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Trinh Luong Mien obtained his Ph D degree in automation and control of technological processes and manufactures at Moscow State University of Railway Engineering (MIIT) in Russia Federation in 2012.

Trinh Luong Mien is a lecturer at Faculty of Electrical and Electronic Engineering – University Transport & Communications in Vietnam since 2004. His main research is the development of intelligent control algorithms for the technological and manufacturing processes in industry and transportation based on fuzzy logic, neuron network, adaptive & optimal theory; study control algorithms & guarantee safe movement of the electrical train in ATP/ATO/ATS/ATC system of the urban railway; design of supervisory control and multi-channel data collection systems.

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