Proceedings of the 2 0 1 IEEE international Conference on Control Applications September 5-7,2001 Mexico City, Mexico
Decoupled Control of Temperature and Relative Humidity using a Variable-Air-VolumeHVAC System and Non-interacting Control Carlos Rentel-GBmez and Miguel VClez-Reyes Electrical & Computer Engineering department University of Puerto Rico, Mayaguez Campus P.O. Box 9042, Mayaguez, Puerto Rico 00681-9042 Tel. +1-787-245-3821,FAX +I-787-831-7564 Email:
[email protected] Abstract-- In this paper, we develop a Nonlinear Noninteracting Control System for temperature and relative humidity in a thermal-space conditioned by a variable-airvolume (VAV) heating, ventilating, and air conditioning (WAC) system. In some industrial processes it is desirable to be able to control temperature and relative humidity independently and accurately. When the controller does not take into account the coupling dynamics between these variables, it is impossible to set one without affecting the other, therefore the importance of decoupling techniques to acbieve accurate control. We demonstrate how decoupled control of temperature and relative humidity is possible using a multivariable cascade control with two loops. The inner-loop is the non-interacting control law used for decoupling, and the outer-loop is a PD controller used for stabilization and control. Simulations are presented at the end of the paper in order to validate the theoretical results. Znder terms-Non-interacting humidity.
I.
control, temperature, relative
INTRODUCTION
Temperature and relative humidity are among the most important thermodynamic variables in commercial and industrial air conditioning and process control. These two variables influence the rate of chemical and biochemical reactions, the rate of crystallization and the density of chemical solutions, the corrosion of metals, the generation of static electricity, the manufacturing of printed circuit boards (PCB) in test chambers, and many other processes and applications [ 1],[2]. HVAC controllers have always been subject of interest among researchers and engineers, mainly due to the unsatisfactory performance of classical controllers in terms of energy efficiency. There are applications however, in which the main objective is to be able to set the output variables at precise values regardless of energy consumption. The main contribution of this paper is the application of non-interacting control in order to decouple temperature and relative humidity in a thermal-space. Once decoupling is achieved, any outer-loop controller can be use for the accurate setting of the output values.
0-7803-6733-2/01/$10.00 Q 2001 IEEE
The paper is organized as follows. Section I1 introduces the mathematical model of the VAV-HVAC system and thermal space. Section I11 presents the design of the Noninteracting controller. Section IV shows the closed-loop simulation results, and finally section V presents the conclusion of this paper.
SPACE MODEL 11. VAV-HVAC AND THERMAL The model used in this paper was presented in [3]. A block diagram of the VAV-HVAC and thermal-space system is shown in Figure.1. It comprises a heat exchanger, a circulating air fan, thermal-space (single-zone), connecting ductwork, dampers and mixing air components. Air is circulating continuously through the system and gets conditioned in the heat exchanger unit. The conditioned air is forced into the thermal-space by the circulating air fan in order to offset the effects of external and internal thermal loads. The control of temperature in the thermal-space is carried out by means of changes in the mass flow rate of supply air or by changes in the flow rate of chilled water supplied to the heat exchanger. The main purpose of the VAV-HVAC system is to control temperature, yet it is going to be used €or the decoupled control of relative humidity as well using the simultaneous variation of chilled water and supply-air flow rates. The differential equations describing the dynamics of this system can be derived from energy conservation principles. A simple procedure to model the heat-transferphenomena taking place in an air conditioning system is by analogy with RC electric circuits. The temperature variable is analog to voltage, and heat flow is analog to current. The thermal-space is modeled by means of thermal capacitors and resistors, and the whole system is analyzed utilizing the well-known voltage and current laws of electric circuits. The dynamics of thermal-space humidity are derived following mass conservation principles. The final model obtained is characterized by the following differential equations [4]
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The mathematical model in (1) characterizes the dynamics of absolute humidity in the thermal-space ( W 3 ) A relation between W, and the desired relative humidity is needed. Absolute humidity is all the moisture present in a given quantity of dry air, it can be expressed as pounds of water vapor per pound of dry air (lbdlbm). Relative humidity on the other hand indicates the amount of moisture in percentage form actually present in the air compared to the maximum amount of humidity that the air could hold under the same environmental conditions. When air contains all the moisture it can hold at a given temperature and pressure, it is saturated and it is said to have 100%r.h.
Claside
U
:
An empirical relation between absolute and relative humidity is given by the following approximate expression based on data from the Psychrometric chart
Figure 1. VAV-HVAC System block diagram.
--dT3 - 60f (T, - T 3 ) - dt
+
V, 1 O.25pV,cp
-=dT2 dt
60hf- f (w2 - w 3 ) + CPVS
60f (T3 - T 2 ) + (0.2360f (To -T3 'he
'he
@,(%)=5OOOW, -1.3881; + l o 7
vhe-
p
where Qr (%) is the relative humidity and is the drybulb temperature in OF. Equation (2) is valid around an operating point of = 75°F and W, = 0.007IbmJlbm.
1-
--60hwf (0.25W0 + o.75W3 - W2 )- 6 ~ 0 0 gPm -
(2)
(1)
Relative humidity variation in terms of temperature is
@p 'he
For the purpose of control design, the VAV-HVAC system is better described in state-space form. Let u,=J u2=gpm, X I = Qr(%), x2=T2, and x3=T3. The state-space representation is obtained by combining (l), (2) and (3).
where h, - Enthalpy of liquid water WO- Humidity ratio of outdoor air hfg- Enthalpy of water vapor V,, - Volume of heat exchanger W, - Absolute Humidity of supply air W3- Absolute humidity of thermal space cp- Specific heat of air
The final form is
TO- Temperature of outdoor air
M O- Moisture load Q, - Sensible heat load
where
T2 - Temperature of supply air T3 - Temperature of thermal space
V, - Volume of thermal space p - Air mass density f- Volumetric flow rate of air gpm - Flow rate of chilled water
f,and g,. i, j = 1,2,3are given by
The following assumptions were made in the derivation of this model: (i) ideal gas behavior, (ii) perfect mixing, (iii) constant-pressure process, (iv) negligible wall and thermal storage, (v) negligible thermal losses between components, (vi) negligible infiltration and exfiltration effects, and (vii) negligible transient effects in the flow-splitter and mixer.
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b(x) =
A(x) is the decoupling matrix and v is the new input (for definition and calculation procedure of the decoupling matrix A(x ) and the Non-interacting control law see [4]). The non-interacting control problem is solvable if and only if the Decoupling matrix A(x) is nonsingular.
and
Pl = 60/Vh, P2= 60(0.25)/Vh,
a; = 6 0 / V , a2= 60h,, l(c,V,) a, = l/(CPVS) a 4
p3 = 60h, l
