1. Introduction
Social expectations for the betterment of life standards lead to widespread use of air conditioners in buildings to improve the comfort level for occupants. Indoor air quality (IAQ) is becoming more vital in light of the fact that individuals spend more time inside buildings. On the other hand, there is trade off between the thermal comfort level of occupants and energy consumption. Around
of building energy is devoured by heating ventilation and air conditioning (HVAC) systems [
1]. The HVAC system utilizes a broad assortment of air conditioning systems. Among those, to achieve thermal comfort for occupants, a variable air volume (VAV) air conditioning system is considered with more energy efficiency [
2]. Researchers have carried out a large number of research works to reduce the energy consumption of HVAC while maintaining IAQ and comfort level.
In this paper, we analyzed the aforementioned problem for the specific scenario of VAV. A lumped parameter type model of multizone VAV is considered, and two control strategies, namely (a) sliding mode control (SMC) and (b) proportional integral derivative (PID) control, are designed. The inside temperature of zones is controlled by varying air flow via damper positions. The chilled mass water flow rate in the cooling coil is varied, and duct pressure is kept constant during the operation cycle. By using the VAV system, we can achieve good comfort levels and less energy consumption [
3]. In VAV air conditioning systems, the provided air is maintained at a fix temperature, and inside room temperatures are managed by manipulating the volume of air furnished to individual room. The return air and supply air are regulated in order to maintain static pressure in the duct. The static pressure in the duct is also controlled by varying fan speed in the air handling unit (AHU) [
4,
5,
6].
The advancement of precise and basic dynamic models for the VAV system is the most vital factor for proficient design. Dynamic models might be changed in structure (straightforward or complex), contingent upon the sort of energy administration capacities and the precision. However, from the functional perspective, inferring straightforward and exact models is of extraordinary significance. Robust sliding mode control (SMC) to increase energy efficiency for the air handling unit (AHU) was designed in [
7]. Indoor humidity and temperature were controlled by variation of air by fan speed and refrigerant velocity in the cooling coil. Indoor temperature and humidity dynamic response were modeled via state space modeling in [
8]. A two-zone model was presented to observe the dynamic behavior of the indoor environment. The ordinary differential equations representing the thermal behavior of zones were transformed into state space format by linear approximation. The authors in [
9] discussed a variable refrigerant flow (VRF) and VAV air conditioning combined control system approach. For this type of combined system, an online optimal control is presented. The results show that the suggested system consumes less energy. However, the hardware complexity due to the hybrid system makes maintenance a difficult task in the long run. An adaptive controller is designed for the decoupled HVAC system via the identification tool box in the system for the control system parameters’ enhancement [
10]. In [
11], the author developed feedback linearization control for VAV air conditioning systems.
An approach to address the baseline performance of the VAV system by characterizing the variations occurring in it was presented in [
12], where those variations in the system were identified and classified into different categories. The authors in [
13] presented a comprehensive review of two types of control strategies for temperature and humidity control. Firstly, a hardware change like additional dehumidifying in the current HVAC system was suggested. Secondly, simultaneous control of the temperature and humidity control algorithms was studied. In [
14], the authors presented and investigative work for multizone buildings in VAV static pressure control by statistically informed data. A control technique to lower the air flow rate in the VAV terminal unit for an office building was presented in [
15]. Minimum air was supplied to the terminal unit by keeping IAQ at an acceptable level. Modeling of an augmented HVAC system including CO2 concentration and its control strategies were presented in [
16]. The proposed augmented HVAC system was MIMO and had no relative degree problem; therefore, the dynamic extension algorithm can be employed, then a feedback linearization technique applied. A linear-quadratic regulator (LQR) was designed to optimize control performance and to stabilize the proposed HVAC system.
In [
17], VAV optimized control was presented, which utilized ventilation based on average time. The proposed strategy replaced the position of the VAV damper between fully closed and partially open when no cooling was required in a zone. The authors in [
18] presented a stepless variable speed drive that was applied in the chiller unit and fan coil of the VAV system. The results of the proposed study show a significant amount of decrease in energy consumption (4.5582 kWh to 2.888 kWh) by using a brushless direct current (DC) motor. At least four different types of strategies to control the VAV system were discussed in [
19]. Control Method ‘A’ used constant air intake and consumed more energy, but had a good comfort level; ‘B’ reduced energy consumption to
; ‘C’ produced up to
energy savings results; outdoor air flow combined with indoor temperature reset can achieve
of energy savings, named as Method ‘D’. Elman neural networks were used to predict the indoor air temperature of the VAV system in [
20]. The basic laws based on the pressure independent and pressure-dependent terminal unit of VAV were designed, then the Elman neural network with control was proposed. The authors in [
21] presented models of an air conditioning system, the fundamental components of which were a cooling tower, a water-water chiller and a reference building. The model of the cooling tower was validated by using exploratory information in a pilot plant. The principle objective was to execute an upgrading control methodology with a specific end goal to diminish both energy and water utilization.
Model predictive control (MPC) is also a popular technique used in VAV air conditioning systems. In [
22], the authors presented a typical word reference and scientific categorization that gave a shared classification to all the building disciplines engaged with building plan and control. Besides, the principle extent of this paper was to characterize the MPC, detailing the structure and basically discussing the results of various existing MPC calculations for building and HVAC framework administration. The authors in [
23] discussed an MPC-based nonlinear control of an air conditioning system for an office in building. Heating and cooling were simultaneously controlled in the office building. The gain linearity and bi-linearity concerned system based on MPC was presented in [
24]. Two main processes were discussed in this study, the bi-linearity of the input and output with uncertainty, as well as the gain nonlinearity of the damper system. In [
25], MPC was developed to reduce energy consumption by a multizone VAV air handling unit. In [
26], the authors exhibited an economic model-based MPC whose fundamental quality was the utilization of the day-ahead value (DAP) to anticipate the energy consumption related to the HVAC.
Health monitoring using a fuzzy neural network for the HVAC system was studied in [
27]. Fuzzy logic combined with neural networks was used for a health monitoring system (HMS) in the VAV unit to identify faulty operation of the system. The artificial neural network (ANN) technique was used to distinguish the type of faults in the system. Zijian and Qing in [
28] presented an event-based strategy for multiple rooms for an HVAC system for energy saving. The authors in [
29] presented a study to examine the distinctive control techniques for HVAC frameworks. The favorable circumstances and detriments of each control technique were talked about, and lastly, the fuzzy cognitive map (FCM) technique was presented as another procedure for HVAC frameworks.
Despite numerous examinations having been performed for dynamic modeling and control of VAV systems, its nonlinear dynamic investigation has not been considered in the past studies. With the existence of nonlinear sources and the multivariable model of VAV, where extraordinary parameters are associated with a complex relation, linear analysis fails to anticipate the phenomena. Furthermore, without a broad pre-learning of VAV system behavior against conceivable uncertainties, the application of the designed controllers may increase energy utilization with a disruptive variable response. Since the HVAC system is uncertainty based and highly nonlinear, SMC may potentially be the best choice because of its insensitive behavior towards disturbances and uncertainties.
The contribution of this paper is that a lumped parameter type nonlinear model of a VAV air conditioning system is examined within the sight of practical harmonic unsettling influences in dynamic state variables. Since the dynamic model of the VAV system is nonlinear, two control techniques, namely (a) sliding mode control and (b) PID control, are developed. The aim is to build accurate and efficient models that can save energy. The temperature setpoint for each zone is achieved by manipulating the position of the supply air damper. The chilled water flow rate in the cooling coil is used to control the temperature of supply air. Two desired commands including a sinusoidal wave form and the sequence of steps are used as a setpoint to ensure robust tracking by the controller. Both models were developed with MATLAB codes, and comparisons will be made on the basis of performance deviations from setpoints and the response to changes in the systems. Furthermore, the setpoint of Zone 1 is different from that of Zone 2, which shows no dynamic coupling loop effect between the zones’ supply air temperature.
The system description of the VAV system and its mathematical modeling are described in
Section 2. Control laws are adopted in
Section 3, and results are presented in
Section 4. Finally, the conclusion is drawn in
Section 5.
4. Results
The tracking objective for both strategies, PID and SMC, is studied in this section. For the temperature setpoint of Zone 1 and Zone 2, two practical waveforms including sinusoidal and the combination of steps were considered; presented in
Figure 5.
Figure 5a,c is the temperature setpoint for Zone 1 and
Figure 5b,d the temperature setpoint for Zone 2. The setpoints were assumed according to weather conditions in summer having a higher outside temperature. The designed strategies were applicable for all types of weather conditions.
Figure 6 shows the tracking result by the PID and SMC of the Zone 1 sinusoidal temperature setpoint. In the magnified figure, it is obvious that the PID shows more overshoot in the beginning and also does not completely track the setpoint; whereas, SMC is tracking the setpoint effectively with negligible overshoot and the steady state. The performance of both controllers for the Zone 2 sinusoidal setpoint is presented in
Figure 7. SMC shows a robust behavior while tracking the target, whereas PID lags in accurate tracking of the sinusoidal reference.
Figure 8 shows the combination of steps setpoint for Zone 1 temperature. Here, PID shows more overshoot at all step changes in the temperature setpoints, while SMC shows less overshoot in the beginning. Furthermore, its is clear from the zoomed part that SMC shows a negligible settling time. For Zone 2, different magnitudes of the combinations of steps were applied, as shown in
Figure 9. Again, SMC showed a better tracking result, while clearly, PID gave the maximum overshoot and settling time. The reason behind the inefficiency of the PID controller is because these controllers are not efficient for nonlinear systems with uncertainties, as compared to SMC; also, HVAC systems are highly nonlinear and influenced by uncertainties because of parametric variations and external disturbances. Furthermore, PID does not handle abrupt changes in the setpoint, and it is also not a robust controller; therefore, it shows more overshoot and the steady state for all of the setpoints. Since the temperature in the duct was constant and the temperature of supply air was controlled by the cooling water flow rate in the coil, the change in temperature of the supply air and cold water by PID and SMC was also analyzed.
Figure 10a shows
by the PID controller for the sinusoidal reference of Zone 1 and Zone 2, and the same
supplied by SMC is represented in
Figure 10b. SMC showed continuous variations and a smooth supply of the air because temperature setpoint was varying for both zones continuously, whereas PID shows lower variations and cannot track the setpoint effectively. The output water temperature from the cooling coil was also analyzed to check its performance. The inlet water temperature
was set to 7
C, since any lower water temperature than this could cause freezing problems in the coil. Output water temperature
from the cooling coil by PID is presented in
Figure 10c, and that for SMC is presented in
Figure 10d, which shows the normal operation of the coil.
Similarly, the air supply
for the combination of steps temperature setpoint to Zone 1 and Zone 2 by PID and SMC is presented in
Figure 11a,b respectively. Since variations were continuously occurring in the setpoint, SMC handled these variations more effectively than PID while maintaining the required amount of cold supply air to both zones. PID again lagged in the required amount of air supply. Water output
from the cooling coil by PID and SMC for the combination of steps reference is presented in
Figure 11c,d. Again, the temperature of the outlet water showed the normal operations of the system.
To analyze controller performance by SMC and PID for sinusoidal reference temperature the setpoint and combinations of steps, we have four cases for three manipulated variables.
Figure 12a shows
(flow rate of cold supply air to Zone 1),
Figure 12b shows
(flow rate of cold supply air to Zone 2) and
(flow rate of cold water) is shown in
Figure 12c for the PID controller having a sinusoidal reference.
The control effort of SMC on the same reference in
Figure 13a shows
;
Figure 13b shows
; and
Figure 13c shows
. By comparing the control effort for PID and SMC, it is obvious that SMC was responding according to the abrupt variations in setpoints, whereas PID was not responding according to the variations in setpoint temperature, and this is the reason that PID was showing more overshoot and steady state error for all of the setpoints.
The combination of steps reference for the PID control effort is presented in
Figure 14a for
, in
Figure 14b for
and
in
Figure 14c.
The respective SMC control effort is presented in
Figure 15a for
, in
Figure 15b for
and
in
Figure 15c. The air supply to zones was maintained by dampers, and from the results, it is clear that flow rate variations matched with the variations in the temperature setpoint of the respective zone. Once again, SMC outperformed the PID in the control action.
The performance index is a common criteria to measure the performance of the system and is adopted to focus on essential system particulars. The system is considered as a perfect control system, when the index reaches the minimum values on selected settings. Four types of performance indices are used to analyze the controllers’ performance.
Integral time absolute error (ITAE).
Integral of absolute error (IAE).
Integral of squared error (ISE).
Integral time squared error (ITSE).
Table 5 shows the numerical values calculated by the performance index of SMC and PID controllers. Values of
,
and
for the combination of steps and sine wave reference show that SMC had the minimum values for all four types of errors as compared to PID.