Advanced control strategies for heating, ventilation, air-conditioning, and refrigeration systems--an overview: Part I: hard control.
In large commercial and residential buildings, energy management control systems (EMCS) play a major role to maintain good control of temperature, human comfort, and overall operational and energy efficiency. In a typical situation, heating, ventilation, air-conditioning, and refrigeration (HVAC&R) systems provide a central air supply at a controlled temperature and a flow rate for heating or cooling a particular unit or zone or entire building complex. The two main requirements of any HVAC&R system is first to provide satisfactory indoor comfort (temperature and relative humidity) conditions to the building housing both humans and equipment and, at the same, time minimize the overall energy consumption. Another important requirement is to prevent the spread of any chemical or biological species from any point where these species are released to the rest of the building. The primary professional organization responsible for all activities of HVAC&R systems is the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), which is located in Atlanta, Georgia, USA, and has been engaged in publishing and updating industry-wide standard handbooks such as ASHRAE (2005, 2006, 2007, 2008). It has been reported that the energy consumption due to HVAC&R systems in commercial and industrial buildings constitutes nearly half of the total world energy consumption according to Payne (1984) and Imbabi (1990b).
The minimization of energy consumption and maximization of indoor user comfort can be combined into a single minimization problem by using the predicted mean value (PMV) and the predicted percentage dissatisfied (PPD) value and defining discomfort instead of comfort value as the square of the difference between set-point temperature and internal room temperature, normalized with respect to set-point temperature. Minimizing the discomfort value gives the optimal (maximum) comfort value given by Fanger (1972, 1984), ISO-1984 (1984), ISO-1995 (1995), ISO-2005 (2005), and Pargfrieder and Jorgl (2002). One of the earliest applications of automatic control is thermostatic control of a building, which is basically an on/off control. Some of the books and handbooks in the area of HVAC&R are Haines (1971, 1987), Hartman (1993), Rogers and Douglas (1993), Levenhagen and Spethmann (1993), Newman and Morris (1994), Levenhagen (1999), Underwood (1999), Hordeski (2001), Haines and Hittle (2003), Brumbaugh (2004a, 2004b, 2004c, 2005), Honeywell (1997), and McDowall (2009). A previous survey by Harrold and Lush (1988) examined HVAC&R controls as a part of larger building services and covered a variety of topics, including those relating to automatic controls. A recent review article by Wang and Ma (2008) published in HVAC&R Research took a different approach, focusing exclusively on supervisory and optimal control techniques arising in HVAC&R in building automation systems (BAS) and building energy management systems (BEMS). In particular, the review addressed various control methods, such as local or decentralized control (DC) with sequencing control, such as ON/OFF control; process control, such as proportional-integral-derivative (PID) control; and supervisory or centralized control (CC) with a model-based method (physical model, gray-box model, black-box model, hybrid model, etc.).
Further, various optimization techniques were discussed in this review by Wang and Ma (2008). From the perspective of the topics on energy, comfort, and control, a review was conducted in Dounis and Caraiscos (2009) of the work initially on conventional (optimal, predictive, and adaptive) control schemes and then the state-of-the art intelligent (neural, fuzzy, neuro-fuzzy, proportional-integral (PI)-fuzzy, adaptive fuzzy proportional-derivative (PD) and PID) control systems for improving the efficiency and indoor environment in buildings, with a particular emphasis on multi-agent control systems (MACS) with simulations using TRNSYS/MATLAB software. Also, see the previous literature review works by Dexter (1988), Kelly (1988), and Sane et al. (2006).
Overview and terminology: hard control (HC) and soft control (SC)
There are various ways of conducting an overview, such as a chronological--or topical--overview. The main purpose of this overview is to provide the reader with a summary of the recent results on the topic of control techniques for HVAC&R systems so that this forms a staging point for further research in the field. Thus, a topical survey based on various topics or control methodologies and within each topic is presented, and a chronological order of the published results follows. However, note that there are a number of situations involving multiple topics; the focus is on
1. HC, such as basic controls involving PID control, optimal control (Anderson and Moore 1990; Naidu 2003; Lewis et al. 2008), nonlinear control (Kristic et al. 1995), robust or H[infinity] control (Zhou and Doyle 1998), and adaptive control (Tao 2003);
2. SC, involving neural networks (NNs), fuzzy logic (FL), genetic algorithms (GAs), and other evolutionary methods (Jang et al. 1997; Tsoukalas and Uhrig 1997; Nguyen et al. 2003; Karray and De Silva 2004; Konar 2005; Kasabov 2007; Sumathi et al. 2008); and
3. hybrid control resulting from the fusion of SC and HC to achieve a better performance (Ovaska et al. 2002; Tettamanzi and Tomassini 2001; Konar 2005; Kasabov 2007; Sumathi etal. 2008).
It is to be noted that the new terminology, the "hard" in HC and "soft" in SC, has been used recently in the control systems community (Ovaska et al. 2002; Karray and De Silva 2004) and has nothing to do with the "hardware" and "software" that is generally used.
Modeling, testing, and validation
A generic piping/process and instrumentation diagram (P&ID) of a typical HVAC&R system available in Department of Energy (DOE) facilities is shown in Figure 1 (courtesy of Idaho National Lab). It shows three zones, two access areas, and the necessary instrumentation and control architecture.
[FIGURE 1 OMITTED]
In a typical HVAC&R system for large buildings, there are three subsystems: boiler and chiller, constituting a primary subsystem; heat pumps and airflow ductwork, called the distribution subsystem; and the subsystem consisting of the environmental zones; the whole configuration is also called a multi-zone space heating (MZSH) system (Zaheer-Uddin et al. 1993; Saboksayr et al. 1995). Here, using the principles of energy conservation and balance, a seventh-order, bilinear, state-space model for a two-zone space heating system was developed with
* seven state variables: boiler temperature, temperature of the evaporator for heat pump 1, temperature of the evaporator for heat pump 2, temperature of the condenser coil for heat pump 1, temperature of the condenser coil for heat pump 2, zone 1 temperature, and zone 2 temperature; * three output variables: boiler temperature, zone 1 temperature, and zone 2 temperature, * five control (input) variables: air flow rate for zone 1 controller 1, air flow rate for zone 2 controller 2, boiler fuel firing rate controller 3, input energy for heat pump 1 via controller 4, and input energy for heat pump 2 via controller 5, essentially grouped into three controllers.
In another detailed study by Zaheer-Uddin and Zheng (1994), as many as 328 nonlinear, time-varying equations were developed for the dynamic models for a two-zone variable airflow volume (VAV) system in terms of subsystem models for environmental zones, cooling and dehumidifier coil, variable air flow rates in the duct, fan motor, and chiller and storage tank, described by nine control input variables--six dampers (for zone 1, zone 2, fan, outdoor air, exhaust air, and recirculating air), fan and chiller energy inputs, and mass flow rate of chilled water to control the temperatures and humidity ratios in the two zones, discharge air conditions, chilled water temperature, outdoor and supply airflow rates, static pressure in the duct system, and fan speed. The transient analysis of the open-loop system performed on the linearized system showed the dynamics of the overall VAV system being composed a slow phenomenon due to the chiller-coil-zone thermal subsystem and a fast phenomenon due to the fan-airflow subsystem. This interaction of slow and fast phenomena gives rise to an interesting avenue for analysis and design of the system using the singular perturbation and time scales (SPaTS) methodology; surprisingly, no significant work has been done (except in Dexter 1988; Zaheer-Uddin and Patel 1995; Zaheer-Uddin and Zheng 2000) in this direction to apply the SPaTS methodology to HVAC&R systems, in spite of the attractive features of SPaTS in terms of order reduction and decoupling of slow and fast dynamics, with the rich literature in this field (see Naidu and Rao 1985; Kokotovic et al. 1986; Naidu 1988, 2002).
In modeling most HVAC&R systems, it was assumed that the system variables, such as temperature and air flow velocity, are not dependent on spatial coordinates within the thermal zone, leading to the lumped-parameter models. However, in reality, these variables, and hence the thermal comfort level, are not homogeneous within the zone/room. A more realistic model with spatial dependency within the room leading to the distributed-parameter model was developed in Liu and He (1994) based on non-isothermal airflow pattern showing downward deflection of a cool jet due to the balance between buoyancy and gravity forces. However, the optimal control settings for the system were obtained for steady-state operations only with the objective of maximizing the comfort level, not only at one point but at several working points within the room while minimizing the total power consumption, resulting in a more accurate prediction of thermal comfort level of a room.
Testing and validation
Issues relating to the optimal location of hardware components influencing the hydronic network design and thermal control task were studied by Franco et al. (2005) using a mathematical model for the thermal-hydraulic network consisting of the hardware elements of a control valve and two booster pumps, leading to the results that the network and the control system characteristics are strongly influenced by the location of the hardware components. The testing of various monitoring and control strategies on the existing buildings seems time consuming and expensive. Alternatively, studies by Imbabi (1990a, 1990b) using integral, reset, compensated, and optimized controllers concluded that the results of small-scale experimental mod els could be extended to full-scale real HVAC&R systems.
A simulator within MATLAB[C] SIMULINK[C] environment, including a building zone and HVAC&R plant emulating the environment of the real controller, was developed in Lahrech et al. (2002), linking the real and simulated conditions via mainly sensor side and actuator side interfaces. The simulated environment contained a building block, an HVAC&R system block, a "bench in" block, and a "bench out" block; the testing method validation was performed using two types of tests: open-loop tests (without a real controller) and closed-loop tests, showing good agreement between the measured and emulated testing methods for heating, fan coil, and chilled ceiling applications.
Dedicated software for HVAC&R systems
Several dedicated software packages have been developed over the years for simulating the buildings and energy usage; see, for example, BLAST (building loads analysis and system thermodynamics; MATLAB and SIMULINK are registered trademarks of The Mathworks, Inc., Natick, MA, USA), originally developed by University of Illinois at Ur bana Champaign (UIUC), Urbana, IL (Blast-UIUC 1983). BLAST features are now being incorporated into the DOE-2 of EnergyPlus. DOE-2 is a computer program that predicts energy usage and costs of a building given the description of the building and its HVAC&R equipment, besides other details. The DOE-2 software was developed by James J. Hirsch & Associates (JJH) in collaboration with Lawrence Berkeley National Laboratory (LBNL), with LBNL DOE-2 work performed mostly under funding from the United States DOE (USDOE; http://www.doe2.com). Also, see other programs such as HVACSIM+ (HVAC Simulation; HVACSIM 1986) and TRNSYS (Transient Energy System Simulation Tool; TRNSYS 1996). It is to be noted that BLAST and DOE-2 have more or less merged to form EnergyPlus (E+), combining the best features and capabilities of BLAST and DOE-2, and it is now more widely used among researchers and practitioners in the HVAC&R field, although DOE-2 is still available (Crawley et al. 2000).
CC and DC
There are two basic types of controls--local control for a single unit and supervisory control for managing several units or zones in a large building complex (Payne 1984; Zaheer-Uddin and Zheng 2000; Wang and Ma 2008). The function of the local controller is to ensure stability first and then to ensure good set-point tracking, where the supervisory control is in charge of coordinating various local controllers for the various subsystems and, at the same time, maintain the overall operation of the entire HVAC&R system.
The HVAC&R systems possess special characteristics of distribution networks with more or less identical basic modular structures for different zones or cells in the building, satisfy the local comfort requirements in each zone or cell, and make an idea candidate for implementation of DCs (Zaheer-Uddin 1992). However, an HVAC&R system has a CC scheme where a single zone temperature is controlled by three controllers: (i) damper controller C1 to regulate the rate of airflow to the zone with temperature Tz, (ii) valve controller C2 regulating the mass flow rate of chilled water (with temperature Ts) flowing in the coil, or (iii) a controller to regulate the input energy to the chiller (with temperature Tc) with three controllers each receiving feedback signals from all three temperature sensors. On the other hand, with three separate controllers each receiving a feedback signal from its related (or nearest) thermal sensor or control point, the HVAC&R system has a DC system.
With the objective of investigating the effect of replacing the rule-based control algorithm with one based on a combination of a building/system model with the optimal supervisory control algorithm by Zhang and Hanby (2008), a prototype building was considered, consisting of a ventilated photovoltaic array, solar air and water heating, a biomass-fired boiler, and a stratified thermal store with the objective of minimizing the net energy consumption by the building that resulted in the substantial improvement of overall system operation and performance. The performance of a central variable water volume (VWV) chiller system in HVAC was analyzed by Jin et al. (2007) with three optimal control strategies with respect to the supervisory control for the optimal resetting of the supply head of a secondary pump (called Delt-P), a supply chilled water temperature (SWT), and a combination of the previous two strategies.
PID control, gain scheduling, and state feedback
The PID controller is the most widely used controller in the industry. Basically, the PID actions relate to present (proportional), past (integral), and future (derivative). Although there are many improved methods of PI/PID controller design, the traditional Ziegler-Nichols (Z-N) techniques (Ziegler and Nichols 1942) are still being used by many HVAC&R control engineers. However, the Z-N method suffers from a long testing time and limited performance; hence, it is best used as a first cut for tuning PID controllers. There are a number of excellent books on this subject (see Astrom and Hagglund 1995, 2006; O'Dwyer 2003; Visioli 2006).
Early investigations using basic single-input-single-output (SISO) control methods, such as PID controllers, faced the problem of tuning the KP, KI, and KD parameters in addition to the inability to take into account the interactions between the various loops (Nesler and Stoecker 1984; Nesler 1986). A four-level HVAC&R control scheme was investigated in Dexter (1988), with the highest (fourth), or supervisory, level focusing on maintaining the desired levels of the internal temperature and relative humidity of the overall building; the next (third) level taking care of temperature and relative humidity of the air supplied by the HVAC&R plant; the second level assuming the responsibility of maintaining the desired performance of the plant actuators and local control loops; and, finally, the lowest (first) or local level taking care of maintaining the desired controller setting based on the system model. Problems associated with discrete-time simulation of an HVAC&R system with the four-level structure were investigated by Dexter (1988) with special reference to the selection of parameters and self-tuning of PID controllers using parameter estimator and control algorithm. The effects of disturbances on the overshoot and settling time using PID controllers were studied in Geng and Geary (1993), and it revealed that tuning rules based on the Z-N method (Ziegler and Nichols 1942) are valid for small normalized time delay and that this, combined with the normalized gain, can be used for further tuning PID controllers.
Deriving a dynamic model of an HVAC system consisting of a zone, heating coil, cooling and dehumidifying coil, humidifier, ductwork, fan, mixing box, and PID controller with the Z-N rule was obtained in Tashtoush et al. (2005) to account for disturbances and to reduce energy consumption and improve the quality of the indoor environment. Using recursive least squares (RLS) with exponential forgetting and model matching for a first-order, dead-time model, an adaptive PI controller was designed by Bai and Zhang (2007) with an automatic adjustment of controller parameters for an HVAC system, with simulations showing superior performance compared to the H[infinity] adaptive PI controller. Using a recursive least square (RLS) algorithm along with the z-domain fitting method by Bai et al. (2008) for estimating the parameters (such as time delay) of an air-conditioning (A/C) process, a Smith predictor was adopted to reduce the effects of the time delay, leading to a new self-tuning PI controller using the integral of time and absolute error (ITAE) with an experimental validation showing a better system performance compared to an adaptive PI controller.
Recent works by Bi et al. (2000) and Visioli (2006) show advanced controller auto-tuning strategies with successful application to both SISO and multi-input-multi-output (MIMO) systems, where decoupling control is used for MIMO systems. In particular, Bi et al. (2000) developed an auto-tuner with special features consisting of different tuning tests--relay plus step test and step test, different first- and second-order plant models with dead-time, and implementation with a commercial, internet-enabled distributed computer-controlled system featuring graphical user interface (GUI). Three control schemes--hot-gas by-pass scheme, cylinder unloading scheme, and suction-gas throttling scheme--Yaqub and Zubair (2001) were investigated for a hydro fluoro carbon (HFC)134 refrigeration system, and it was found that the cylinder-unloading scheme is the most suitable because of its higher coefficient of performance (COP). Several tuning methods, in general, for PID controllers (Kamimura et al. 2002) and, in particular, a tuning method (Ozawa et al. 2003) with constraints on control input for a single-zone environmental space cooling system, showed a particularly over damped response with no overshoot, thus pre venting the long oscillations when using integral squared time error criterion in the performance index.
Using some of the recent results in PID controllers involving Hurwitz polynomials to improve the performance and robustness, some simple and intuitive design tools are developed and applied to two examples on the temperature control of a VAV unit and evaporator super-heat control using an electronic expansion valve (Lim et al. 2009). A hybrid of mechanical and electronic controls for evaporator super-heat control was proposed by Elliott and Walton (2009) in terms of inner control for regulating the evaporator pressure and outer control to regulate evaporator super-heat, resulting in improved transient performance compared to mechanical valves, more robust performance to large changes in operating conditions and motor failure, and less actuator effort compared to electronic valves.
Considering the dynamics near an operating point, a simple linear model was obtained by Flesch and Normey-Rico (2010) for control of the output temperature of a calorimeter for evaluating the performance of refrigerant compressors, leading to the design of a dead-beat compensator (DBC).
Recently in Rasmussen and Alleyne (2010), vapor compression cycle of an A/C system was considered with an alternative local model network gain-scheduling strategy using Youla parameterization to improve stability and linear matrix inequalities (LMIs) for guaranteeing global asymptotic stability, resulting in a nonlinear controller that can "effectively regulate evaporator super-heat while meeting changing demands for cooling capacity with guaranteed closed-loop stability (p. 1224)."
State feedback control
This section includes the topics of controllability and observers as well as state feedback. Using a third-order, bilinear, single-zone HVAC&R model (with three states [temperature of supply air, temperature of thermal space, and humidity ratio of thermal space], two outputs [thermal space temperature and humidity ratio], and two controls [volumetric flow rate of air and flow rate of chilled water]), linearized around an operating point, an observer-based, disturbance rejection, state feedback, nonlinear controller for this bilinear model (Mohler 1991a, 1991b) was designed based on the Lyapunov approach involving the algebraic Riccati equation while estimating online the thermal loads acting as disturbances. It was found that the controller minimizes the effect of large thermal loads maintaining the comfort level in the thermal space. A multivariable controller was designed by Zaheer-Uddin (1993) to control boiler temperature and hot water temperature for a heating system for hot water and space heating using the pole placement technique (Patel and Munro 1982).
For a single-zone VAV HVAC&R nonlinear model described by three state variables (temperature of thermal space, humidity ratio of thermal space, and temperature of supply air), two control variables (volumetric flow rate of air and flow rate of chilled water), and two outputs (temperature and humidity ratio of thermal space), a state feedback controller was developed in Arguello-Serrano and Veclez-Reyes (1999) to maintain thermal comfort in the thermal space in the presence of time-varying thermal loads (disturbances) by first linearizing the model around an operating point and designing a state and thermal load observer, and then designing a disturbance-rejection state feedback controller based on Lyapunov stability and the algebraic Riccati equation. The methodology resulted in reducing the effect of thermal loads by extracting more heat from the thermal space, thereby reducing the supply air temperature.
Two control strategies of condenser super-heat regulation (CSR) and evaporator super-heat regulation (ESR) were examined in Yeh et al. (2009) for a cascade structure consisting of slow and fast dynamics due to vapor compression cycle and indoor dynamics. The two strategies were combined with an experimental setup to achieve both transient performance and steady-state power savings.
Distributed parameter control
Using the distributed parameter model in Liu and He (1994) for a room rather than a lumped parameter model to take care of the thermal comfort level at different locations within the room by describing the spatial distribution of air temperature and velocity at steady-state conditions, a recursive optimization algorithm was developed for a set of comfort indices at different locations within the room at steady-state conditions rather than using a dynamic model involving time and spatial coordinates.
First of all, in a recent editorial of HVAC&R Research publication by Radermacher and Abdelaziz (2008), it was clearly articulated that "optimization," a process or methodology, is to "provide a significant reduction in energy consumption and material utilization." Thus, it appears that out of all control techniques, optimal control took the lion's share of application to the HVAC&R field, which is not surprising due to the nature of optimization in terms of energy savings and human comfort. Keeping in view the chronological nature of the overview, what follows is divided into three subsections: early developments focusing on modeling and optimization (up to 1989), continuing developments (1990-1999), and recent developments focusing on experimentation and applications to specific real-world situations (2000-2010).
Early developments: up to 1989
One of the earliest applications of dynamic and static optimization (Kaya 1978; Hartman 1980; Kaya et al. 1982) was to find optimal control policies to minimize the overall energy expenditure and simultaneously control room temperature, room humidity, and outside wind velocity to keep the room at a comfort zone, as recommended by ASHRAE. A comparative study was made with conventional control methods consisting of a heating/cooling thermostat and humidistat, claiming energy savings of 38.5% with an optimal control strategy. A similar treatment was given by Nizet et al. (1984) by using the airflow rate as a control variable for a simplified model to minimize the total energy cost and thermal comfort penalty using discretization of the original continuous optimal control problem, and by solving the resulting problem using a conjugate gradient method (Fletcher 1980) to realize energy savings of 12% to 30% compared to the case without using the conjugate method.
A combination of PID, feed-forward, and optimal control for regulating the temperature within a thermal space was developed in Cherchas et al. (1985) to maintain a set-point value with a linear cost function. In particular, a mathematical model for a single environmental space was developed in terms of both exact and simplified equations, using the principles of conservation of mass, humidity, and energy (Borresen 1981). The model had as the two state variables a dry bulb temperature (T(t)) and a moisture content or humidity ratio (w(t)), and as the three control variables, it had an air inlet volumetric flow rate (f (t)) and a space-sensible load (q(t)) to control the temperature and a supply air humidity ratio (wi(t)) to control the moisture content. With a simple cost function in terms of f (t) and q(t), a feed-forward and feedback control algorithm was developed and implemented in discrete form. In a follow-up work by Townsend et al. (1986), for a single zone described by zone temperature and moisture content in the zone as the two state (output) variables, inlet supply air volumetric flow rate and heat input rate as the two control variables, and the objective function composed of energy cost, comfort, and start-up, an optimal bang-bang switching control strategy was obtained using the Pontryagin maximum principle (Kirk 1970; Naidu 2003), yielding lower operating costs compared to the previous work in Cherchas et al. (1985). An optimal control strategy using the Pontryagin maximum principle (Pontryagin et al. 1962) was applied to a heat pump system, when the storage capability was available and time-of-day energy incentives were offered by electrical utility company, using a single-zone model and a simple space load and cost function to be minimized as the cost of purchasing electrical energy (Rink et al. 1988), yielding extremal trajectories with one bang-bang interval and one singular interval. Also see the related works by Le et al. (1987) and Zaheer-Uddin (1989) for a more accurate single-zone model and Zaheer-Uddin (1991) for digital control. With a performance criterion to maximize human comfort and to minimize the energy and operating costs, a fuzzy optimal controller was developed by Shoureshi and Rahmani (1989).
Continuing developments: 1990-1999
A group of researchers (House etal. 1991) developed an optimal control methodology for a representative HVAC&R system. The procedure involved discretizing the continuous optimal control problem and was called the discrete time method (DTM). In particular, the temperatures within heat exchanger and thermal space were the two state variables, and heat input to heat exchanger and volumetric airflow rate were the two control variables. Assuming the system is initially at the steady-state condition, the performance criterion to be minimized was composed of five terms: disturbance rejection as a penalty for the system not at steady state, thermal comfort penalty, fuel usage, penalty for the fan associated with airflow rate, and the power required to operate the fan. For solving the optimal control problem, a sequential quadratic programming (SQP) was implemented with the DTM. It was found that with the bang-bang (like in a simple room thermostat), fuel is 49% higher than that with the optimal control. Further, using tge performance index in terms of a comfort penalty for deviations of the zone air temperature from the set-point value and the cost for energy consumption, an optimal control strategy is compared with a conventional control strategy for a two-zone building and HVAC&R system with two zone envelope temperatures as state variables and energy usage for cooling and heating coils. It was found by House and Smith (1995b) that there is a cost savings of 11% with the optimal strategy. Here, the optimal control was obtained by discretizing the continuous optimal control problem (Tseng and Arora 1989). Also see House and Smith (1995a) for the same problem treated using a systems approach, accommodating a variety of system conditions, constraints, and different set-points for different zones, resulting in energy savings of 24%.
The application of modern techniques, such as optimal and adaptive control, to HVAC&R systems was explored in Zaheer-Uddin (1993), which also included a very good literature review. Next, using the linearized model, which consisted of zone air temperature and zone air humidity ratio as the two state variables and mass flow rate of supply air as the control variable, the linear quadratic regulator (LQR) theory (Anderson and Moore 1971) was applied to regulate the temperature and humidity, at the same time rejecting any disturbances. For an HVAC&R system consisting of two chillers (one for direct chilling and the other ice-storage charging), a cooling tower, an air handler, a condenser and chilled water pumps, and an ice-storage tank, a comprehensive analysis of the optimal control was presented by Kintner-Meyer and Emery (1995) for minimizing the operating cost over a 24-hour period. The cost function consisted of the costs for electricity consumption and the demand charge, and the main result showed significant reduction in operating costs (compared to a conventional control scheme) due to "free cooling" through early morning ventilation and by shifting cooling loads from peak to off-peak hours. In another work by Zaheer-Uddin and Patel (1995), a nonlinear multi-zone environmental system was modeled as a linear reduced-order (second-order) model based on the fast (second-order) and slow (fifth-order) subsystems using SPaTS analysis (Naidu 1988; Kokotovic et al. 1986; Naidu 2002). A reduced-order fast model was retained by neglecting the slow subsystem, although in the normal SPaTS literature, the fast subsystem is neglected while retaining the slow subsystem and an optimal tracking control was designed for set-point changes. Two techniques of differential dynamic programming (DDP) and nonlinear programming (NLP) were compared as applied to three cases of optimal control of an HVAC&R system, described by temperature of air exiting the heat exchanger and temperature of thermal space being controlled as the two state variables, heat input to the system and air flow rate from outside as the two control variables, and the cost function. It was found that DDP was more efficient than NLP, although NLP is more robust (Kota et al. 1996). Using an autoregressive (AR) model with three input (manipulated) variables (opening of cooling water valve, heater current, and humidifier current) and two outputs (indoor temperature and humidity) for an HVAC&R system model, a new optimal preview control using linear quadratic Gaussian (LQG) optimal control with a feed-forward compensation (Stengel 1986) was implemented in Kasahara et al. (1998) to improve tracking and to suppress the interaction between different loops. An optimal control for HVAC&R and related systems include Zheng and Zaheer-Uddin's (1999) discharge air system (DAS), consisting of a cooling and de-humidifying coil, a chilled storage tank, and an electric coil for re-heating. Simulation results were compared with experimental data using optimal control strategies to step changes in set-points for the two cases of heating with temperature control and cooling with temperature and humidity control. The optimal cost function was formulated in terms of the discharge air temperature and its set-point as the state variable; and the mass flow rate of chilled water as the control variable for the heating case; discharge air temperature, discharge air humidity ratio, and their set-points as the state variables; and input energy to chiller, the mass flow rate of chilled water, and electric heater energy as the three control variables. Simulations using the numerical search (gradient) method (Mufti 1970) for optimal control showed smoother and rapid responses in discharge air temperature and air humidity ratio, while tracking performance showed significant improvement.
Recent developments: 2000-2010
For the time-scheduled operation of an HVAC&R system, optimal control strategies were developed in Zaheer-Uddin and Zheng (2000), using a two-zone VAV heating (VAVH) model consisting of a heat pump, a storage tank, water and airflow networks, and two environmental zones.
Here, the time schedule of the building operation was divided into three stages/modes: the setback mode between 5 PM and 7 AM of the next day, the start-up mode between 7 AM and 8 AM, and the working normal mode between 8 AM and 5 PM of the day, thus leading to the three-stage optimization control. Recognizing that the airflow subsystem is faster than the environmental zones (slow) subsystem, the optimal supervisory control problem was cast in the singularly perturbed structure and solved using the SPaTS methodology (Kokotovic and Sannuti 1968; Naidu 1988). A similar approach by Zaheer-Uddin and Zheng (2001), involving multi-stage optimization and SPaTS methodology, was developed for a single-zone space heating (SZSH) system with different operating strategies of constant volume (CV; where zone temperature alone is modulated), VAV (where airflow rate is modulated) and a more general VAV called general variable-air-volume (VAVN) (air-supply temperature and flow rate are continuously modulated), and with three-mode building time-scheduled operation. The results showed that the VAVN strategy offered a operating costs savings of 25% compared to the CV strategy.
A simple second-order model was used for the HVAC&R system in Tigrek et al. (2002) with two state variables--temperature immediately following the heat exchanger and temperature of the thermal zone, two control variables--the heat input to the heat exchanger and the volumetric airflow rate, and a nonquadratic (cubic) term in the performance criteria to apply the optimal control theory to obtain state and co-state equations and linearize them to remove non-causality. Further, an adaptive controller was designed using RLS to take care of changes in external temperature and thermal load variance over time and the difficulty of accurately measuring these variables. A combined utilization of active (ice storage) and passive (precooling) inventory for the reduction of electrical utility costs using common time-of-use rate differentials led to the design of an optimal controller, resulting in utility cost savings and substantial on-peak electrical demand reductions (Henze et al. 2004).
An existing HVAC&R system installed at the Montreal campus of the Ecole de Techologie Superieure (ETS) has 70 interior zones and has more than 60 set-point variables to be optimized with the multi-objective criteria of minimizing the energy consumption (resulting from fan energy use and chiller energy use) and maximizing the building thermal comfort (represented by PPD in terms of PMV) by choosing the optil set-points for the supervisor control strategy. Two different evolutionary algorithms were given by Deb (2001): the nondominated sorting GA (NSGA) and the elitist NSGA (NSGAII), which were evaluated and compared with Pareto-optimal solutions (Engwerda 2005). It was concluded that NSGAII performs better with energy demand lessened by 18.8% for July 29 and by 19.5% for July 25-31.
In addition to using a direct digital control (DDC) system and HVAC set-points as control variables, a method was developed in Xu et al. (2005) combining Lagrangian relaxation (LR), NNs, stochastic dynamic programming (SDP), and heuristics with numerical testing and prototype implementation. Here LR, a decomposition and coordination approach, is used to transform the original problem into a separable structure by introducing two new variables; NNs are used to predict system dynamics; uncontrollable loads and SDP are used to solve the HVAC unit subproblems with a thermal load described by a single-state Markov chain; and heuristics are used to obtain feasible solutions. A mathematical basis for a complete simulation-based SQP (CSB-SQP) methodology was developed and applied to a simple model arising in determining the optimal control for the operation of HVAC&R building systems (Sun and Reddy 2005).
An experimental study was carried out on a commercial building's passive and active thermal storage inventory using a hybrid control consisting of model-based optimal control and model-free reinforced learning control; the proposed method, compared with model-based predictive optimal control, was implemented on a full-scale laboratory facility (Liu and Henze 2006a, 2006b). A simulated reinforcement learning consists of two phases: a simulated learning phase (where a learning controller is trained by a simulator without using the actual response) and an implemented learning phase (where the learning controller is expected learn and improve while in direct contact with the environment). The hybrid approach was validated by an experimental study, and it was found that the hybrid approach achieved cost savings of 8.3% compared to the case using measured data, while the quality of the simulator remained a key disadvantage. A simple nearoptimal method was developed by Braun (2007) for controlling the charging and discharging thermal storage systems having real-time pricing (RTP) by determining the effective on-peak and off-peak periods. The performance was measured relative to a benchmark optimization problem, resulting in annual costs of about 2% of the costs with optimal control with the additional features of low hardware costs and a simplified controller architecture. Another survey by Sane et al. (2006) of literature focused on HVAC&R controls and optimization provided an overview on building dynamics (air-side dynamics, chilled water dynamics, loads and disturbances, energy costs) and control problems in chilled water dynamics (control related to flow control, supply temperature, resource allocation with chilled sequence) with a presentation of an example on dither-based optimal control. For an HVAC&R system consisting of an air-to-air heat exchanger and a water-to-air heat exchanger (Komareji et al. 2007), an objective function to be minimized was formed in terms of powers due to primary and tertiary pumps, fan, and wheel rotation and thermal power. Optimal set-points were computed for two cases of unequal water flow of the tertiary circuit and the supply (primary/secondary) circuit. See the related work by Komareji et al. (2009) that used a simplified optimal control structure using the linearized model from the primary water flow to the inlet air temperature.
Realizing that the modern buildings are complex, highly uncertain nonlinear, and multi-dimensional dynamic systems with wide varieties of disturbances, the estimation and control problem for a distributed parameter model of a multi-room building was addressed by Borggaard et al. (2009), using the distributed parameter LQR theory combined with finite elements to compute both feed-back functional gains and observer functional gains for thermal control of a 3D room in a typical HVAC&R system. For simultaneously controlling the indoor air temperature and humidity for thermal comfort and indoor air quality (IAQ) by varying the speeds of both the compressor and supply fan in an experimental direct expansion (DX) A/C system, a MIMO control strategy involving the LQG technique was developed by Qi and Deng (2009) to take care of disturbance rejection and command tracking and improve superheat control, as reported in Qi et al. (2010). A receding horizon optimal control (RHOC) at a supervisory level was applied in Lukasse et al. (2009) to control the climate of storage facilities for potatoes and onions with the results from both simulation and full-scale experimentation. An online optimal control strategy consisting of a model-based performance predictor to get simplified air-handling unit (AHU) models, cost function, optimization technique, and supervisory and local control schemes for various units of chillers, variable-speed pumps, and heat exchangers was presented in Ma and Wang (2009) to realize energy efficiency, robustness, and tracking with a simulated environment. An optimal control strategy was evaluated by Yu and Chan (2010) for controlling the cooling towers and condenser water pumps in a water-cooled chiller system, claiming that the load-based speed control to the cooling tower fans resulted in 8.6% annual energy and 9.9% operating cost savings compared to the case without using the proposed methodology.
Model predictive control (MPC)
A novel supervisory controller was successfully executed in Henze et al. (2005) using a three-step procedure for a model-based predictive optimal control for building a thermal storage inventory in a test facility in real time using time-of-use differentiated electricity prices without demand charges based on their earlier works (Henze et al. 1997). A MPC strategy was used in Yuan and Perez (2006) to maintain ventilation air requirements and temperature of multiple zones for VAV systems to achieve acceptable IAQ. The results were demonstrated by experimentation with four different typical weather conditions. A hierarchical structure based on minimizing the generalized predictive control (GPC) criterion to tune conventional PID controller parameters was proposed in Xu et al. (2006), which was applicable to a wide range of operating conditions for a cooling coil unit in an HVAC system. In Xu and Li (2007), using sequential step changes, the original coupled HVAC&R plant was decoupled into four subsystems, and a practical GPC technique along with a novel parameter identification was presented, thereby providing less computation compared to the original coupled system, and was demonstrated by simulations of an HVAC&R plant. A nonlinear MPC technique along with an optimization algorithm was applied in Xi et al. (2007) to control the temperature and humidity of an HVAC system, which was a two-by-two nonlinear dynamic model using support vector regression (SVR) and constraints on control variables to generate real-time control signals. It showed good performance in tracking a reference trajectory and steady-state errors and superior performance compared to the neuro-fuzzy controller. Using the PMV and a psychrometric chart to characterize occupants' thermal comfort, different strategies based on MPC were proposed in Freire et al. (2008) for optimization of thermal comfort and minimization of energy consumption. The results were demonstrated by simulations for two case studies relating to controller performance analysis and varying metabolic rate (ASHRAE 2005) and clothing index (Parsons 1988). A robust MPC method was presented by Huang and Wang (2008) for controlling the temperature of AHUs using two loops--one outer loop using Lyapunov analysis and another inner loop with an integral controller--to improve system performance in the presence of model uncertainties and constraints. The novelty of this approach is the adaptation of overlapping modes to make sure that the controller does not switch often among the operating modes. The application of this methodology to a typical AHU and a comparison of the results with an anti-windup PI controller shows higher robustness and overall performance improvement without the need for online tuning.
A related work on the application of an LMI-based robust MPC strategy was reported in Huang and Wang (2009) for a discrete-time constraint process, with time delay treated as an uncertainty for a typical AHU. Another investigation from Huang et al. (2009) presented a robust MPC strategy for the temperature control VAV A/C (VAVAC) system to take care of uncertainties and nonlinearities using the Takagi-Sugeno (T-S) fuzzy model with a local controller consisting of two loops (an inner-loop integral controller and an outer-loop min-max predictive controller) and a global controller based on the parallel distributed compensation technique with experimental justification for acceptable control performance without any on-site tuning. See a related work by Huang et al. (2009) for a first-order plus time-delay model for the AHU with uncertain time-delay and system gain, using an offline LMI-based robust MPC algorithm and giving a comparison with a traditional PI control technique. A novel technique for temperature control of tankless water heaters (TWHs) was developed by Henze et al. (2009) based on MPC to minimize the outlet temperature error with an experimental demonstration of a physical prototype tankless heater system (THS) with an integral performance criterion.
Describing the dynamics of VAV AHUs as a first-order, a time-delay model with uncertainties, a control input rate-limit, and saturation constraints, a new robust temperature control strategy was presented in Huang et al. (2010), using an offline robust MPC. Simulations of the VAV AHU showed enhancement of robustness with less operator intervention.
Robust or H[infinity] control
The robust control methodology takes care of model uncertainty and the nonlinearities associated with the system (see Green and Limebeer 1995; Zhou and Doyle 1998; Chen 2000; Sinha 2007).
For a two-zone space heating system (Zaheer-Uddin et al. 1993), an analytical bilinear model was developed with seven state variables, three output variables, and five control variables; it was linearized about an operating point to get a linear state space model. A decentralized robust controller was designed to asymptotically regulate the two zone temperatures to the desired set-points in the presence of unknown disturbances in the outdoor temperatures and any nondestabilizing perturbations in the parameters of the system. In particular, two different controller designs were obtained, considering the system as a linear, constrained, robust servomechanism problem (LCRSP) (Davison and Ferguson 1981) and as a nonlinear, constrained, servomechanism problem (NCSP) (Davison 1976). A comparative study of simulations showed that the decentralized controllers are good for multi-zone space-heating systems.
A simple model for hot water heating of fresh air to a controlled downstream duct temperature and a benchmark controller were developed in Underwood (2000a) using MATLAB[C] and SIMULINK[C]. Next, after providing some basic concepts of a robust control theory for a fifth-order state space model of an air heating plant with three outputs and one input, a fixed-parameter robust controller based on H[infinity] design with structured uncertainty was developed by Underwood (2000b), and the simulation results showed a good comparison with a locally optimized PID controller. A robust control strategy combining freezing, gain scheduling, I-term reset, and feedback transition control was developed in Wang and Xu (2002, 2004) to overcome the instability during transition processes between different control modes while combining the demand-controlled ventilation (DCV) and economizer control, providing savings in energy requirement.
Although a comparison of PID and H[infinity] controllers for the temperature control of a single-zone room showed better performance with large perturbations, the PID controllers will continue to play a leading role for control of HVAC systems (Noda et al. 2003).
It was shown by both theoretical and experimental results in Anderson et al. (2007,2008) that the application of the MIMO robust control methodology vastly (as much as 300%) improves performance and constraints, as was demonstrated by building an experimental setup to test a variety of HVAC&R controllers, including the well-known SISO PI controllers. The experimental system, in particular, consisted of five subsystem models--blower, mixing box, boiler, water flow control valve, and heating coil--and the control software used included MATLAB[C] with tool boxes Simulink, Real-Time Workshop and Windows Target. The four key control variables in a DAS are the input air and water temperatures and the corresponding flow rates supplied to the heating coil. The H[infinity] robust controller was designed based on the structured singular value ([micro]) and implemented with the experimental system.
Nonlinear and adaptive control
For the single-zone VAV HVAC&R system by Semsar-Kazerooni et al. (2008), a bilinear model was considered for describing both temperature and humidity dynamics; a back-stepping controller was designed for the feedback linearized model, considering heat and moisture loads as measurable disturbances; and a stable observer was designed for nonmeasurable disturbances backed by simulation results for optimal energy consumption. Also see related results by He and Asada (2003). A feedback linearization technique available for the design of nonlinear control systems was applied by Thosar et al. (2008) to design a controller for a VAVAC model. It was simulated with a laboratory-scale plant and showed superior performance in keeping comfort and optimal energy compared to the conventional PI controller. In a typical room temperature control system using a standard controller, such as a PI controller, it was found that temperature periodically oscillated around the constant reference value with an unacceptablly high amplitude. The combination of well-known techniques (linearization, inward approach, and describing function) proved to be a valuable tool to find controllers with superior performance compared to the PI-controller (Rehrl et al. 2009).
One of the earliest works by Farris and McDonald (1980) to apply adaptive control for HVAC&R systems focused on DDC for solar-heated buildings, with a single-zone air space and room air temperature as the output of the system. In particular, an adaptive optimal control (AOC) strategy was designed using a linearized model of the original nonlinear HVAC&R system and closed-loop optimal obtained via the matrix Riccati equation in Zelikin (2000). With zone temperature and hot water temperature as the two state variables, and heat pump input as the control variable, an adaptive control strategy by Astrom and Wittenmark (1989) was applied to a discharge air temperature model (Zaheer-Uddin 1993) for the discharge air temperature to track the optimal reference temperature in the presence of disturbances. Another class of adaptive systems, known as model-following or model-reference adaptive control (MRAC), was applied to a VAV system with zone, coil, and water temperatures as the three state variables; mass flow rate of supply air, mass flow rate of chilled water, and input energy to the chiller as the three control variables; and a second-order model as the reference model for the VAV system. The simulations showed good adaptability of the actual zone temperature with its reference value. For a fan-coil heating (FCH) with two thermal zones described by three outputs (two zone temperatures and boiler temperature), three inputs (two mass flow rate controllers, and one flow rate of natural gas to the burner), and a fifth-order dynamic disturbance, a robust adaptive controller was designed in Singh et al. (2000) using the continuous-time least squares (CTLS) algorithm (Astrom and Wittenmark 1989) to estimate a linear model of the original nonlinear FCH system. Then, this estimated linear model was used to design a linear feedback controller based on the LQR technique (Naidu 2003). The results showed that the robust adaptive controller was able to reject rapidly the effect of both static and dynamic disturbances and take care of unmodeled dynamics in the actuators. Various control strategies relating to air-bypass, reset, setback, improved start-stop times, economizer, and CO2 were investigated by Mathews et al. (2001) using QuickControl[C] software developed by Motion Control, resulting in improving the comfort and saving energy (60%) for a particular HVAC system.
The single-zone VAV HVAC&R nonlinear model in Arguello-Serrano and Velez-Reyes (1999), consisting of three state variables (temperature of thermal space, humidity ratio of thermal space, and temperature of supply air), two control variables (volumetric flow rate of air and flow rate of chilled water), and two outputs (temperature and humidity ratio of thermal space), was generalized as a class of an interconnected MIMO system consisting of several dynamical subsystems. A decentralized nonlinear adaptive controller (DNAC) was developed by Huaguang and Cai (2002) in terms of a state feedback FL controller (SFLC) for the inner loop and a frequency-domain adaptive compensator (FDAC) for the outer loop with the global objective of minimizing the error between the actual output and desired trajectory in the presence of disturbances, approximated as a Fourier integration function. The resulting DNAC provided higher precision, smaller overshoot, and shorter settling time, with better overall performance than the SFLC and other controllers.
An energy management control (EMC) strategy was developed by Huang et al. (2006) for a single-zone VAV HVAC&R system composed of a zone model, cooling coil model, heat pump and storage model, heat pump COP model, and fan-motor model. The EMC consisted of five functions: outdoor air economizer cycle, programmed start/stop lead time, load reset, and occupied time adaptive control strategy. The objective function to be optimized was the system power composed of heat pump input power, fan power, and pump power, providing the optimal set-points that are used as tracking signals for the adaptive controllers. This control strategy resulted in 17% energy savings compared with the no-EMC strategy.
An adaptive controller was designed in Albieri et al. (2009) for a single scroll compressor, using packaged air-cooled water chillers with MATLAB[C]/SIMULINK[C] simulations and a state-of-the-art experimental facility to achieve excellent regulation performance.
Concluding remarks on Part I: HC techniques
The main HC techniques discussed above are
1. PID control, gain scheduling, and state feedback;
2. optimal control;
3. model predictive control;
4. robust or H[infinity] control; and
5. nonlinear and adaptive control.
The contributions of the HC techniques to the HVAC&R field are summarized below:
1. The traditional control techniques, such as the PID control, have been a dominant area of research and applications to the field of HVAC&R.
2. The area of optimal control dominated the research efforts in HVAC&R, mainly due to the attractive feature of energy savings.
3. On the other hand, the MPC has the advantage of arriving at a control strategy when the complete knowledge of model is not readily available; there are some notable contributions in this HVAC&R field.
4. Robust control provides attractive features for the situation model parameter uncertainty and external disturbances and needs further investigation for the HVAC&R field.
5. Finally, the area of nonlinear and adaptive control gives an entirely different approach to deal with the nonlinear model and the fact that the parameters of the system are slowly time-varying or uncertain. Surprisingly, there are not many works dealing with nonlinear control approaches to the HVAC&R field, although adaptive control has a good record of applications to the field.
6. It appears that most control techniques discussed here did not take into account the various constraints on states and controls to reflect the realist situations.
Part II of the overview will address SC techniques and the fusion of HC and SC techniques as applicable to the HVAC&R field. Some of the future directions of research to achieve better modeling, analysis, design (control), and security will be discussed for overall performance enhancement of HVAC&R systems.
The funding provided for this research activity, performed under subcontract support of a laboratory-directed research and development (LDRD) project focusing on areas of both energy science and national security at the Idaho National Laboratory (INL), Idaho Falls, is gratefully acknowledged.
A/C = air-conditioning
AHU = air-handling unit
ANF = adaptive neuro-fuzzy
ANFIS = adaptive neuro-fuzzy inference system
ANN = artificial neural networks
AOC = adaptive optimal control
AR = autoregressive
ASHRAE = American Society of Heating, Refrigerating and Air-Conditioning Engineers
BACS = building automation and control systems
BAS = building automation systems
BEMS = building energy management system
BLAST = building loads analysis and system thermodynamics
CC = centralized control
CGI = common gateway interface
CI = computational intelligence
CIBSE = Chartered Institution of Building Services Engineers
COP = coefficient of performance
CRIM = commercial refrigerator/incubator module
CSB-SQP = complete simulation-based sequential quadratic programming
CSR = condenser super-heat regulation
CTLS = continuous time least squares
CV = constant volume
DAS = discharge air system
DBC = dead-beat compensator
DC = decentralized control
DCV = demand-controlled ventilation
DDC = direct digital control
DDP = differential dynamic programming
DNAC = decentralized nonlinear adaptive controller
DOE = Department of Energy
DTM = discrete time method
DX = direct expansion
EMC = energy management control
EMCS = energy management control systems
ESR = evaporator super-heat regulation
ETS = Ecole de Techologie Supecrieure
FCH = fan-coil heating
FDAC = frequency-domain adaptive compensator
FIS = fuzzy inference system
FL = fuzzy logic
FLC = fuzzy logic control or controller
FPID = fuzzy proportional, integral, derivative
GA = genetic algorithm
GENESYS = generic embedded system
GFC = Gupta fuzzy controller
GPC = generalized predictive control
GUI = graphical user interface
HC = hard computing or control
HFC = hydro fluoro carbon
HVAC = heating, ventilation, and airconditioning
HVAC&R = heating, ventilation, air conditioning, and refrigeration
IAQ = indoor air quality
ICIS = instrumentation, control, and intelligent systems
ICS = industrial control systems
INL = Idaho National Laboratory
ITAE = integral of time and absolute error
ISU = Idaho State University
JJH = James J. Hirsch & Associates
LBNL = Lawrence Berkeley National Laboratory
LCRSP = linear, constrained, robust servomechanism problem
LDRD = laboratory-directed research and development
LMIs = linear matrix inequalities
LQG = linear quadratic Gaussian
LQR = linear quadratic regulator
LQT = linear quadratic tracker
LR = Lagrangian relaxation
MACS = multi-agent control systems
MFC = Mamdani fuzzy controller
MICNO = mixed-integer, constraint, nonlinear optimization
MIMO = multi-input, multi-output
MOGA = multi-objective genetic algorithm
MPC = model predictive control
MRAC = model-reference adaptive control
MZSH = multi-zone space heating
NCSP = nonlinear, constrained, servomechanism problem
NLP = nonlinear programming
NN = neural networks
NNDC = neural network based decentralized controller
NSGA = non-dominated sorting genetic algorithm
NSGAII = elitist non-dominated sorting genetic algorithm
P&ID = piping/process and instrumentation diagram
PD = proportional-derivative
PI = proportional-integral
PID = proportional-integral-derivative
PMES = performance map and exhaustive search
PMV = predicted mean value
PPD = predicted percentage dissatisfied
RBF = radial basis function
REA = robust evolutionary algorithm
RHOC = receding horizon optimal control
RLS = recursive least squares
RTP = real-time pricing
SC = soft computing or control
SDP = stochastic dynamic programming
SFLC = state feedback fuzzy logic controller
SISO = single-input, single-output
SpaTS = singular perturbation and time scales
SQP = sequential quadratic programming
SVR = support vector regression
SWT = supply chilled water temperature
SZSH = single-zone space heating
TCP/IP = transmission control protocol/internet protocol
TES = thermal enclosure system
THS: = tankless heater system
TWH = tankless water heater
UIUC = University of Illinois at Urbana Champaign
USDOE = United States Department of Energy
VAV = variable airflow volume
VAVAC = variable airflow volume air conditioning
VAVH = variable air volume heating
VAVN = general variable-air-volume
VC = visual comfort
VWV = variable water volume
Z-N = Ziegler-Nichols
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Received April 5, 2010; accepted November 1, 2010
D. Subbaram Naidu, PhD, is Director, School of Engineering. Craig G. Rieger, PhD, is ICIS Distinctive Signature Lead.
D. Subbaram Naidu (1), * and Craig G. Rieger (2)
(1) Department or Electrical Engineering and Computer Science, Idaho State University, Pocatello, ID, USA
(2) Idaho National Laboratory, Idaho Falls, ID, USA
* Corresponding author e-mail: firstname.lastname@example.org
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|Author:||Naidu, D. Subbaram; Rieger, Craig G.|
|Publication:||HVAC & R Research|
|Date:||Jan 1, 2011|
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