1、4836 Model Predictive Control of Supply Air Temperature and Outside Air Intake Rate of a VAV Air-Handling Unit Shui Yuan Ronald A. Perez, PhD, PE ABSTRACT This paper presents an integrated approach to controlling dry-bulb supply air temperature and outside air intake rate of an air-handling unit (AH
2、U) by adopting a model predictive control strategy. The dynamics ofthe AHU are modeled with a multi-input-multi-output (MIMO) model that has a linear structure and time-variant gains. The model predictive control (MPC) controller can respond properly to different working conditions by assigning diff
3、erent weighting factors and constraint limits to a convex quadratic optimization problem. Weighting factors andconstraint limits can be tuned in an intu- itive way and their control effects are easy to understand. A building simulator was created based on the jrst-principle component models develope
4、d in ASHRAE research project RP-825. The simulation-based experiments demonstrated that good temperature andflow rate controls were both achieved by using MPC. INTRODUCTION An air-handling unit (AHU), as a subsystem of a build- ings air distribution system, has two basic functions-condi- tioning and
5、 distributing air into thermal zones through ductwork and bringing enough outside air into a building to meet the ventilation requirement. The functions are expected to be performed with energy consumption as low as possible. Figure 1 shows a schematic of a single-duct variable-air- volume (VAV) air
6、-handling unit. Air is drawn from thermal zones by an extract fan, part of it is released through the exhaust damper, and the rest is recirculated and mixed with fresh air drawn in from ambient. The amount of outside air can be adjusted by varying positions of the three interlocked dampers. The mixe
7、d air then flows through a filter, a heating coil, and a cooling coil in sequence and is discharged into the thermal zones by a supply fan. Each damper is driven by a motor with a linkage. The flow rates of hot and chilled water entering the coils are regulated by motor-driven control valves. In a V
8、AV system, static pressure in supply-air duct should be maintained at some setpoint so that the volume flow rate of supply air varies based on demand of the thermal zones. In order to pressurize a building against infiltration, a volume flow rate difference between the supply and extract air is kept
9、 intentionally, which requires that the rotational speed of supply and extract fans both be under closed-loop controls. The AHU controller manipulates dampers and heating and cooling coils to regulate the dry-bulb temperature of the supply air. For the control of supply air temperature, since there
10、is one controlled variable (the supply air temperature) and three control elements (the dampers, the heating coil, and the cool- ing coil), a split-range control is commonly used in such a situ- ation (Astrm and Hgglund 1995). The spilt-control of supply air temperature is also called AHUsequencing
11、strategy (ASHRAE 1999b). The sequencing control uses a single proportional-plus-integral (PI) controller, which generates control signals based on the difference between supply air temperature and its setpoint. Based on the magnitude of the PI controllers output, only one of the dampers or the heati
12、ng coil and cooling coil will be under control by receiving nonzero control signals, while the other two are inactive receiving zero control signals. There are three operating states in terms of active components, i.e., mechanical cooling (when cooing coil is active), free cooling (when dampers are
13、active), and mechanical heating (when heating coil is active). For the _ Shui Yuan is a doctoral student and Ronald A. Perez is an associate professor in the Department of Mechanical Engineering, University of Wisconsin-Milwaukee. 02006 ASHRAE. 145 Il I ,I I I I I I I purpose of energy saving, the A
14、HU controller usually includes air-side economizer control that uses outside air to take partial cooling load of supply air. When the outside air conditions permit, i.e., when its dry-bulb temperature or enthalpy is lower than that of recirculated air, the outside-air damper will fully open to intro
15、duce 100% outside air. When outside air condi- tions are not favorable for energy saving, the outside-air damper will be set to its minimum position. The minimum position of the outside-air damper is expected to bring in a minimal amount of outside air to maintain indoor air quality (IAQ). Due to th
16、e economizer, a fourth operating state should be added to the sequencing control-partial free plus mechan- ical cooling (when the cooling coil is active and the outside- air damper is fully open). One drawback of the AHU sequencing strategy is using only one controller to control three components th
17、at have quite different dynamics and whose dynamics vary under different working conditions. Tuning such a controller is difficult (Astrm and Hgglund 1995). Another drawback is that the sequencing strategy may oscillate between two operating states. The occurrence of such a problem is due to the fac
18、t that the state transition is determined based on the difference between supply air temperature and its setpoint. When large overshoot or undershoot, caused by poorly tuned PI control- lers or state shifting, appear in the supply air temperature, alternate jumps between operating states may take pl
19、ace. An experiment conducted by Seem et al. (1999) showed that the dampers and heating coil alternately oscillated between their limit positions, which means the sequencing control worked alternately in free cooling and mechanical heating states. This unstable control led to supply air temperature o
20、scillating I 1 1 I AIRMWRATB Figure 1 Schematic of a single-duct VAV air-handling unit. around its setpoint. Such unstable control actions affect the system performance adversely in terms of poor setpoint track- ing, waste of energy, and unnecessary wearing of mechanical components. Using three sepa
21、rate PI controllers to control the dampers and the heating and cooling coils and using an ad hoc control- ler to manage the state transition of the sequencing control have been proposed (Seem et al. 1999; ASHRAE 1999b). The ad hoc controller is built based on the concept of a finite state machine, a
22、 modeling tool of event-driven systems, The ad hoc controller allows only one PI controller to operate at any time and determines whether or not a state transition is needed. If output of the then-active controller has reached and stayed at its limit for a time period equal to a predefined transitio
23、n delay, the sequencing control will be shifted to an appropriate state. The value of the delay should be carefully selected in order to achieve good control performance and avoid the oscillation problem. Xu et al. (2004) addressed the same issue by a similar methodology. They also used three dedica
24、ted PI controllers and one ad hoc controller, which was called a “freezing scheme.” The ad hoc controller always allowed one PI control- ler to be in charge while freezing outputs of the other two at zero. In addition, they applied a gain scheduling scheme to the PI controllers to improve their perf
25、ormance under different working conditions and obtain smooth transitions between operating states. ANSUASHUE Standard 62-2004, Ventilation for Acceptable Indoor Air Qualis, (ASHRAE 2004) specifies minimum ventilation rates for commercial and residential buildings in order to maintain IAQ acceptable
26、to human occu- 146 ASHRAE Transactions: Research pants. This brings another objective to AHU control design. A fixed minimum position of the outside-air damper can ensure a predetermined minimum outside-air intake rate in constant- air-volume (CAV) systems, but it does not work in variable- air-volu
27、me (VAV) systems (Mumma and Wong 1990; ASHRAE 1999a). In VAV systems, if the outside-air damper is positioned at a fixed position, the outside air intake rate is approximately a constant percentage of supply airflow rate (Janu et al. 1995; Kettler 1998). Closed-loop control is a straightforward way
28、to handle this problem. Various approaches involving feedback control have been investigated to achieve a minimum outside air intake rate (Mumma and Wong 1990; Kettler, 1998; Krarti et al. 2000; Schroeder et al. 2000). However, since the minimal intake is usually deter- mined based on a buildings de
29、sign occupancy, keeping mini- mal intake is not an energy-efficient way to maintain IAQ. When the building is underoccupied, more outside air than necessary will be introduced, which may result in wasted energy. Demand-controlled ventilation (DCV) has been put forward to tackle this problem, which r
30、equires that an indica- tor of occupancy or air quality be detected and the AHU controller adjust outside air intake rate correspondingly. One issue related to implementation of DCV is how to combine outside air intake rate control with the traditional AHU sequencing strategy. Janu et al. (1 995) bu
31、ilt a dedicated PI controller to control outside air flow. They used an ad hoc controller called a “controller manager” to compare the output of the outside airflow controller with that of AHU sequencing control and pick the greater of the two to control the dampers in the mixing box. It was reporte
32、d that the ad hoc controller included special provisions to make the interacting controllers stable. Wang and Xu (2002) also adopted a PI controller to control the outside intake rate and extended AHU control logic to include a new state, which was called “DCV mode.” From the above review, we can se
33、e that if we follow such a track that utilizes single-input-single-output (SISO) control- lers to deal with a multi-input-multi-output (MIMO) task, we have to use up to four PI controllers and three ad hoc control- lers to implement both supply air temperature and outside air intake rate controls on
34、 an AHU. Tuning and maintaining such a set of controllers is not trivial. For example, each PI control- ler has to be tuned separately; some of the PI controllers may need gain scheduling, which means more controller parame- ters have to be tuned; the ad hoc controllers have to be care- fully design
35、ed to handle every possible situation, in particular to avoid alternate jumps between operating states; and possi- ble interactions among controllers have to be figured out in order to adjust controllers parameters in applications. In view ofthe above issues, we suggest a MIMO strategy to control th
36、e supply air temperature and outside air intake rate by adopting model predictive control (MPC). MPC was developed in the 1970s and has had many successful applications in the process industries since then (Qin and Badgwell 2003). The MPC controller uses a linear MIMO model to predict the supply air
37、 temperature and outside air intake rate over a finite time period, and it solves a constrained convex quadratic optimiza- tion problem to find the control signals that minimize the difference between setpoints and the predicted outputs over the same time period. The advantages of applying MPC inclu
38、de: Only a single controller is used to control both tempera- ture and flow rate. The behavior of actuators can be managed in an intuitive way by selecting different weighting factors and con- straint limits of the optimization problem, and the effects of weighting factors and constraint limits are
39、easy to understand. The operating states are determined according to work- ing conditions, so fluctuations in supply air temperature cannot cause alternate jumps between states. The controller can be tuned separately for each state without affecting its performance in other states. The controller ta
40、kes saturation and rate limitation of actuators into account. The impact of nonlinearities on the controller perfor- mance is reduced by using variable steady-state gains. MODEL PREDICTIVE CONTROL STRATEGY Use of Prediction in HVAC Controls The concept of prediction has been applied to HVAC controls
41、 by many researchers. Athienitis (1988) used a frequency domain thermal network model to anticipate the temperature response of a room to external and internal heat gains. The predicted temperature was used to find a profile for the setpoint of an on/off controller of a heater. Dexter and Haves (1 9
42、89) applied unconstrained generalized predictive control (GPC) to control a heating and a cooing coil to regulate the temperature of a single thermal zone in a CAV system. MacArthur and Foslien (1993) proposed a controller with a receding-horizon policy and end-time constraints for HVAC applications
43、, and an auxiliary nonlinear optimization process was built into the controller to minimize operation cost. Curtiss et al. (1 993) built a cluster ofneural networks to predict the n-time-step-ahead outlet air temperature of a heating coil, which involved a back propagation learning routine to produc
44、e control inputs based on the difference between setpoint and the nth-step-ahead prediction. Ling and Dexter (1994) used GPC with constrained control inputs and a rule-based super- vising controller to control temperature in a single zone and a CAV AHU. Sousa et al. (1 997) built a fuzzy model of a
45、fan-coil unit to predict supply air temperature and determined the control signals by discrete branch-and-bound optimization strategy. Wang and Jin (2000) proposed a genetic-algorithm- based optimizer to find the optimal setpoints for HVAC components in which a set of incremental dynamic models were
46、 employed to predict the response of a building and its ASHRAE Transactions: Research 147 HVAC plant. Chen (2002) applied GPC to a full-scale test room with a floor radiant heating system. Skqanc et al. (2003) applied model predictive functional control (MPFC) to a simple air-conditioning pilot plan
47、t. Liu and Henze (2004) considered a multi-zone building model to predict zonal temperatures and used dynamic programming to find optimal zone temperature setpoint profiles. A literature review reveals that the concept of prediction was mainly used to allocate optimal setpoints in most HVAC applicat
48、ions; in limited cases where both prediction and opti- mization were involved in dynamic feedback controls, input/ output constraints were treated simply as boundary conditions of an optimization problem rather than as a means to change the behavior of a controller; few applications of MPC on AHU in
49、 VAV systems have been reported. Formulation of Model Predictive Control Figure 2 shows a conceptual block diagram of MPC. It explicitly uses an internal model to predict plant outputs over a finite time interval in the future called “prediction horizon.“ It solves a convex quadratic optimization problem to find a sequence of control inputs over a control horizon and uses the very first one as the actual control input at the current step. It uses a receding horizon strategy, i.e., it repeats one and two above at every control interval. Figure 3 illustrates the behavior of a SISO p
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