1、Kaustubh Phalak is a doctoral student in Department of Civil, Architectural and Environmental Engineering, University of Miami, Coral Gables, FL. Dr. Gang Wang is assistant professor in Department of Civil, Architectural and Environmental Engineering, University of Miami, Coral Gables, FL. Performan
2、ce Comparison of Cascade Control with Conventional Controls in Air Handling Units for Building Pressurization Kaustubh Phalak Gang Wang, PhD, PE Member ASHRAE ABSTRACT Buildings are maintained at slightly positive pressure by air handling units (AHUs) to reduce infiltration of unconditioned outdoor
3、air. The conventional AHUs rely either on direct building pressure control or volume tracking control with a single loop proportional integral (PI) controller to maintain positive building pressure. Even though this type of control structure is simplistic, it is observed that it may lead to hunting
4、of return fan speed, especially with direct building pressure control. For the direct building pressure control, accurate and stable building pressure measurement is challenging due to wind and intermittent pressure changes caused by the opening of doors. On the other hand, the building static press
5、ure is highly sensitive to the differential airflow therefore; the error in airflow measurement makes the volume tracking method unfavorable. In general, cascade control makes the control system more adaptive and robust. In this case, the primary controller reads the building static pressure and det
6、ermines the differential flow rate setpoint for secondary controller which then controls the return fan speed. The purpose of this paper is to evaluate the performance of the cascade control on the building static pressure in comparison with the two conventional controls by simulation. Performance o
7、f the two conventional controls as well as cascade control is simulated. The results conclude that the cascade control improves the stability of the system by reducing the sensitivity to the change in the operating conditions and controller gains. INTRODUCTION In centralized HVAC systems, building p
8、ressure is either controlled by return fan or relief air damper. It is been observed that active components have better control over the controlled variables. When the performance of return fan and relief damper is compared it is observed that the return fan has a better control over building pressu
9、re than the relief air damper (Wang, 2015). The return fan in the AHU is either directly controlled by the building pressure or indirectly with difference in supply and return airflow. In the direct building pressure feedback control loop, the building static pressure is measured by a differential p
10、ressure sensor and is controlled by modulating the return fan speed. The controlled building static pressure is slightly above the atmospheric pressure therefore, wind and thermal effects significantly affect the accuracy of the building static pressure measurement. Fluctuations in the reading of pr
11、essure get passed on to the return fan control signal and that could lead to erratic changes in return fan speed. This makes the direct building static pressure control difficult. On the other hand, the building static pressure could also be controlled by the difference between the supply and return
12、 airflow rates. Using this technique the building static pressure could be indirectly controlled by maintaining the airflow rate difference at its setpoint (Trane 2002) or return fan linearly tracking supply fan (Phalak, 2015). Airflow sensors installed at the supply and return duct measure the supp
13、ly and return airflow rates and the return fan speed is modulated to maintain the airflow rate difference at its setpoint. This needs calibration for the desired building static pressure. This building pressure control technique is known as flow or volume tracking control. Even though it is consider
14、ed one of the stable control methods this often does not account for the variation in exhaust airflow and the infiltration. Exhaust airflows is often not measured and infiltration could not be exactly determined and is affected by multiple factors like daily use if building, occupant behavior and ag
15、e of the building. Also the airflow difference is dependent on airflow meters which need calibration, fully developed flow, and are not often accurate. Therefore the calibrated volume tracking control may not be able to maintain positive building pressure for change in operating condition. Therefore
16、 a cascade control method is been suggested which stabilizes the system, does not need frequent calibration and can eliminate the inaccuracy of the flow meters. Cascade control is often considered as adaptive and robust type of control method and widely used in other applications where PI controller
17、s are used. In this type of control method two controllers are used. In this case, the first controller uses the instantaneous building static pressure measured to determine the corrected reference differential flow. This reference differential flow is then compared with actual differential flow and
18、 return fan is modulated accordingly. The objective of this paper is to compare direct pressure control, volume tracking control and cascade control for stability using root locus analysis. To compare the control performance initially a model is developed for single duct VAV system. Equations for st
19、eady state gains are derived using the mass conservation equation. Using these steady state gain constants and time constants, plant transfer functions are derived. These transfer functions are then used in the three feedback control method to develop dynamic models for plant and derive the open loo
20、p transfer function. A test case is developed to check the stability of these transfer function and the control methods. Root locus analysis provides a graphical representation of variation in roots with changing operating condition. Root locus analysis is run with transfer functions of these three
21、control method using MATLAB. The plots help to determine the stability of the systems at changing operating conditions and controller gains. THEORY Here a single duct VAV system is under consideration. In following subsections equations for steady state gain constants are derived along with room tim
22、e constant. These gains and time constants are used to derive the plant transfer functions. Later each control is discussed after applying corresponding feedback control to the basic plant block diagram shown in Figure 1(b). For each of these control methods transfer function is derived in the respe
23、ctive subsection. Description of the System Figure 1(a) shows the basic schematic of the system under consideration. For model simplicity we assume that the return plenum is at constant pressure. Supply and exhaust flow from the supply and exhaust fans are two disturbance inputs. Building pressure i
24、s controlled by a control input, the return fan speed. The infiltration (Qinf) is dependent on envelope resistance factor (Sinf), which is an envelope characteristic and building pressure (PRM). (1) In steady state if the pressure is constant the return airflow can be determined using the mass conse
25、rvation. (2) The return fan head is demanded by the return air duct pressure loss and the building static pressure. (3) This return airflow from above equation along with required return fan head from return duct resistance factor, determine the required return fan speed. (4) Figure 1 (a) Network sc
26、hematic of a single duct VAV system and (b) block diagram for a single duct VAV system Steady State Gains and Time Constant In the derivation of the plant equations the model is assumed to be linear. The change in building pressure (PRM) is function of the change in supply, exhaust and return airflo
27、w. ( ) (5) Also the change in return airflow is function of change in return fan speed and building pressure, (6) The steady state gains K1, K2 and K3 represent the change in magnitude. However physical systems have a time constant due to inertia. Here inertia of motor shaft, fan blades and the time
28、 delay of VFD is lumped in a single time constant T3. Value of T3 is often assumed to be less than 5s (Karunakaran, 2009). The time constant T1 is due to the room or building volume and its derivation is discussed further. The time constant for pressure sensor and flow meters is selected from the sp
29、ecification datasheet of sensor manufacturers. From equation (1)-(6) the steady state gains are calculated as, ( ) (7) ( ) (8) ( ) (9) The volume of the building provides a delayed response in building pressure to the change in any of the flow rate in or out of the volume. This time constant T1 can
30、be given as: ( ) (10) Plant Transfer Functions From Figure 1(b) following transfer functions can be derived. These functions are used to the open loop transfer function in each control method. ( ) (11) (12) Direct Pressure Control In case of direct pressure control a feedback loop from building stat
31、ic pressure is added Figure 2(a). The building static pressure is measured by a differential pressure sensor with time constant TS1. The measured building pressure is then compare with the building pressure setpoint (RP) and based on the difference the controller with gain KC1 calculates corrected r
32、eturn fan speed () to maintain the building pressure (PRM). The closed loop transfer function for the system, (13) Therefore the open loop transfer function for the direct pressure control, ( ) (14) Volume Tracking Control In volume tracking control no feedback from building pressure is used to cont
33、rol the return fan speedFigure 2(b). Supply and return flows are measured with airflow meters with time constant of TS2. This difference is then compared with differential airflow setpoint (RdQ). This setpoint is often determined at the time of commissioning or by a thumb rule, 0.05 to 0.15cfm/ft2 (
34、Taylor, 2014) for typical buildings. The controller with gain KC2 determines the return fan speed () to maintain the difference in supply and return air. The closed loop transfer function for the volume tracking control can be derived as, (15) Therefore the open loop transfer function is, ( ) (16) C
35、ascade Control In cascade control Figure 2(c) feedback from building pressure as well as difference in supply and return airflow is used to control the return fan speed. The building static pressure is measured with a differential pressure sensor with time constant TS1. The measured building pressur
36、e is then compare with the building pressure setpoint (RP) and from the difference a reference value for differential airflow is determined by the first controller. This reference is then compared with the difference in supply and return flows measured with airflow meters with time constant of TS2.
37、The second controller with gain KC2 then determines the return fan speed () to maintain the building static pressure. The closed loop transfer function, (17) The open loop transfer function for cascade control, ( )(18) Figure 2 Block diagram for (a) direct pressure control, (b) volume tracking contr
38、ol and (c) cascade control TEST CASE A single duct VAV AHU is designed using the equipment selection software of a AHU manufacturer (Trane, 2014). The design supply airflow rate is 18.8m3/s (40,000 CFM) and the design return airflow rate is 17.9m3/s (38,000 CFM). The design airflow rate difference b
39、etween the supply air and return air is 0.9 m3/s (2,000 CFM) for space pressurization at 12.5 Pa (0.05 inch of water) to balance with the design exhaust airflow rate of 0.7 m3/s (1,500CFM) and the infiltration airflow rate of 0.2 m3/s (500CFM). The return fan follows a normalized head-flow fan curve
40、 HRF/HRFD =-0.733(QRA/QRAD)2+0.744(QRA/QRAD)+0.9892. Using mentioned design values and equation (7), (8), (9), and (10) values of K1, K2, K3 and T1 are determined. For a medium sized motor and fan system time constant T3 of 2s (Karunakaran, 2009) is used. From manufacturers specification sheets of p
41、ressure sensor, time constant for pressure sensor TS1 and flow meter TS2 are obtained as 20s and 22s. At design condition plant gain and time constant are, K1=105.6 Pa/(m3/s); K2=0.0137 m3/s/Pa; K3=17.6 m3/s; T1=11.8 s. Root locus analysis of a system provides an insight about the stability of the s
42、ystem. With equations (14), (22), (24) and above calculated gains and time constant, root locus analysis is performed for direct pressure control, volume tracking control and cascade control. Equation (14) is the open loop system gain for the direct pressure control. The AHU with feedback of direct
43、pressure control is modeled in Simulink and the controller is tuned. The tuned controller gain of 0.005 is substituted for KC1 in equation (14) for the root locus analysis. At design condition the plant gain is, =760.7 and the system gain is =3.7. Figure 3 (a) Root locus analysis of direct pressure
44、control (b) expanded view From equation (14) it is clear that the direct pressure control will have three poles and no zeros. Same is observed in root locus analysis in Figure 3 (a). The curve extends in the right-hand side of imaginary (y) axis. This indicates that the system can be unstable for hi
45、gher absolute gain values. For the tuned controller the system gain is 3.7 in which the controller gain is constant however the plant gain can vary. Figure 3 (b) shows the two points with the system gain values. The design condition lies in the range of the two points shown. As the system gain excee
46、ds 5.1, it is evident that the system will be unstable. The controller gain for root locus analysis in Figure 3 is 0.005, if the controller is not properly tuned then even for controller gain of 0.0065 the system will be unstable at 15 Pa (0.06 inwg) building pressure. Fluctuations of 20 Pa (0.08 in
47、wg) in building pressure setpoint of 12.5 Pa (0.05 inwg) is not uncommon. This suggests that the system stability is very sensitive to controller gain and building pressure. This may encourages setting the controller gain at low value which may ensure the stability but will slow down the system resp
48、onse. Form equation (16) it is evident that the root locus analysis of volume tracking control will have three poles and one zero. This addition of a zero provides excellent stability to the system. Figure 4(a) shows that the system curve at design condition which never enters the positive quadrants
49、 of real axis. This ensures stability at all the system gains. Figure 4 Root locus analysis of volume tracking control at (a) setpoint building pressure (b) low building pressure and (c) high building pressure The zero introduced in the plot is due the room time constant T1 which increases with increase in building pressure. Also one of the poles due to the term changes the position of the pole due to non-linearity of system. This changes the shape of the curve at different operating conditions.
