1、I n t e r n at i o n a 1 J ou r n a 1 of H e at in g ,Ve n t il at in g, Air-conditioning and Refrigerating Research HVAC nor may any part of this book be reproduced, stored in a reheval system, or msmined in any form or by any mcans-electronic, photocopying, recording, or other-without permission i
2、n writing from ASHRAE. Abslrac Ei (Engineering Information, inc.) Ei Compendex and Engineering index; IS1 (Institute for Scientific Information) Web Science and Research Alert; and BSRIA (Building Services Research / , /,/,/,/, II I Capillary tube flow Y/If/II/I/1f1/1/11/,/,/,/qf I l Figure 2. Flow
3、inside a capillary tube Subcooled Liquid Region: The subcooled liquid region begins at the inlet of the capillary tube and ends at the point where the pressure has dropped to the saturated pressure. The conservation of mass relation for this region is (1) m Gc = - = constant AC The refrigerant behav
4、es as an incompressible fluid with constant specific volume and dynamic viscosity. The conservation of momentum relation applied to the control volume of length dz as indicated in Figure 2 gives where the momentum flows carried by the fluid into and out of the control volume are equal and cancel out
5、. The wall shear stress T, is given by (3) where the coefficient of friction fis a function of Reynolds number Re. In general, the-Reynolds number for fluid flowing in a capillary tube is greater than 10 O00 and the flow is fully turbulent. The coefficient of friction was assumed to be that for smoo
6、th tubes and given by the turbulent relations for Re 2 lo5: for lo5 I w 4 w I t? 4 A l- VI a which represents the pressure gradient in the subcooled liquid region. Metastable Liquid Region: HVACn P- O R lu -I a W I I U ni W v1 W e P- oo U 4 3 I W 4 e I VI e i- VI a a VOL. 6. No. 2 HVAC when the dome
7、stic cold water temperature rises to 30“C, the gas valve setting decreases 20%. One solution to this problem is to sense the domestic cold water temperature and include feedforward curves for a variety of domestic cold water temperatures; however, this requires the addition of a sensor, which increa
8、ses the cost of the product. It also does not eliminate the time and expense required to predetermine the feedforward relationships in a laboratory for each type of boiler or eliminate the uncertainties due to flow sensor miscalibration. A second solution is to develop a control algorithm that adapt
9、s to the changing conditions and automatically adjusts the feedforward relationship between the steady-state valve setting and DHW flow rate. The rest of this paper describes the adaptive fuzzy control algorithm that was developed to solve this problem, along with the laboratory test results that co
10、mpare the AFC algorithm with a conventional PI controller with feedforward compensation. O VI w I I V E 4 W v) w pc E oa V I W pc I v) a a a n f- v) 120 HVAC this means that the adaptation mechanism adjusts the controller parameters directly and a system identifier is not required. Numerous general
11、references on adaptive fuzzy control exist, includ- ing Cox (1993) and Wang (1994). Haissig et al. (1998) provide some specific background on the AFC. Input Membership Functions Feedback control of the DHW temperature is performed by measuring the DHW temperature, comparing it to the desired set poi
12、nt, and adjusting the gas valve accordingly (Figure 4). The gas valve setting is directly related to the burner pressure and controls the amount of heat supplied to the heat exchanger(s). The DHW flow rate sensor information is fed back to the controller for feedforward compensation. Each input to a
13、nd output from the controller has an associated set of membership functions. The AFC has two inputs (Figure 4). One input is the DHW temperature error input e, where which is the feedback input. The other input is the DHW flow rate input Vdhu, which is the feed- forward input. The first input e has
14、three membership functions with the linguistic labels-Negative, Zero, and Positive (Figure 5). When e is Negative, the DHW temperature is too warm; when e is Posi- tive, the DHW temperature is too cold. For an error inside the deadband, the gas valve position that is commanded is constant for a cons
15、tant DHW flow rate. The distance between points C and E (or D and C) defines the size of the deadband and is known as the biuserror. The equations for calculating the degrees of membership p, pzero, and pp, in the membership functions Nega- tive, Zero, and Positive for a given e are straightforward
16、and can be calculated from the geome- try shown in Figure 5. Combi-Boiler 9 o- r Q Q m =o 3 v) O O VI 9 u- u) P O O O O N J W w pc I VI 4 a ta t Lci Figure 4. Block Diagram of the Control System. The AFC acts as an adaptive PI controller with feedforward compensation to control the domestic hot wate
17、r temperature 122 HVAC C is at the center of the universe of discourse, which is zero. A and B are equidistant from C; D and E are equidistant from C.) a 3 r 1 8 E P Q-4 O Medium O0 E $A t2 Universe of Discourse DC E B Figure 6. Membership Functions for Domestic Hot Water Flow Rate Input (A and B de
18、fine the range of the universe of discourse; C is at the center of the universe of discourse, which is zero; A and B are equidistant from C; D and E are equidistant from C.) - : I L- .Lu- -L-L:- I _I :- -.:.I- .L- 1: :-*:- ll.,.l 1 -. ine seconu input vdhit.) iias LIIICC IIIGIIUGIIII IUIICLIUI WILII
19、 LIIG IIIIUIXIL ILJGI LUW, Medium, and High (Figure 6). The equations for calculating the degrees of membership pbw, pMed, and pHigh for a given vdhw are straightforward and can be calculated from the geometry shown in Figure 6. Output Membership Functions The output membership functions are fuzzy s
20、ingletons. A fuzzy singleton has a degree of mem- bership of 1 at a single point along the universe of discourse and a degree of membership of O else- where. The AFC has nine output membership functions, one for each rule in the controller (Figure 7). Each membership function has an associated lingu
21、istic label for convenience. The output mem- bership functions have the linguistic labels UNegLow, UNeg,$fed, UNegHigh, UZerobw, uZeroMed, UZeroHigh, UposLOiv, pr, a smaller value, a slower learning rate. The control designer should select y so that the controller adapts to long-term process changes
22、 but not noise and short-term disturbances. Because an analytical means of selecting y had not been developed, y was selected using trial and error along with experience from previous applications. LABORATORY TESTING Laboratory Test Facility The AFC was tested in a laboratory after simulation testin
23、g demonstrated favorable perfor- mance. A manufacturer that supplies controls for combi-boilers performed the tests in their lab- oratory. The AFC was compared to a PID plus feedforward algorithm they developed. VOLLME 6, NUMBER 2, APRIL 2000 127 The test appliance was a high-capacity combi-boiler w
24、ith single-heat-exchanger construction. The combi-boiler could be operated at the normal operating set points with DHW flow rates ranging from 4 to 9 L/min. The DHW supply temperature could not be varied; it was a fairly constant 9C. Three types of fuel could be used: G20, G25, and G3 i. G20 and G25
25、 are typically referred to as natural gas. Unlike the United States, which has only one type of natural gas, Europe has two. G20 is 100% methane, whereas G25 is 86% methane and 14% nitrogen. G31 is propane. When G31 was used, the combi-boiler injectors were changed, as they would be in a normal inst
26、allation. The AFC and PI plus feedforward algorithms were implemented on an NEC microprocessor. A PC with a data acquisition system logged the DHW temperature, DHW flow rate, commanded gas valve current, and other test data. PID with Feedforward Compensation to Benchmark Performance The AFC performa
27、nce was benchmarked relative to the performance of a PID plus feedfor- ward algorithm. The feedforward relationship between the DHW flow rate and steady-state gas valve position was optimized for G20 fuel and the nominal inlet water temperature of 9C. The gains for the PID feedback controller were c
28、hosen to have a quick response without a large amount of overshoot. The manufacturer selected the gains using the laboratory facility, combining trial and error with their extensive experience with combi-boiler control tuning. When the DHW flow rate was constant, the controller acted as a convention
29、al PID controller. When the controller sensed a change in the DHW flow rate, it first increased or decreased the gas valve to the steady-state value for that DHW flow rate and then applied the feedback correction. AFC Configuration Parameters The configuration parameters for the AFC are summarized i
30、n Table I. uod, was selected based on simulation and laboratory performance, as were biaserrur, biasfr,., and y. u od,in,v and uodmaori were set to the minimum and maximum DHW flow capacity of the combi-boiler. We initialized the locations of the output membership functions that map the domestic hot
31、 water flow rate to the steady-state valve position to 35%. This ensured that the combi-boiler DHW temperature would not be hot enough to scald anyone, even at the low DHW flow rates, before the AFC learns the correct locations of the membership functions. Table 1. Configuration Parameters for the A
32、daptive Fuzzy Controller Parameter Laboratory Testing Value Umaximum 5 “C 3 Umin 9 Umin 1 .O“C 0.2 L/min 0.06 0% 100% c er A I r m eo m O O m u- m r- O n O O o lu E I VY U cs c VI Laboratory Performance Metrics first is SSE, the sum squared DHW temperature deviation from the set point over the test:
33、 In addition to plotting the test data, the performance was benchmarked with two metrics. The 128 HVAC&R RESEARCH 4 Ill where n is the number of test samples. SSE measured comfort-how much the temperature var- ied from the desired set point as DHW was used. The second is SSDU, the sum squared change
34、 in the gas valve position over the test: n 2 SSDU = lu(i)-u(i- i) i=2 SSDU measured how much the gas valve moved to control the temperature. The controller should reposition the gas valve as infrequently as possible to minimize wear. O D O Summary and Discussion of Laboratory Test Results The labor
35、atory tests were run with a standard DHW flow rate step profile that ranged from a minimum of 4 L/min to a maximum of 9 L/min (Figure 9). The DHW flow rate was constant for 200 s between steps. This exercised the controller through the typical operating range for the boiler. The DHW temperature set
36、point was 50C and the performance was tested for G20, G25, and G3 1 fuels. The same tests were run for both the AFC and the PI plus feedfonvard controller that was used as a benchmark. Table 2 summarizes the laboratory test results for three fuels. The AFC performance was after training. The AFC was
37、 trained by repeating the DHW flow rate profile twice until the steady-state valve positions were learned for the different DHW flow rates. For the nominal con- dition, G20 fuel, the AFC reduced the sum squared set point error by 18.4% and the sum squared control effort by 23.4%. For the off-nominal conditions, the sum squared set point error was reduced by 50% for G25 and 70% for G3 1. The sum squared control effort was reduced by 42% Figure 9. Domestic Hot Water Flow Rate Profile for Laboratory Testing.
