1、Editorial: Smart HVAC accepted July 8, 2008This paper describes the development of a novel approach to temperature control of tanklesswater heaters (TWHs). Conventional methods of controlling TWHs typically allow a highdegree of error in the outlet water temperature when subjected to disturbances in
2、 flow rate orinlet water temperature. Poor control affects comfort, safety, and energy consumption associ-ated with TWHs. The novel control approach presented here uses model predictive control(MPC) to minimize the outlet temperature error. A dynamic heat transfer model of an electricTWH is develope
3、d and validated and used within a MPC-based controller. The controller isinterfaced to a physical prototype TWH and tested using an experimental test bed developed forthis project. An integral performance criterion is used to compare performance and to tune theMPC in a standardized series of tests,
4、also developed for this project. MPC is shown to provideexcellent control of the prototype TWH.INTRODUCTIONTankless water heaters (TWHs), also called instantaneous or demand water heaters, haveboth advantages and disadvantages when compared to storage water heaters. Some of theadvantages are that th
5、ey are smaller, they have a longer life, they can provide a continuousstream of heated water, and they typically use less energy than their storage counterparts. Twomain disadvantages are that they require a large power input and that the outlet temperature isdifficult to control. There are several
6、mechanisms that lead to reduced energy consumption when using TWHsinstead of storage water heaters. Storage water heaters use a tank to store hot water, which con-tinuously loses heat to the surrounding environment (often called standby losses). TWHs do notstore hot water, so these standby losses ar
7、e eliminated (Johnson and Clark 2006).Less obvious, but very significant, is the potential for TWHs to decrease the heat loss throughthe hot water distribution system. Heat loss through piping systems is typically at least 10% to20% and often 50% of total water heating energy (ASHRAE 2007; Baskin et
8、 al. 2004; Hiller2005). If point-of-use TWHs are used, they can nearly eliminate this energy loss. Even if a cen-tralized TWH system is used, these losses can be significantly reduced. The reason is that TWHsnormally supply hot water at a much lower temperature than storage water heaters. Storagewat
9、er heaters are kept quite hottypically 60Cto increase their hot water supply capacity.But the hot water usage temperature is much lower; the preferred temperature for showers, forexample, ranges from 36C to 42C (Herrmann et al. 1994; Ohnaka et al. 1994; Rohles andGregor P. Henze is a professor in th
10、e Department of Civil, Environmental, and Architectural Engineering, University ofColorado, Boulder, CO. David P. Yuill is president and Andrew H. Coward is a research scientist at Building Solutions,Inc., Omaha, NE. 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, In
11、c. (www.ashrae.org). Published in HVAC Haissig and Woessner 2000; Underwood 1999). Very few scien-tific publications discuss the difficulty of controlling TWHs: Haissig and Woessner (2000) andHarris (1993a) both present work on improving control in TWHs and discuss the control challenge.Harris concl
12、udes that there are fundamental control problems with TWHs. Johnson and Clark(2006) suggest that TWHs are inappropriate for users who need good temperature stability. How-ever, a vast number of patents have been filed describing various strategies to improve the control ofTWHs. The strategies includ
13、e blending heated water with cold water (Kubik 2006), heating a num-ber of chambers connected in series separately (Sturm et al. 2007), gain scheduling, including asmall water tank to add thermal capacitance to the system (Harris 1993b), and using adaptive fuzzycontrol (Haissig et al. 1998). This sh
14、ows that manufacturers are aware of the control problems andare working toward solving them. However, several commercially available TWHs have beentested by the authors and were found to control temperature poorly, including overshoots up to 25Cthat last several seconds, oscillations with a period o
15、f one minute and amplitude of 14C, and so on.Part of the problem may be that temperature control performance is difficult to describe, quantify,and measure, and there are no current standards, published methods of test, or rating systems fortemperature control performance of TWHs. Thus, it is diffic
16、ult for a developer to know whether achange in control is an improvement in control. A future paper by the authors will attempt to addressthis problem.Several methods of control technology were considered for the current project. Feedback(including optimally-tuned PID) and simple feedforward control
17、s have been tested, producingresults that are deemed unacceptable, demonstrating that advanced control methods must be used.Advanced control methods include adaptive control, robust control, expert systems, fuzzy logic,artificial neural networks, and model predictive control (MPC) (Burns 2001). Hais
18、sig and Woess-ner (2000) developed a method to use adaptive fuzzy control for a gas-fired combi-boiler (a TWHused to provide both domestic hot water and space heating). Adaptive fuzzy control was reportedto provide acceptable results by using a flow rate sensor to provide feedforward data to rapidly
19、account for changes in flow, which are frequent in domestic hot water systems. The cold watersupply temperature is not measured; rather it is assumed to vary slowly, so that the adaptive partof the controller will compensate for the changes without significant sacrifices to comfort.For the current p
20、roject, we considered the wide array of possible applications and believethat it is important to develop a controller that can handle rapid variations in inlet water tem-perature. Such variations occur when a TWH is used as a booster on a solar (or other alterna-tive energy) domestic water heating s
21、ystem, when used as a point-of-use heater (the pipesupplying the heater will contain a plug of water at ambient temperature if it has not beenrecently used), etc.VOLUME 15, NUMBER 1, JANUARY 2009 5METHODOLOGYThe work presented in this paper focuses on development of a controller for an electric TWH.
22、In the United States, 39% of water heaters use electric resistance heat, compared to 54% that usenatural gas combustion (DOE 2001). Although the thermal transients of the heat exchanger arevery different for a gas-fired TWH, the control methods described here could easily be adaptedfor use with a ga
23、s TWH. A significant factor in a gas heaters control performance would be thegas valves modulation capabilities. The subject TWH has three chambers of 3.2 cm diameter copper pipe connected in seriesthrough headers. Each chamber contains a 6 kW tubular heater, consisting of a nickel-chromiumresistanc
24、e wire element, surrounded by powdered magnesium oxide insulation, wrapped in anaustenitic nickel-based alloy sheath. Each tubular heater is controlled by a bidirectional triodealternating current switch. These heaters are controlled together (i.e., there is one control signal).The heat input can mo
25、dulate in a quasi-continuous (resolution of 0.8% of full scale) range from 0to 18 kW. The total volume of water in the heating chambers and headers is approximately 0.4 L. Accurate temperature control of TWHs is only possible when accounting for the dynamicthermal response of TWHs to variations in w
26、ater flow rate, inlet water temperature, setpointchanges, and other unmeasured disturbances. Conventional feedback control cannot account forthe plant dynamics in an anticipatory fashion, nor does it allow for the inclusion of constraints,such as a maximum allowable overshoot error (for scald protec
27、tion). As a consequence, we use acontrol method that is based on a model for the TWH, commonly referred to as model predictivecontrol. To develop such a controller, the following methodology was adopted:a. TWH modeling and validation: We created and tuned a dynamic model of the TWH,accounting for th
28、e thermal mass of the components of the tubular heater and heat exchangewith the environment, in addition to the heat required to heat the water flow. We developedlumped parameter thermal models of the TWH and validated these models using experimen-tal data from dynamic tests conducted in an experim
29、ental test bed. The expected benefit ofusing a dynamic model of the heater is that good control performance can be attained regard-less of whether the heater has been used in the last two seconds or two hours. A popular tech-nical computing environment (MathWorks, Inc. 2007a) and associated block-ba
30、sed dynamicsystems analysis front end (MathWorks, Inc. 2007d) were used for modeling.b. Experimental test bed: An instrumented test bed was constructed to provide measuredresponse data that were used to validate and refine the model. This test bed is described ingreater detail later in the section t
31、itled “Experimental Test Bed Description.”c. Development of a MPC for TWHs: The block-based dynamic systems analysis framework isextended by a commercially available toolbox for the design of MPCs (MathWorks, Inc. 2007b).Rapid control prototyping is accomplished with the help of a further extension
32、of the capabilitiesof the block-based dynamic systems analysis frontend to automatically generate, package, andcompile source code from the block models to create real-time software applications on a varietyof systems (MathWorks, Inc. 2007c). The complete system provides automatic code generationtai
33、lored for a variety of target platforms, a rapid and direct path from system design to implemen-tation, and a simple graphical user interface with an open architecture. In the present work, weselected a popular hardware target platform for controller evaluation in the laboratory setting(MathWorks, I
34、nc. 2007e). d. MPC controller evaluation: The performance of the MPC controller is fine-tuned by minimiz-ing the integral squared error (ISE) performance metric over a 60 s interval. Experimentationhas shown that the majority of disturbances have settled within this interval. The ISE algorithmwas se
35、lected because it more strongly penalizes larger-magnitude errors and minimizes theweighting of smaller errors, which is similar to human perception of water temperature. For6 HVAC are the timerate changes of the state variables; are the input variables, andare parameters. We can express Equations 8
36、 through 11 inmatrix-variable or state-space notation:where is a vector of state derivatives, x and u are vectors of state and input variables, is avector of output variables, and A, B, C, and D are matrices of parameters. Specifically:Rd12L-lnrori-=T dTdt-CbTbTwTb()Rvb=CsTsTwTs()RvsTinsTs()+ Rdo=Ci
37、nsTinsTsTins()RdoTiTins()+ Rdi=CiTiTinsTi()RdiQs+=TbTwTbCbRvb-=TsTwTsCsRvs-TinsTsCsRdo-+=TinsTsTinsCinsRdo-TiTinsCinsRdi-+=TiTinsTiCiRdi-QsCi-+=TbTsTinsand Ti, ,Twand QsRvsRvbRdoRdiCbCsCinsCiand , ,xAx Bu+=yCxDu+=xy10 HVAC this is known as feedforward control. Essentially, MPC provides feedback com-
38、pensation for unmeasured disturbances and feedforward compensation for any measured distur-bance. MPC design requires a model of the impact that v and u have on . The plant model wasdeveloped and validated in the above sections. The feedforward control portion uses the plantmodel to calculate the u
39、adjustments needed to keep at its setpoint. This calculation considersthe effect of any known constraints on the adjustments (typically, an actuator upper or lowerbound or a constraint on how rapidly u can vary). One may also specify bounds on the controlledvariable . These constraint specifications
40、 are a distinguishing feature of MPC and can be par-ticularly valuable when one has multiple control objectives to be achieved via multiple adjust-ments (a MIMO plant) or when safety, physical limits, or other operational constraints need tobe considered. If the plant model is accurate, the plant re
41、sponds quickly to adjustments in u, andno constraints are encountered, feedforward compensation can counteract the impact of v per-fectly. In application, model imperfections, physical limitations, and unmeasured disturbancescause the to deviate from its setpoint r. Therefore, MPC design includes a
42、disturbance modelFigure 14. Block diagram of a SISO MPC toolbox application (MathWorks, Inc. 2007b).Note: d = Unmeasured disturbance; unknown but for its effect on the plant output. The controller provides feedback compensation for such disturbances.r = Setpoint (or reference); the target value for
43、the output.u = Manipulated variable (or actuator); the signal the controller adjusts in order to achieve its objectives.y = Measured disturbance (optional). The controller provides feedforward compensation for such disturbances as they occur to minimize their impact on the output.= Output (or contro
44、lled variable); the signal to be held at the setpoint. This is the “true” value, uncorrupted by measurement noise.y = Measured output. Used to estimate the true value, .z = Measurement noise. Represents electrical noise, sampling errors, drifting calibration, and other effects that impair measuremen
45、t precision and accuracy.yyyy yyyyy18 HVAC this calculation also considers the known constraints. Various noise effects can corrupt the measurement. The signal z in Figure 14 represents sucheffects. They could vary randomly with a zero mean or could exhibit a nonzero, drifting bias.MPC design uses a
46、 model in combination with its model to remove the estimatednoise component (filtering).The above feedforward/feedback actions comprise the controllers regulator mode. MPC designalso provides a servo mode, in which it adjusts u such that tracks a time-varying setpoint. In gen-eral, setpoint tracking
47、 accuracy depends on the plant characteristics (including constraints), theaccuracy of the model, and whether or not future setpoint variations are known in advance.If so, it provides feedforward compensation for these. Setpoint changes are only very rarely knownin advance, so no such knowledge is a
48、ssumed in this work.Snapshot of a Typical Sampling InstantMPC design generates a discrete-time controllerone that takes action at regularly spaced,discrete time instants. The sampling instants are the times at which the controller acts. The inter-val separating successive sampling instants is the sa
49、mpling period, (also called the controlinterval). This section provides more details on the events occurring at each sampling instant.Figure 15 shows the state of a hypothetical SISO MPC system that has been operating for manysampling instants, where integer k represents the current instant. The latest measured output, yk, andprevious measurements, yk1, yk2, ., are known and are the filled circles i
