Patent Publication Number: US-8538597-B2

Title: System and method for regulating temperature in a hot water heater

Description:
BACKGROUND OF THE INVENTION 
     The subject matter disclosed herein relates generally to hot water heaters, and in one embodiment to a hot water heater configured with a proportional-integral-derivative (PID) control to vary the temperature of a fluid in the hot water heater. 
     Hot waters heaters are typically configured with limited control as to the temperature of the fluid (e.g., water) disposed therein. High and low threshold temperatures are often used to maintain the temperature of the fluid. Fluid temperature at or below the low threshold temperature will activate a heating device. Likewise temperatures at or above the high threshold temperature will deactivate the heating device. 
     Hot water heaters of this configuration are susceptible to peak demand, which can drain fluids at hotter temperature (e.g., hot water) from the water heater at a rapid rate. This rate often exceeds the rate of heating of the fluid. Thus the temperature of the fluid can remain near the lower threshold value until the end of the period of peak demand. 
     Moreover, because the control structure is effectively limited to the high and low threshold values, hot water heaters of this configuration expend a great deal of energy. Outside of the period of peak demand, fluid that is left in the hot water heater for extended periods of time will cool. This cooling will eventually activate the heating device, which is thereafter left active until the fluid reaches the high threshold temperature. Such cycling will occur variously over the course of time, during which little if any need or usage of the fluid will occur despite the expenditure of energy that is required to heat the fluid. 
     Therefore it would be advantageous to have a hot water heater that can maintain the temperature of the fluid, while also reducing the energy necessary to heat the fluid. 
     BRIEF DESCRIPTION OF THE INVENTION 
     In one embodiment, a hot water heater comprises a tank holding a volume of a fluid and a monitoring device in communication with the volume, the monitoring device comprising a sensor for generating an input indicating a change in the temperature of the fluid. The hot water heater also comprises a PID control responsive to the input, the PID control including modules having one or more of a proportional control module, an integral control module, and a derivative control module. The hot water heater further comprises a heating element coupled to the PID control, the heating element responsive to a PID output from the modules, wherein each of the modules is assigned a term, and wherein the term is defined by a gain parameter with a value that corresponds to the change in temperature of the fluid. 
     In another embodiment, an appliance comprises a vessel having a volume, an inlet and an outlet permitting ingress and egress of a fluid into the volume, and a feedback mechanism coupled to the volume. The appliance further described wherein the feedback mechanism implements a PID control scheme having one or more gain parameters, each with a value that results from the ingress and the egress of the fluid from the volume. 
     In yet another embodiment, a method of regulating temperature of fluid in a hot water heater. The method comprises steps for measuring an operating condition of the hot water heater and generating an input indicative of the operating condition. The method also comprises steps for setting one or more of a proportional gain, an integral gain, and a derivative gain to correlate the input to a target value, and modifying the operating parameters of the hot water heat based on the correlated input. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference is now made briefly to the accompanying drawings, in which: 
         FIG. 1  is a side, cross-section of an exemplary embodiment of a hot water heater. 
         FIG. 2  is a side, cross-section of another exemplary embodiment of a hot water heater. 
         FIG. 3  is a side, cross-section of yet another exemplary embodiment of a hot water heater. 
         FIG. 4  is a schematic diagram of an exemplary control device; 
         FIG. 5  is a flow diagram of an exemplary embodiment of a method for regulating temperature of water in a hot water heater such as the hot water heaters of  FIGS. 1-3 . 
         FIG. 6  is a schematic diagram of an exemplary demand management system; 
         FIG. 7  is a plot of a PID response for operation of embodiments of a hot water heater such as the hot water heaters of  FIGS. 1-3 . 
     
    
    
     Like reference characters designate identical or corresponding components and units throughout the several views, which are not to scale unless otherwise indicated. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Described below are embodiments of a hot water heater that are configured to maintain consistent temperatures of fluid (e.g., water) during times of peak consumption. Unlike conventional hot water heaters that operate a heater element according to high and low temperature thresholds, however, these embodiments utilize a feedback mechanism such as one or more variations of a proportional-integral-derivative (PID) control scheme that meters in real-time the amount of heat input into the volume of fluid in the hot water heater. By providing this dynamic interaction, the inventors have developed a temperature control scheme that is more efficient than conventional schemes for hot water heaters because the heater element is controlled in response to operating conditions of the hot water heater, e.g., high and low demand for fluid from the hot water. 
     By way of example, and referring now to  FIG. 1 , there is provided an embodiment of a hot water heater  100  that is made in accordance with concepts of the present disclosure. As depicted in  FIG. 1 , the hot water heater  100  includes a vessel  102  such as a cylinder  104  (e.g., a tank) defining a volume  106 . The volume  106  is accessible via openings  108  in the vessel  102 , which include an inlet  110  for ingress of cold water, an outlet  112  for egress of hot water, a drain valve  114 , and a relief valve  116  to release gas from the volume  106  into the environment surrounding the hot water heater  100 . The hot water heater  100  further includes a feedback mechanism  118  that has a monitoring device  120  and a heating device  122 , each in communication with the volume  106 , and each coupled to a control device  124  such as a PID control  126  that implements the PID control scheme mentioned briefly above. 
     The monitoring device  120  includes various sensors, meters, and similar devices that can generate an input indicative of changes to the fluid temperature inside of the vessel  102 . Exemplary changes correspond to certain operating characteristics of the hot water heater  100  such as fluid conditions and/or operating conditions of the hot water heater  100 . Flow rates such as the rates of ingress and egress of fluid into the vessel  102 , temperatures profiles of fluid in the vessel  102 , and energy consumption are all examples of suitable operating characteristics for use in connection with the feedback mechanism  118 . 
     The heating device  122  is configured with heating elements for influencing conditions of the fluid in the vessel  102 , such as by injecting heat into the fluid in a manner that affects the temperature of the fluid. Heating elements of the type used herein include those elements found on electric, gas, and hybrid-type hot water heaters. Exemplary electric elements include resistive elements with associated hardware such as relays (e.g., a silicon-controlled rectifier (SCR)) and switches (e.g., a triode for alternating current (TRIAC)). Combustion and combustion devices such as gas burners are likewise compatible with hot water heaters constructed using the concepts of the hot water heater  100 . In one example, the hot water heater  100  includes a burner and an adjustable valve such as a thermal expansion valve (TXV) that varies the flow of gas (e.g., natural gas and propane) to the burner. Moreover, hybrid-type hot water heaters include combinations of electric and gas elements, as well as other elements typically associated with refrigeration cycles and refrigeration products. Elements of hybrid-type hot water heaters can include compressors, condensers, and evaporators, all of which are compatible with refrigerants and similar fluids that exhibit thermodynamic properties for transferring heat. By way of example, in one hybrid-type hot water heater the vessel  102  is surrounded by the condenser so as to inject heat into the fluid in the vessel, thus effectuating the change in temperature. These hybrid-type hot water heaters can likewise include elements such as resistive heating elements that are placed in communication with the vessel  102 . 
     The control device  124  and the PID control  126  of  FIG. 1 , includes one or more groups of electrical circuits that are each configured to operate, separately or in conjunction with other electrical circuits, to generate an output. This output is reflective of an error between the value of the input and some target or expected value such as a target temperature T target  for the fluid in the vessel  102  which can be prescribed by a user or by factory setting. The electrical circuits of the PID control  126  can communicate with other circuits (and/or devices), which execute high-level logic functions, algorithms, as well as firmware and software instructions. Exemplary circuits of this type include, but are not limited to, microprocessors, field programmable gate arrays (“FPGAs”) and application specific integrated circuits (“ASICs”). While all of the elements, circuits, and devices function individually in a manner that is generally understood by those artisans that have ordinary skill in the electrical arts, it is their combination and integration into functional electrical groups and circuits that generally provide for the concepts that are disclosed and described herein. 
     In connection with the PID control scheme, the electrical circuits and circuitry of the PID control  126  may be implemented in a manner that can physically manifest theoretical analysis and logical operations, which are necessary to characterize the changes, e.g., in the temperature of the fluid, and equate such changes with the appropriate output therewith. These electrical circuits can replicate in physical form an algorithm, a comparative analysis, and/or a decisional logic tree, each of which operates to assign the output and/or a value to the output that correctly reflects one or more of the nature, content, and origin of the changes that occur and that are reflected by the relative inputs from, e.g., the monitoring device  120 . 
     Discussing now an implementation of the feedback mechanism  118  described above, construction of the hot water heater  100  permits delivery of hot fluid from the volume  106  through the outlet  112  to various parts of residential and commercial buildings. Cold fluid is dispersed into the volume  106  via the inlet  110 , and more particularly the cold water is generally flowed into the bottom of the vessel  102  as hot water is displaced from the volume  106 . During periods of high demand, hot fluid is removed from the volume  106  and replaced with cold fluid at a rate that can cause the temperature of the fluid within the volume  106  to fall precipitously away from a target temperature T target . 
     In one embodiment, the feedback mechanism  118  is configured to avoid rapid changes and subsequent adjustments in the temperature of the fluid in the vessel  102 . This configuration allows the hot water heater  100  to maintain the fluid temperature at the target temperature T target  despite changes in the usage and delivery demands. Moreover, by providing this control in response to demand, embodiments of the hot water heater  100  reduce peak power consumption in lieu of consistent and stabilized insertion of heat that substantially eliminates rapid spikes normally required by demand and usage peaks. 
     These features are compatible with the various configurations of the heating device  122  described above and contemplated herein. When used in connection with electric heating elements, the PID control  126  continuously modulates in one example the amount of voltage and/or current to the respective resistive element by driving a SCR or TRIAC based on differentials such as temperature differentials of the fluid in the vessel  102  and/or flow rates of the fluid into and out of the vessel  102 . In one embodiment of the hot water heater  100 , these variations are generated via pulse width modulation (PWM) in combination with a switching device coupled to the heating element (and/or coupled to the associated hardware such as the SCR and TRIAC). 
     For gas heating elements the PID control  126  changes in one example the operating condition of the adjustable valve (e.g., the TXV valve) that is coupled to the burner. These changes proportionally adjust the flow of the gas to the burner element. In one embodiment, these adjustments change the relative position of the TXV valve to modify the amount of gas permitted to reach the burner, thus influencing the combustion occurring at the burner and the subsequent heat injected into the fluid. 
     The PID control  126  is likewise compatible with heating elements used in hybrid-types of the hot water heater  100 . For hybrid-type designs that utilize a compressor and more particularly a variable-speed compressor, the PID control  126  provides a variable voltage and/or current such as to an inverter or other electrical circuit for regulating the speed of the variable-speed compressor. This regulation can reduce start-up losses associated with operation of such compressors such as by providing continuous feedback as to the necessary fluid flow and related operating parameters for the hybrid-type design. In addition to, or in lieu of, control of the compressor, the PID control  126  is also compatible with other elements of the hybrid-type design such as the fans and pumps. In one embodiment, the PID control  126  controls one or more of the fans coupled to the condenser and the evaporator. Moreover, in hybrid-type designs that include elements found in electric and/or gas types of hot water heater  100 , the PID control  126  is further configured to operate in one example as discussed in connection with the electric heat elements and the gas heat elements discussed above. 
     Referring now to  FIGS. 2 and 3  and in view of the foregoing construction of the hot water heater  100 , implementation of the PID control scheme such as embodied by the control device  124  with the PID control  126  can vary as per the relative inputs used by the feedback mechanism  118 . For purposes of the discussion that follows, like numerals are used to identify like components as between  FIGS. 1-3 . 
     In  FIG. 2 , for example, there is depicted an exemplary embodiment of a hot water heater  200  includes a vessel  202  such as a cylinder  204  (e.g., a tank) defining a volume  206  with openings  208 . The openings  208  include an inlet  210  for ingress of cold water, an outlet  212  for egress of hot water, a drain valve  214 , and a relief valve  216  to release gas from the volume  206  into the environment surrounding the hot water heater  200 . The hot water heater  200  further includes a feedback mechanism  218  that has a monitoring device  220  and a heating device  222 , each in communication with the volume  206 , and each coupled to a control device  224  such as a PID control  226  that implements the PID mechanism mentioned briefly above. 
     The hot water heater  200  also includes a flow measurement device  228  for monitoring the flow of fluid such as the flow into and/or out of the hot water heater  200 . The flow measurement device  228  includes one or more flow meters  230 , illustrated in the present example as an inlet flow meter  232  coupled to the inlet  210  and an outlet flow meter  234  coupled to the outlet  212 . Exemplary flow meters  230  can vary, with one construction of the flow measurement device  228  utilizing flow meters  230  that can measure flow rate, flow temperature, as well as other flow properties of the fluid. The flow measurement device  228  is likewise incorporated as part of the feedback mechanism  218 , with one particular construction being implemented wherein the flow meters  230  are coupled to the control device  224 . 
     In  FIG. 3 , there is provided yet another exemplary embodiment of a hot water heater  300  which, similar to the hot water heater  100  and  200  above, includes a vessel  302  such as a cylinder  304  (e.g., a tank) defining a volume  306  with openings  308 . The openings  208  include an inlet  310  for ingress of cold water, an outlet  312  for egress of hot water, a drain valve  314 , and a relief valve  316  to release gas from the volume  306  into the environment surrounding the hot water heater  300 . The hot water heater  300  further includes a feedback mechanism  318  that has a monitoring device  320  and a heating device  322 , each in communication with the volume  306 , and each coupled to a control device  324  such as a PID control  326  that implements the PID mechanism mentioned briefly above. 
     The hot water heater  300  also includes a temperature measurement device  336 . The temperature measurement device  336  includes a plurality of temperature sensors  338  such as thermocouples, thermistors, and similarly constructed elements for measuring temperature of the fluid in the hot water heater  300 . The temperature sensors  338  are arranged in the example of  FIG. 3  as an array  340  that is within the hot water heater  300 . The temperature measurement device  336  is incorporated as part of the feedback mechanism  318 , with the temperature sensors  338  and/or the array  340  generally being coupled to the control device  324 . 
     By way of example, in operation the flow measurement device  228  and the temperature measurement device  336  generate inputs such as an analog or a digital input. These inputs are received by the control device (e.g., the control device  224 ,  324 ), wherein processing of the input such as by PI, PID, and related variations of the PID control scheme in the PID control (e.g., the PID control  226 ,  326 ) generates an output. This output controls operation of the heating device (e.g., the heating device  222 ,  322 ) such as by providing known variation in voltage, current, or other operating parameter to the respective heating device to insert heat to the fluid in a manner consistent with the concepts disclosed and contemplated herein. One example of a PID control scheme as it relates to implementation in the PID control is discussed below in connection with  FIG. 4 . 
     Referring now to  FIG. 4 , there is depicted one example of a control device  400  for use in connection with the hot water heater  100 ,  200 , and  300  above. In one embodiment, the control device  400  is implemented as the control device  124 ,  224 , and  324 . The control device  400  includes a PID control  402  (e.g., the PID control  126 ,  226 ,  326 ), a processor  404 , a memory  406 , and a signal conditioning device  408 , all of which are coupled together via one or more buses  410 . The PID control  402  includes a three-term control structure  412 , which incorporates one or more of a proportional control module  414 , an integral control module  416 , and a derivative control module  418 . The three-term control structure  412  provides a PID output  420  to the signal conditioning device  408 , which in turn generates a control output  422  such as the output discussed above for controlling operation of, e.g., the heating device  122 ,  222 ,  322 . 
     Use of the proportional control module  414 , the integral control module  416 , and the derivative control module  418  permits implementation of one or more variations of the PID control scheme. Such implementations are representative of one or more mathematical algorithms, wherein each module contributes to the overall value of the PID output  420  a term of the mathematical algorithm. An exemplary algorithm for use in connection with the three-term control structure  410  of  FIG. 4  is provided immediately below. It is contemplated, however, that other algorithms are likewise compatible with the scope and spirit of the concepts of the present disclosure. 
     By way of example, the three-term control structure  410  implements a three-term control scheme, which involves manipulation of one or more of separate terms. Each term is implemented by one of the modules such as the proportional control module  412 , the integral control module  414 , and the derivative control module  416 . Manipulation of the terms (individually or collectively) is effective to modify or change the value of the PID output  420 , and in turn the value of the control output  422  that is delivered to the hot water heater (e.g., the hot water heater  100 ,  200 , and  300 ). The control output  422  is in one example in the form of control or instructive signals that can activate and deactivate, e.g., the heating device  122 ,  222 , and  322 . 
     In one embodiment, the PID output  420  of the PID control  402  is defined in accordance with Equation (1) below:
 
 u ( t ) P   OUT   +I   OUT   +D   OUT   Equation (1)
 
where u(t) is a value for the PID output  420 , P out  is a proportional term of the PID output  420 , I out  is an integral term of the PID output  420 , and D out  is the a derivative term of the PID output  420 . As discussed in more detail below, each of the terms corresponds to a gain parameter that is assigned a value in response to inputs from, e.g., the flow measurement device  228  ( FIG. 2 ) and the temperature measurement device  336  ( FIG. 3 ) discussed above.
 
     The proportional term P out , also known as gain and/or the gain term, is useful to make changes to the PID output  420  that are proportional to an error value. In one example, the error value defines a change in the target temperature T target  for the fluid in the hot water heater (e.g., the hot water heater  100 ,  200 , and  300 ). In one example, the proportional term P out  is defined in accordance with Equation (2) below:
 
 P   OUT   =K   P   e ( t ),  Equation (2)
 
where K p  is the proportional gain parameter, e is the error value, and t is time and/or instantaneous time.
 
     The integral term I out , also known as reset and/or reset term, is useful to make changes to the PID output  420  that are proportional to both the magnitude of the error value and the duration of the error value over time. In one example, the integral term I out  is defined in accordance with Equation (3) below:
 
 I   OUT   =K   i ∫ 0   t   e (τ) dτ,   Equation (3)
 
in which K i  is the integral gain parameter, e is the error value, t is time or instantaneous time, and τ is a dummy integration value.
 
     The derivative parameter D out , also known as rate and/or rate term, is useful to make changes to the PID output  420  based on the rate of change of the error value such as by determining the slope of the error value over time. In one example, the derivative term D out  is defined in accordance with Equation (4) below: 
                       D   OUT     =       K   d     ⁢     ⅆ     ⅆ   t       ⁢     e   ⁡     (   t   )           ,           Equation   ⁢           ⁢     (   4   )                 
where K d  is the derivative gain parameter, e is the error value, and t is time or instantaneous time.
 
     In one embodiment, one or more of the terms including the proportional term, the integral parameter, and the derivative parameter are summed to calculate the value for the PID output  420  (e.g., u(t)) as illustrated in Equation (5) below: 
     
       
         
           
             
               
                 
                   
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     Referring back to  FIG. 4 , each of the proportional control module  412 , the integral control module  414 , and the derivative control module  416  can be configured as electrical circuitry. Utilizing discrete elements such as resistors and capacitors, processors such as ASICs and FPGAs, as well as combinations of various electrical devices, these modules can effectuate the changes, calculations, determinations the various parameters described above. These elements and components are selected in connection with the relevant theory of PID control and the PID control schemes described herein. 
     Focusing next on the other components of the control device  400 , in one embodiment, the processor  404  is a central processing unit (CPU) such as an ASIC and/or an FPGA that is configured to control operation of PID control  402 . This processor can also include state machine circuitry or other suitable components capable of controlling operation of, e.g., the control device  404  and the PID control  402  as described herein. The processor  404  in one example provides to the PID control  402  inputs in the form of feedback and other information that characterizes the energy demand for the household. In one example, the PID control  402  is configured to generate the control output  420  in response to this feedback. 
     The memory  406  includes volatile and non-volatile memory and can be used for storage of software (or firmware) instructions and configuration settings. Like the signal conditioning device  408  includes analog-to-digital (A/D) converter, digital-to-analog (D/A) converters, as well as other components such as inverters that can generate output  412  in a form suitable to communicate with, e.g., the heating device  122 ,  222 , and  322 . Although  FIG. 4  shows the PID control  402 , the processor  404 , the memory  406 , and the signal conditioning device  408  as discrete components, this need not be the case. For example, one or more of these components can be contained in a single integrated circuit (IC) or other component. As another example, the processor  404  can include internal program memory such as RAM and/or ROM. Similarly, any one or more of functions of these components can be distributed across additional components (e.g., multiple processors or other components). 
     For further discussion of the operation of embodiments of the hot water heater  100 ,  200 , and  300 , reference can now be had to  FIG. 5 , in which there is illustrated a method  500  for regulating temperature of water in a hot water heater. The method  500  includes various steps  502 ,  504 ,  506 ,  508 , and  510  that facilitate control of the temperature of the fluid found in the hot water heater. As depicted in  FIG. 5 , the method  500  includes a step  502  for measuring an operating condition of the hot water heater. These operating conditions can include temperature and flow rate, variations of which occur in connection with changes in the demands placed on the hot water heater. In one example, peak demands such as during morning and evening hours can displace greater amounts of hot water from the hot water heater. This displacement can lead to a reduction in the overall temperature of the water. 
     To avoid the reduction in temperature, however, the method  500  also includes a step  504  for generating an input indicative of the operating condition. Inputs can arise from, for example, temperature and flow sensors placed in various positions within the hot water heater (e.g., array  340  ( FIG. 3 )) and peripheral to the hot water heater (e.g., the inlet flow meter  232  ( FIG. 2 ) and the outlet flow meter  234  ( FIG. 2 )). The method  500  further includes a step  506  for setting one or more of a proportional gain, an integral gain, and a derivative gain. This setting can correlate the input to a target value. This target value includes the target temperature T target . The target temperature T target  identifies the desired temperature of the water in the hot water heater. As discussed more below, embodiments of the method  500  are configured to limit the changes in the temperature of the water such as during the peak demands. 
     For example, the method  500  includes a step  508  for determining whether the input varies from the target value such as by implementing a three-term control scheme. When using temperature sensors and probes, this determination compares the temperature values encoded in the input to the target temperature T target . On the other hand, for purposes of flow meters and other non-temperature specific devices, this determination compares the respective information encoded in the input to target values relating the input to, e.g., the target temperature T target . 
     Differences between the temperature of the water in the hot water heater and the target temperature T target  in an amount that is different from a threshold value (e.g., ±2° C.), causes the method  500  to move to a step  510  for modifying the operating parameters of the hot water heater. More particular to the various configurations of water heaters discussed above, these modifications can alter the heat input from the respective heating element. Moreover, in connection with the continuous feedback provided by in the embodiments of the hot water heater  100 ,  200 , and  300 , the method  500  step through the various steps  502 ,  504 ,  506 ,  508 , and  510  to continuously monitor and maintain, e.g., the temperature of the water in the hot water heater. 
     By way of further example, and with reference now to  FIGS. 6 and 7 , an implementation of the concepts explained above are illustrated in connection with an exemplary embodiment of a demand management system  600  ( FIG. 6 ) and a PID response curve  700  ( FIG. 7 ). The demand management system  600  is useful to manage energy consumption for, e.g., a household. The demand management system  600  includes a demand management module  602  and a control device  604  (e.g., control device  400 ) that is coupled to a hot water heater  606  (e.g., the hot water heater  100 ,  200 , and  300 ). The demand management module  602  includes a processor  608  and a memory  610 , coupled with busses  612 , as well as in one example an interface  614  that is configured to communicate via a control link  616  such as wire or other transmitting medium to other parts of the demand management system  600 . 
     The demand management module  602  is configured to receive information about energy consumption and requirements for the household. This information is instructive of the amount of energy required to efficiently operate, e.g., the hot water heater  606 . In one embodiment, and with reference now to the PID response curve  700  of  FIG. 7 , an implementation of the three-term control scheme is illustrated, wherein the three-term control scheme is useful for reducing peak power consumption such as by deferring the heat input (or “loading”) that is supplied to the hot water heater. In the PID response curve  700 , there is depicted a PID response  702  that defines the input power (in Watts) provided to change the temperature of the water in the hot water heater as a function of time (e.g., hours). The PID response  702  includes a plurality of response curves  704 , including a first PID response  706  and a second PID response  708 , each having a profile  710  defined by one or more settings (such as gain settings) for generating the required input power in the manner indicated by the profile  710 . 
     Selection amongst the response curves  704  for use in the control device  604  is done in one example in response to the demand placed on the hot water heater  606 . During periods of high demand for hot fluid, where the amount of input power to maintain the temperature of the fluid is greatest, the control device  604  can operate the hot water heater  606  in accordance with the first PID response  706 . As per the profile  710  depicted in  FIG. 7 , the input power is ramped up to a peak value quickly. This response is useful to maintain the temperature of the water during periods of rapid changes in the flow and/or temperature of the hot water in the hot water heater. On the other hand, when hot water is not required or when demand is limited, the control device  604  can operate the hot water heater  606  in accordance with the second PID response  708 . Here the profile  710  illustrates that input power is not only minimized, ramping up to a peak value that is lower than the peak value of the first PID response  706 , but also applied over a longer period of time. By way of comparison, whereas conventional systems may utilize only certain threshold values and only one value of input power to heat water, the control device  604  of the present disclosure can modify operation of the hot water heater  606  to vary the input power in response to demand such as by selecting from among the plurality of response curves  704 . 
     In view of the foregoing, in one embodiment, values for the proportional gain, the derivative gain, and the rate gain are found on or correspond to the profile  710 . Selection amongst the response curves  704  is responsive to other feedback and signals that arise outside of the feedback mechanisms (e.g. the feedback mechanism  118 ,  218 ,  318 ) discussed above. This feedback can arise from other parts of the demand management system  600  such as from other devices and/or operative components that are useful to manage energy consumption for, e.g., the entire household. In one example, the demand management module  602  or other device integrated into the demand management system  600  is configured to provide to the feedback mechanism one or more inputs indicative of preferred power consumption or other metrics describing power consumption at the household level. The feedback mechanism can respond to such inputs by selecting the proper values for the proportional gain, the derivative gain, and rate gain for use by the control device  604 , such as by selecting one or more of the response curves  704  discussed in connection with  FIG. 7  above. 
     It is contemplated that numerical values, as well as other values that are recited herein are modified by the term “about”, whether expressly stated or inherently derived by the discussion of the present disclosure. As used herein, the term “about” defines the numerical boundaries of the modified values so as to include, but not be limited to, tolerances and values up to, and including the numerical value so modified. That is, numerical values can include the actual value that is expressly stated, as well as other values that are, or can be, the decimal, fractional, or other multiple of the actual value indicated, and/or described in the disclosure. 
     This written description uses examples to disclose embodiments of the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.