INTRODUCTION Tankless water heaters (TWHs)@ also called instantaneous or demand water heaters@ have both advantages and disadvantages when compared to storage water heaters. Some of the advantages are that they are smaller@ they have a longer life@ they can provide a continuous stream of heated water@ and they typically use less energy than their storage counterparts. Two main disadvantages are that they require a large power input and that the outlet temperature is difficult to control. There are several mechanisms that lead to reduced energy consumption when using TWHs instead of storage water heaters. Storage water heaters use a tank to store hot water@ which continuously loses heat to the surrounding environment (often called standby losses). TWHs do not store hot water@ so these standby losses are eliminated (Johnson and Clark 2006). Less obvious@ but very significant@ is the potential for TWHs to decrease the heat loss through the hot water distribution system. Heat loss through piping systems is typically at least 10% to 20% and often 50% of total water heating energy (ASHRAE 2007; Baskin et al. 2004; Hiller 2005). If point-of-use TWHs are used@ they can nearly eliminate this energy loss. Even if a centralized TWH system is used@ these losses can be significantly reduced. The reason is that TWHs normally supply hot water at a much lower temperature than storage water heaters. Storage water heaters are kept quite hot-typically 60??to increase their hot water supply capacity. But the hot water usage temperature is much lower; the preferred temperature for showers@ for example@ ranges from 36??to 42??(Herrmann et al. 1994; Ohnaka et al. 1994; Rohles and Konz 1982). TWHs can supply water at the temperature needed for a given application and can significantly reduce distribution losses. Supplying lower-temperature hot water has other advantages. One is that the amount of time spent waiting for hot water to arrive for use will be reduced because the 40??hot water flow rate will be higher than that of the 60??hot water to get the same volume and temperature at end use. This reduces wasted water and time. A second advantage is that the risk of scalding injuries is reduced. This was the impetus for one member of the research team developing a feedforward controlled electric TWH in 1986. One of the previously mentioned disadvantages of TWHs is that they are difficult to control. Accurate control of the outlet water temperature is important not only for comfort but also for safety. This is particularly true when the heated water is not mixed at end use@ for example in a shower. The traditional approach to control TWHs is to use PI or PID feedback control@ in which the manipulated variable (control output) is adjusted in response to the error sensed by the outlet temperature sensor (Daugherty 1995; Haissig and Woessner 2000; Underwood 1999). Very few scientific publications discuss the difficulty of controlling TWHs: Haissig and Woessner (2000) and Harris (1993a) both present work on improving control in TWHs and discuss the control challenge. Harris concludes that there are fundamental control problems with TWHs. Johnson and Clark (2006) suggest that TWHs are inappropriate for users who need good temperature stability. However@ a vast number of patents have been filed describing various strategies to improve the control of TWHs. The strategies include blending heated water with cold water (Kubik 2006)@ heating a number of chambers connected in series separately (Sturm et al. 2007)@ gain scheduling@ including a small water tank to add thermal capacitance to the system (Harris 1993b)@ and using adaptive fuzzy control (Haissig et al. 1998). This shows that manufacturers are aware of the control problems and are working toward solving them. However@ several commercially available TWHs have been tested by the authors and were found to control temperature poorly@ including overshoots up to 25??that last several seconds@ oscillations with a period of one minute and amplitude of 14?? 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 for temperature control performance of TWHs. Thus@ it is difficult for a developer to know whether a change in control is an improvement in control. A future paper by the authors will attempt to address this problem. Several methods of control technology were considered for the current project. Feedback (including optimally-tuned PID) and simple feedforward controls have been tested@ producing results 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). Haissig and Woessner (2000) developed a method to use adaptive fuzzy control for a gas-fired combi-boiler (a TWH used to provide both domestic hot water and space heating). Adaptive fuzzy control was reported to provide acceptable results by using a flow rate sensor to provide feedforward data to rapidly account for changes in flow@ which are frequent in domestic hot water systems. The cold water supply temperature is not measured; rather it is assumed to vary slowly@ so that the adaptive part of the controller will compensate for the changes without significant sacrifices to comfort. For the current project@ we considered the wide array of possible applications and believe that it is important to develop a controller that can handle rapid variations in inlet water temperature. Such variations occur when a TWH is used as a booster on a solar (or other alternative energy) domestic water heating system@ when used as a point-of-use heater (the pipe supplying the heater will contain a plug of water at ambient temperature if it has not been recently used)@ etc.