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Two methods of computing coplanar, minimum-fuel, power-limited transfers are developed, based on approximate solutions obtained by the averaging method. In the first method, the average solution provides estimates of the initial adjoint variables; in the second, it provides approximations of the optimal controls in feedback form. Both trajectory variables and orbit elements are used in developing these methods. Canonical transformations are derived to convert between these sets of coordinates. The accuracy of the methods for computing coplanar, minimum-fuel, power-limited transfers is assessed for a variety of initial and final orbits. Some initial steps are taken toward the characterization of coplanar, minimum-fuel, power-limited transfers for a wide range of thrust to weight ratios. Circle to ellipse and ellipse to ellipse transfers are considered. Details of the trajectories and thrust profiles for a few illustrative cases are presented. These trajectories and thrust profiles are compared to analytical results obtained using the averaging method and to the analytic solution for infinitesimal transfer. The secular behavior of minimum-fuel transfer is predicted by the averaging results. The shape and orientation of the osculating orbits are predicted quantitatively, while the size is predicted qualitatively. The analytic solution for infinitesimal transfer predicts the qualitative behavior of the thrust during each revolution. Some general principles of minimum-fuel, power-limited transfer are revealed.

This paper describes an innovative adaptive fuzzy control (AFC) algorithm for regulating the domestic hot water temperature of a combi-boiler or instantaneous hot water heater when using a domestic hot water flow rate sensor. The AFC automatically learns the feedforward relationship between the domestic hot water flow rate and the gas valve position and adapts to process changes such as variations in the inlet water temperature, controller set point, gas composition, and flow sensor miscalibration without requiring additional sensors or a system identifier.Laboratory tests under typical operating conditions show that the AFC reduces the set-point error between 18% and 70% and reduces control effort between 23% and 41% when compared with a conventional proportional-integral-derivative (PID) feedback controller with feedforward compensation. The AFC's memory and processing requirements are comparable to those for a PID plus feedforward algorithm, so it is a realistic replacement for a conventional PID algorithm with feedforward compensation. WHAT IS A COMBI-BOILER?A combi-boiler is a domestic central heating boiler system that provides both domestic hot water and central heating water. These systems are popular in Europe and Asia because they efficiently provide both domestic hot water and central heating water in a small appliance that can be mounted on a bathroom or kitchen wall.There are two basic types of combi-boiler construction. The first type has two heat exchangers: an air-to-water heat exchanger that heats the central heating water and a water-to-water heat exchanger that heats the domestic hot water. The second type has a double-spiral construction with an air-to-water heat exchanger that heats both the central heating water and domestic hot water.A dual-heat-exchanger combi-boiler as shown in Figure 1 has a number of components, that include the primary and secondary heat exchangers, a combustion chamber, a pump, a fan, and various valves. The primary heat exchanger maintains the central heating water at 80°C when domestic hot water is not needed. The secondary heat exchanger heats the domestic hot water to a set point that varies from 50°to 60°C.When the combi-boiler is providing central heat, the boiler circulates water through the convector distribution system. When the combi-boiler senses a demand for domestic hot water with a flow switch or flow sensor, the central heating water is diverted through the secondary heat exchanger by a three-way valve to heat the domestic cold water.The domestic hot water set point for a combi-boiler is usually a constant ranging from 50°to 60°C. Traditionally, combi-boilers have been controlled using a PID controller (or one of its Christine M. Haissig is a staff research scientist and Michael Woessner is a principal research scientist at the Honeywell Technology Center, Minneapolis, Minnesota. Downloaded by [University of New Mexico] at 07:47 14 October 2014 118 HVAC&R RESEARCHderivatives, such as the proportional or proportional-integral (PI) controller) that adjust...

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