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A dynamic system model of a two-zone variable air volume heating, ventilation and air conditioning and refrigeration (VAV-HVAC&R) system is considered. The system model consists of two environmental zones, an HVAC system and a water-cooled vapor compression chiller. Five adaptive controllers were designed to achieve good tracking control of set points of zone air temperatures, discharge air temperature, chilled water supply temperature and static pressure of the VAV-HVAC&R system. The PI controller gains were updated online using adaptive neural networks and an auto-tuning algorithm. Simulation results show that adaptive PI control gave faster response and less overshoot compared to conventional constant gain PI control. The control responses tracked set-points closely and remained stable over a typical day simulation of building operation under variable load conditions.

A fuzzy-set based uncertainty analysis method is these studies, the uncertain parameters are treated as fuzzyemployed to study the effects of uncertain parameters on HVAC valued parameters, bounded by suitable minimum and (Heating, Ventilation, and Air-Conditioning) system modeling maximum extremes. The extremes and membership function and describe the associated inaccuracies in HVAC system model ., (x=jO 1], which represents the probability distribution, predictions. In this study, the uncertain parameters, i.e. the zone ' . . .cooling loads, heat transfer coefficients, chilled water and vagueness, ambiguities or impreclsion of the parameter are condenser water mass flow rate, water temperature at condenser determined from experimental data or expert knowledge. The inlet, and mean void fraction in the evaporator are considered model is then expressed as fuzzy-valued function and is and treated as fuzzy parameters. The extended transformation analyzed using fuzzy mathematics.approach is used to evaluate the uncertainties in the model The foundation of the fuzzy mathematics is the extension outputs including time history of the zone temperature and principles introduced by Zadeh["], which extend standard humidity, discharge air temperature, temperature of chilled mathematical concepts to compute fuzzy-valued problems. water and condenser water. The upper and lower bounds of these But this method is not practical due to the infinite number of outputs are determined for each a-cut level, and the fuzzy computations it would require [']. More recent and practical description of the outputs are derived as well. method is based on a-cut concept and interval mathematics, in I. INTRODUCTION which the fuzzy-valued parameters are decomposed into intervals at same u-cut level and the fuzzy algebraicIn the recent past, numerous simulation models have been computations are therefore decomposed into interval calculus.developed for predicting energy and control performance of Interval mathematics based fuzzy arithmetic has one main HVAC (Heating, Ventilation, and Air-Conditioning) systems.drawback, over-estimation: the spectrum of solutions obtained In these models, the values of some parameters are either are more or less wider than the correct one because the derived from expert knowledge or determined using interactions between fuzzy-valued parameters in the interval identification techniques. However, for the complex HVAC mathematics are neglected as shown in [3], [4], [6] and [7]. systems, some parameters cannot be determined either Several algorithms were developed to reduce or minimize because of the unavailability of the data or due to the large the solution range, such as the vertex method for monotonic scatter in data from one test to another. Such parameters functions proposed in [5] and interacting algorithm in [3]. The include: refrigerant void fraction in heat exchangers, heat vertex method is further developed to transformation method transfer coefficients and system loads. As a consequence, in [6] and [7] and s...

The accuracy of model predictions plays an important role in model-based applications. However, mathematical models exhibit more or less uncertainties. In this study, a full-scale dynamic model of a two-zone variable air volume heating, ventilation, air-conditioning and refrigeration (VAV-HVAC&R) system is considered. A fuzzy set-based uncertainty analysis method is employed to study the effects of uncertain parameters on HVAC&R system modelling and describe the associated inaccuracies in HVAC&R system model predictions. In this study, uncertain parameters, i.e. zone cooling loads, heat transfer coefficient, chilled water and condenser water mass flow rate and water temperature at condenser inlet are considered and treated as fuzzy parameters. The extended transformation approach is used to evaluate the uncertainties in the model outputs including time history of the zone temperature, discharge air temperature, temperature of chilled water and condenser water. The upper and lower bounds of these outputs are determined for each a-cut level, and the probability distributions of the outputs are presented. Practical applications: Compared to monitoring of real systems, model-based simulation provides an easier, faster and cheaper substitute to gather operating information and evaluate operating performance of HVAC&R systems. However, simulation results obtained from traditional methods by which model equations are solved with predetermined values cannot accurately represent the possible responses of the system. Thus investigating the probability distributions of the simulation results under parameter uncertainties is very important to ensure the accuracy of the model predictions. The fuzzy set-based uncertainty analysis method presented here helps in identifying the upper and lower bounds of model outputs by quantifying the range within which the responses fall under parameter uncertainties. Also, the contributions of individual uncertain parameters to the uncertainties of model outputs help in identifying the impact parameters.