Mathematical modeling and optimized fractional-order pid control for water-cooled chillers using particle swarm optimization algorithm

Water-cooled chiller, as the most adopted chiller type, is a crucial component of the air-conditioning system. The paper is dedicated to developing an intelligent fractional-order proportional-integral-derivative (PID) controller based on the particle swarm optimization (PSO) algorithm to obtain the optimized parameters in the fractional-order PID controller. First, a dynamic mathematical model for the water-cooled chiller is developed, which involves the dynamic modeling of the most important components in the water-cooled chiller, i.e., condenser, compressor, evaporator, and expansion valve. The energy, mass, and momentum conservation equations, as well as some empirical equations, are adopted in this model. Meanwhile, an optimized variable-speed fractional-order PID controller, incorporated into the PSO algorithm, is developed to control the input power of the compressor in the water-cooled chiller. Simulation results illustrate that (i) the temperature of the chilled water leaving the water-cooled chiller calculated by the model agrees well with its actual measurement, where the maximum relative error between these two temperatures is 1.6% only, thereby verifying the accuracy and the effectiveness of this dynamic model and its solving scheme, and (ii) the optimized variable-speed fractional-order PID controller provides better (or optimized) house temperature control performance and higher coefficient of performance (COP) value than the realworld adopted variable-speed controller, where the integral absolute error for house temperature is reduced by 15% and the average COP value is improved by 8.7%, respectively.