Abstract
In order to improve the performances of air conditioning systems, it is desirable to track time-varying trajectories generated by optimization algorithms, which H∞ synthesis techniques have been proved to successfully solve. However, the control-oriented models of vapor compressor cycles used for algorithm development, even if built from first-principles, suffer from model uncertainties introduced by modeling assumptions, calibration inaccuracies, and linearization errors. The differences between the actual plant and the control-oriented model, mainly in the form of unmodeled dynamics and parameter uncertainty, undermine the stable margin as well as the performance of the closed-loop system with H∞ controllers. In order to solve the problem, the concept of the structured singular value μ is used to analyze the influences of model uncertainties on robust stability and robust performance. Based on μ analysis results, μ synthesis techniques compared to H∞ methods achieve better stability and performance margins over the same set of uncertainties. Furthermore, simulation results show that the μ controller achieves better performances of output tracking and disturbance rejection than the H∞ controller for the automotive air conditioning system studied.
Nomenclature
TP | = | two phase |
SH | = | superheated |
SC | = | subcooled |
N | = | compressor speed |
T | = | temperature |
a | = | air |
c | = | condenser |
cmp | = | compressor |
e | = | evaporator |
g | = | gas |
h | = | enthalp |
l | = | liquid |
p | = | pressure |
v | = | valve |
m | = | mass flow rate |
Q | = | heat transfer rate |
Green symbols
α | = | valve position |
γ | = | void fraction |
δ | = | uncertainty |
ρ | = | density |
ζ | = | normalized phase region length |
μ | = | structured singular value |