Improving tracking performance of automotive air conditioning system via μ synthesis

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