1 Copyright © 2003 by ASME Proceedings of IMECE’03 2003 ASME International Mechanical Engineering Congress & Exposition Washington, D.C., November 16-21, 2003 IMECE 2003-41460 APPLICATION OF MULTIVARIABLE ADAPTIVE CONTROL TO AUTOMOTIVE AIR CONDITIONING SYSTEMS Rajat Shah Andrew G. Alleyne Bryan P. Rasmussen Department of Mechanical & Industrial Engineering University of Illinois at Urbana-Champaign Urbana, IL-61801 Fax: 217-244-6534, email: alleyne@uiuc.edu ABSTRACT This paper presents the application of a multivariable adaptive control strategy to a typical automotive air conditioning system. First, an experimentally validated physical model for the air conditioning cycle is introduced. This is followed by the application of a multi-input multi- output (MIMO) parameter estimation algorithm to recursively identify an equivalent discrete time state space model of the system. A Linear Quadratic Regulator (LQR) design is implemented on the estimated model with the objectives of reference tracking and disturbance rejection. Simulation studies are performed to explore the idea of modulating the electronic expansion valve opening and air flow rate over the evaporator for controlling the efficiency and capacity of a general automotive air conditioning unit. The results demonstrate the efficacy of the MIMO controller for these objectives. 1. NOMENCLATURE Variable Definition Variable Definition A,B,C State Space Matrices h Enthalpy J Cost Function k Discrete Time Step K State Feedback gain p Pressure L Kalman Gain Matrix t Time P Covariance Matrix u Input Q , R Weighing Matrices x States T Temperature y Output U Fluid Velocity y ˆ Estimated Output V Volume z Length Dimension a Area α Heat Transfer Coeff. c v Orifice Factor ε Innovations Vector d Pipe Diameter ε ˆ Aposteriori Error e Apriori Error ρ Density Variable Definition Subscript Definition ∆ Gradient j jth Output ω Compressor Speed k Compressor θ Parameter Vector kri Compressor Inlet Subscript Definition kro Compressor Outlet 1 Region 1 n Observability Index 2 Region 2 o Outlet ai Air r Refrigerant c Condenser ss Steady State e Evaporator v Valve i Inlet w Wall 2. INTRODUCTION A majority of air conditioning and refrigeration devices operate using a vapor compression cycle. A typical subcritical cycle is shown in Fig. 1. volts Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor 2 1 3 4 P h 1 2 3 4 Liquid Vapor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor 2 1 3 4 Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Compressor 2 1 3 4 P h 1 2 3 4 Liquid Vapor P h 1 2 3 4 Liquid Vapor m c air m e air rpm volts Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor 2 1 3 4 P h 1 2 3 4 Liquid Vapor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor 2 1 3 4 Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Condenser (Receiver) Evaporator (Receiver) Expansion Valve Compressor Compressor 2 1 3 4 P h 1 2 3 4 Liquid Vapor P h 1 2 3 4 Liquid Vapor m c air m e air m c air m e air rpm Figure 1: Subcritical Vapor Compression Cycle The working fluid absorbs heat as it evaporates, and then is compressed to a high pressure where heat is rejected as the fluid condenses [1]. The difficulty of modeling the complex thermofluid dynamics associated with these phase changes has