Control-Oriented Modeling of Transcritical Vapor Compression Systems

This paper presents a methodology for developing a low order dynamic model of a transcritical air-conditioning system, specifically suited for multivariable controller design. An 11th-order nonlinear dynamic model of the system is derived using first principles. Analysis indicates that the system exhibits multiple time scale behavior, and that model reduction is appropriate. Model reduction using singular perturbation techniques yields physical insight as to which physical phenomena are relatively fast/slow, and a 5th-order dynamic model appropriate for multivariable controller design. Although all results shown are for a transcritical cycle, the methodology presented can easily be extended to subcritical cycles.

[1]  Piet M.T. Broersen,et al.  Hunting of Evaporators Controlled by a Thermostatic Expansion Valve , 1980 .

[2]  B. L. Bhatt,et al.  A system mean void fraction model for predicting various transient phenomena associated with two-phase evaporating and condensing flows , 1978 .

[3]  G. L. Wedekind,et al.  A Generalization of the System Mean Void Fraction Model for Transient Two-Phase Evaporating Flows , 1981 .

[4]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[5]  H. Harry Asada,et al.  Modeling of Vapor Compression Cycles for Multivariable Feedback Control of HVAC Systems , 1997 .

[6]  W. F. Stoecker,et al.  Theoretical Model for Predicting the Transient Response of the Mixture-Vapor Transition Point in Horizontal Evaporating Flow , 1968 .

[7]  Predrag Stojan Hrnjak,et al.  Performance of the Prototype of a Transcritical R744 Mobile A/C System , 1999 .

[8]  Svend Tollak Munkejord,et al.  Heat Transfer and Pressure Drop for Flow of Supercritical and Subcritical CO2 in Microchannel Tubes , 2000 .

[9]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[10]  R. Isermann,et al.  Modeling and Control of a Refrigerant Evaporator , 1985, 1985 American Control Conference.

[11]  Morten Willatzen,et al.  A general dynamic simulation model for evaporators and condensers in refrigeration. Part II: simulation and control of an evaporator , 1998 .

[12]  W. F. Stoecker.  Stability of an Evaporator-Expansion Valve Control Loop , 1966 .

[13]  D. Didion,et al.  A simulation model of the transient performance of a heat pump , 1982 .

[14]  Morten Willatzen,et al.  A general dynamic simulation model for evaporators and condensers in refrigeration. Part I: moving-boundary formulation of two-phase flows with heat exchange , 1998 .

[15]  Xiang-Dong He,et al.  Dynamic modeling and multivariable control of vapor compression cycles in air conditioning systems , 1996 .

[16]  Y. Çengel,et al.  Thermodynamics : An Engineering Approach , 1989 .

[17]  J. Chato,et al.  Experimental Investigation of Void Fraction During Horizontal Flow in Larger Diameter Refrigeration Applications , 1998 .

[18]  W. R. Zahn,et al.  A Visual Study of Two-Phase Flow While Evaporating in Horizontal Tubes , 1964 .

[19]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[20]  Hubertus Tummescheit,et al.  Moving Boundary Models for Dynamic Simulations of Two-Phase Flows , 2002 .

[21]  B.D.O. Anderson,et al.  Controller design: moving from theory to practice , 1993, IEEE Control Systems.

[22]  D. Naidu.  Singular Perturbation Methodology in Control Systems , 1988 .

[23]  W. Wagner,et al.  A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple‐Point Temperature to 1100 K at Pressures up to 800 MPa , 1996 .

[24]  Karl Johan Åström,et al.  Drum-boiler dynamics , 2000, Autom..

[25]  P. S. Hrnjak,et al.  Experimental Study of System Performance Improvements in Transcritical R744 Systems for Mobile Air-Conditioning and Heat Pumping , 2002 .

[26]  H. Harry Asada,et al.  Multivariable control of vapor compression systems , 1998 .

[27]  C. K. Rice.  The effect of void fraction correlation and heat flux assumption on refrigerant charge inventory predictions , 1987 .

[28]  Gerhard Schmitz.  Numeric simulation of an integrated CO 2 cooling system , 2000 .

[29]  Sean N. Brennan.  On Size and Control: The Use of Dimensional Analysis in Controller Design , 2002 .

[30]  Predrag Stojan Hrnjak,et al.  Control strategies for transcritical R744 systems , 2000 .

[31]  J. MacArthur.  Transient heat pump behaviour: a theoretical investigation , 1984 .

[32]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[33]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[34]  J. MacArthur,et al.  Unsteady compressible two-phase flow model for predicting cyclic heat pump performance and a comparison with experimental data , 1989 .

[35]  Eric W. Grald,et al.  A moving-boundary formulation for modeling time-dependent two-phase flows , 1992 .