This thesis details the efforts to develop a dynamic model of a transcritical vapor compression system suitable for multivariable control design purposes. The modeling approach is described and the developed models are validated with experimental data. The models are nonlinear, independent of fluid type, and based on first principles. Linearized versions of the nonlinear models are presented. Analysis of the linearized models and empirical models created using system identification techniques suggest that lower order models are adequate for the prediction of dominant system dynamics. Singular perturbation techniques are used to justify model reduction.Based on the reduced order models, the dominant dynamics of these systems are identified and described in terms of physical phenomena. Although all results presented are for a transcritical vapor compression cycle with carbon dioxide as the working fluid, the methodology and results can be extended to both subcritical and transcritical systems.iv
This brief uses an air conditioning system to illustrate the benefits of iteratively combining first principles and system identification techniques to develop control-oriented models of complex systems. A transcritical vapor compression system is initially modeled with first principles and then verified with experimental data. Both single-input-single-output (SISO) and multiinput-multi-output (MIMO) system identification techniques are then used to construct locally linear models. Motivated by the ability to capture the salient dynamic characteristics with low-order identified models, the physical model is evaluated for essentially nonminimal dynamics. A singular perturbation model reduction approach is then applied to obtain a minimal representation of the dynamics more suitable for control design, and yielding insight to the underlying system dynamics previously unavailable in the literature. The results demonstrate that iteratively modeling a complex system with first principles and system identification techniques gives greater confidence in the first principles model, and better understanding of the underlying physical dynamics. Although this iterative process requires more time and effort, significant insight and model improvements can be realized.
This paper presents the application of a multivariable adaptive control strategy to a typical automotive air conditioning system. An experimentally validated physical model for the air conditioning (a/c) cycle is first presented and is subsequently used to choose a relevant model structure for indirect adaptive control. Recursive identification of this model structure is carried out using a multi-input multi-output (MIMO) parameter estimation algorithm to obtain an equivalent discrete-time state space model of the a/c system. Linear quadratic regulator (LQR) design is implemented on the estimated model with the objectives of reference tracking and disturbance rejection. Simulation studies are presented to evaluate the advantages of using the electronic expansion valve and the air flow rate over the evaporator to control the efficiency and the capacity of a general automotive a/c unit using this adaptive control approach. The results demonstrate the efficacy of the MIMO controller and motivate further research in this area.
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