Bryan P. Rasmussen

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.

Model-driven system identification of transcritical vapor compression systems

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 multi-input-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.

Model-based predictive control of a multi-evaporator vapor compression cooling cycle

This paper presents a decentralized control architecture for multiple evaporator vapor compression systems using model-based predictive control. Vapor compression systems are widely used for heating, air-conditioning and refrigeration, and constitute a major part of total US energy use. Advanced control strategies have the potential to significantly increase energy efficiency, while delivering the necessary amount of cooling capacity. This paper proposes a decentralized control approach based on a study of interacting dynamics, wherein the cooling capacity of each evaporator is controlled by a multi-input, multi-output MPC controller and standard PI controllers are used to regulate system pressures by modulating compressor speed and discharge valve opening. This is in contrast with traditional single-input, single-output control approaches, which can result in undesired dynamic behavior. The efficacy of the proposed control architecture is demonstrated on an experimental system.

Gain Scheduled Control of an Air Conditioning System Using the Youla Parameterization

Vapor compression systems form the basis for the majority of air conditioning and refrigeration systems. A primary control challenge addressed here is the coupled nonlinear multiple-input-multiple-output (MIMO) dynamics associated with the multiphase heat and mass transfer in the primary refrigerant loop. This paper develops a MIMO gain scheduled control strategy to regulate system efficiency while meeting changing demands for cooling capacity. An approach based on the Youla parameterization is shown to be a generalization of the more common local controller network method, while exposing several degrees of design freedom that can be exploited to improve stability. The challenge of guaranteeing stability of the nonlinear closed loop systems, despite endogenous and arbitrarily fast gain scheduling, is addressed. Experimental results confirm the effectiveness of the proposed approach.

Moving-Boundary Heat Exchanger Models With Variable Outlet Phase

Vapor compression cycle systems using accumulators and receivers inherently operate at or near a transition point involving changes of phase at the heat exchanger outlets. This work introduces a condenser/receiver model and an evaporator/accumulator model developed in the moving-boundary framework. These models use a novel extension of physical variable definitions to account for variations in refrigerant exit phase. System-level model validation results, which demonstrate the validity of the new models, are presented. The model accuracy is improved by recognizing the sensitivity of the models to refrigerant mass flow rate. The approach developed and the validated models provide a valuable tool for dynamic analysis and control design for vapor compression cycle systems.

Dynamic modeling for vapor compression systems—Part I: Literature review

This two-part article provides an introduction to dynamic modeling for vapor compression systems. Part I provides a detailed review of current literature in this area. Both physics- and data-based approaches are discussed with their associated advantages and limitations. Physics-based modeling paradigms include (1) lumped parameter approaches that qualitatively capture gross pressure and cooling transients, (2) moving boundary approaches that seek to model the dynamic variations in phase transition points, and (3) finite-control volume approaches that use discretized models that include temperature and parameter gradients in an effort to achieve greater accuracy. These models are based on first principles, but yet require time-consuming tuning and validation with experimental data. Data-based approaches offer faster model generation but are specific to the system and conditions from which the data originated.

A model-based predictive supervisory controller for multi-evaporator HVAC systems

Multi-evaporator vapor compression cooling systems are representative of the complex, distributed nature of modern HVAC systems. Earlier research efforts focused on the development of a decentralized control architecture for individual evaporators that exploits the constraint-handling capabilities of model predictive control while regulating the pressure and cooling setpoints. This paper presents a global controller that generates the setpoints for the local controllers; this controller balances the goals of cooling zone temperature tracking with optimal energy consumption. To accommodate the inherent limitations of the system, a Model Predictive Control (MPC) based approach is used. The improved efficiency and the effects of the tuning parameters are demonstrated upon an experimental system.

Dynamic modeling for vapor compression systems—Part II: Simulation tutorial

This two-part article provides an introduction to dynamic modeling for vapor compression systems. Part II presents example physics-based models for each component with a discussion on common assumptions and model variations. For two-phase heat exchangers, examples for both moving boundary and finite-control volume approaches are given, along with their associated advantages and limitations. Particular modeling challenges, such as model initialization, validation, and numerical simulation, are also addressed, and sample simulation results are utilized to compare modeling paradigms and illustrate key issues. Rather than advocating the use a particular software tool, this article provides a general tutorial on constructing dynamic simulations of vapor compression systems, outlining potential challenges and possible solutions.

Stable controller interpolation for LPV systems

This paper examines the gain-scheduling problem with a particular focus on controller interpolation with guaranteed nonlinear stability. For linear parameter varying model representations, a method of interpolating between controllers utilizing the Youla parameterization is proposed. Quadratic stability despite fast scheduling is guaranteed by construction, while the characteristics of individual controllers designed a priori are recovered at the design points.

Advances in Energy Systems Modeling and Control

This paper gives an overview of dynamic modeling for energy systems related to vapor compression cycles. Basic components of these systems are described and equations of state are developed. For the heat exchangers, these equations of state are based on a moving boundary models. A reduction of system model order, and insight into primary dynamic modes, is presented. These reduced order models are an aid to control and diagnostic approaches. After developing the models, a software simulation environment, termed Thermosys, is introduced and used to validate the modeling efforts using a benchtop experimental system. Finally, a brief overview of control strategies is given. The intent is to present the typical controls engineer with a starting point for understanding and controlling these types of systems.