Thermal Therapy: Stabilization and Identification

44 pages, In "Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology", A. Belmiloudi (Ed.), InTech (Open Access Publisher), Vienna, 2011 - ISBN 978-953-307-550-1International audienceMotivated by topics and issues critical to human health and safety of treatment, the problem studied in this chapter derives from the modeling and stabilizing control of the transport of thermal energy in biological systems with porous structures. First, the modeling of thermal transport by perfusion within the framework of the theory of porous media is presented and the governing equations are established. The thermal processes within the tissues are predicted by using some generalized uncertain evolutive nonlinear bioheat transfer type models with nonlinear Robin boundary conditions, by taking into account porous structures and directional blood flow. Afterwards the existence, the uniqueness and the regularity of the solution of the state equation are presented as well as stability and maximum principle under extra assumptions. Second, we introduce the initial perturbation problem and give the existence and uniqueness of the perturbation solution and obtain a stability result. Third, the real-time identification and robust stabilization problems are formulated, in different situations, in order to reconstitute simultaneously the blood perfusion rate, the porosity parameter, the heat transfer parameter, the distributed energy source terms and the heat flux due to the evaporation, which affect the effects of thermal physical properties on the transient temperature of biological tissues, and to control and stabilize the desired online temperature and thermal damage provided by MRI measurements. Because, it is now well-known that a controlled and stabilized temperature field does not necessarily imply a controlled and stabilized tissue damage. This work includes results concerning the existence of the optimal solutions, the sensitivity problems, adjoint problems, necessary optimality conditions and optimization problems. Next, we analyse the case when data are measured in only some points in space-time domain, and the case where the body Ω is constituted by different tissue types which occupy finitely many disjointed subdomains. Some numerical strategies, based on adjoint control optimization , in order to perform the robust control, are also discussed. Finally, control and stabilization problems for a coupled thermal, radiation transport and coagulation processes modeling the laser-induced thermotherapy in biological tissues, during cancer treatment, are analyzed

Optimal temperature distribution for a nonisothermal Cahn--Hilliard system with source term

In this note, we study the optimal control of a nonisothermal phase field system of Cahn--Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. The system couples a Cahn--Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier form, the constitutive law of the heat flux is assumed in the form given by the theory developed by Green and Naghdi, which accounts for a possible thermal memory of the evolution. This has the consequence that the balance law of internal energy becomes a second-order in time equation for the thermal displacement or freezing index, that is, a primitive with respect to time of the temperature. Another particular feature of our system is the presence of the source term in the equation for the order parameter, which entails additional mathematical difficulties because the mass conservation of the order parameter, typical of the classic Cahn--Hilliard equation, is no longer satisfied. In this paper, we analyze the case that the double-well potential driving the evolution of the phase transition is differentiable, either (in the regular case) on the whole set of reals or (in the singular logarithmic case) on a finite open interval; nondifferentiable cases like the double obstacle potential are excluded from the analysis. We prove the Fréchet differentiability of the control-to-state operator between suitable Banach spaces for both the regular and the logarithmic cases and establish the solvability of the corresponding adjoint systems in order to derive the associated first-order necessary optimality conditions for the optimal control problem. Crucial for the whole analysis to work is the so-called ``strict separation property'', which states that the order parameter attains its values in a compact subset of the interior of the effective domain of the nonlinearity. While this separation property turns out to be generally valid for regular potentials in three dimensions of space, it can be shown for the logarithmic case only in two dimensions

Optimal temperature distribution for a nonisothermal Cahn--Hilliard system in two dimensions with source term and double obstacle potential

In this note, we study the optimal control of a nonisothermal phase field system of Cahn--Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It couples a Cahn--Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier form, the constitutive law of the heat flux is assumed in the form given by the theory developed by Green and Naghdi, which accounts for a possible thermal memory of the evolution. This has the consequence that the balance law of internal energy becomes a second-order in time equation for the thermal displacement or freezing index, that is, a primitive with respect to time of the temperature. Another particular feature of our system is the presence of the source term in the equation for the order parameter, which entails further mathematical difficulties because the mass conservation of the order parameter is no longer satisfied. In this paper, we study the case that the double-well potential driving the evolution of the phase transition is given by the nondifferentiable double obstacle potential, thereby complementing recent results obtained for the differentiable cases of regular and logarithmic potentials. Besides existence results, we derive first-order necessary optimality conditions for the control problem. The analysis is carried out by employing the so-called deep quench approximation in which the nondifferentiable double obstacle potential is approximated by a family of potentials of logarithmic structure for which meaningful first-order necessary optimality conditions in terms of suitable adjoint systems and variational inequalities are available. Since the results for the logarithmic potentials crucially depend on the validity of the so-called strict separation property which is only available in the spatially two-dimensional situation, our whole analysis is restricted to the two-dimensional case

Integrated Dynamic Facade Control with an Agent-based Architecture for Commercial Buildings

Dynamic façades have significant technical potential to minimize heating, cooling, and lighting energy use and peak electric demand in the perimeter zone of commercial buildings, but the performance of these systems is reliant on being able to balance complex trade-offs between solar control, daylight admission, comfort, and view over the life of the installation. As the context for controllable energy-efficiency technologies grows more complex with the increased use of intermittent renewable energy resources on the grid, it has become increasingly important to look ahead towards more advanced approaches to integrated systems control in order to achieve optimum life-cycle performance at a lower cost. This study examines the feasibility of a model predictive control system for low-cost autonomous dynamic façades. A system architecture designed around lightweight, simple agents is proposed. The architecture accommodates whole building and grid level demands through its modular, hierarchical approach. Automatically-generated models for computing window heat gains, daylight illuminance, and discomfort glare are described. The open source Modelica and JModelica software tools were used to determine the optimum state of control given inputs of window heat gains and lighting loads for a 24-hour optimization horizon. Penalty functions for glare and view/ daylight quality were implemented as constraints. The control system was tested on a low-power controller (1.4 GHz single core with 2 GB of RAM) to evaluate feasibility. The target platform is a low-cost ($35/unit) embedded controller with 1.2 GHz dual-core cpu and 1 GB of RAM. Configuration and commissioning of the curtainwall unit was designed to be largely plug and play with minimal inputs required by the manufacturer through a web-based user interface. An example application was used to demonstrate optimal control of a three-zone electrochromic window for a south-facing zone. The overall approach was deemed to be promising. Further engineering is required to enable scalable, turnkey solutions

Finite-time thermodynamics of port-Hamiltonian systems

In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell's demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.Comment: To appear in Physica D (accepted July 2013

Neural networks for small scale ORC optimization

This study concerns a thermodynamic and technical optimization of a small scale Organic Rankine Cycle system for waste heat recovery applications. An Artificial Neural Network (ANN) has been used to develop a thermodynamic model to be used for the maximization of the production of power while keeping the size of the heat exchangers and hence the cost of the plant at its minimum. R1234yf has been selected as the working fluid. The results show that the use of ANN is promising in solving complex nonlinear optimization problems that arise in the field of thermodynamics

An assessment of the load modifying potential of model predictive controlled dynamic facades within the California context

California is making major strides towards meeting its greenhouse gas emission reduction goals with the transformation of its electrical grid to accommodate renewable generation, aggressive promotion of building energy efficiency, and increased emphasis on moving toward electrification of end uses (e.g., residential heating, etc.). As a result of this activity, the State is faced with significant challenges of systemwide resource adequacy, power quality and grid reliability that could be addressed in part with demand responsive (DR) load modifying strategies using controllable building technologies. Dynamic facades have the ability to potentially shift and shed loads at critical times of the day in combination with daylighting and HVAC controls. This study explores the technical potential of dynamic facades to support net load shape objectives. A model predictive controller (MPC) was designed based on reduced order thermal (Modelica) and window (Radiance) models. Using an automated workflow (involving JModelica.org and MPCPy), these models were converted and differentiated to formulate a non-linear optimization problem. A gradient-based, non-linear programming problem solver (IPOPT) was used to derive an optimal control strategy, then a post-optimization step was used to convert the solution to a discrete state for facade actuation. Continuous state modulation of the façade was also modeled. The performance of the MPC controller with and without activation of thermal mass was evaluated in a south-facing perimeter office zone with a three-zone electrochromic window for a clear sunny week during summer and winter periods in Oakland and Burbank, California. MPC strategies reduced total energy cost by 9–28% and critical coincident peak demand was reduced by up to 0.58 W/ft2-floor or 19–43% in the 4.6 m (15 ft) deep south zone on sunny summer days in Oakland compared to state-of-the-art heuristic control. Similar savings were achieved for the hotter, Burbank climate in Southern California. This outcome supports the argument that MPC control of dynamic facades can provide significant electricity cost reductions and net load management capabilities of benefit to both the building owner and evolving electrical grid

Identification of heat exchange process in the evaporators of absorption refrigerating units under conditions of uncertainty

Проведено аналіз функціонування випарників абсорбційно-холодильних установок блоку вторинної конденсації типового для України агрегату синтезу аміаку. Обґрунтована необхідність мінімізації температури вторинної конденсації за рахунок створення автоматизованої адаптивної системи оптимального програмного управління. Встановлені рівняння для чисельної оцінки невизначеності теплового навантаження випарника та коефіцієнту теплопередачі. Розроблено алгоритмічне забезпечення щодо розв’язання задач ідентифікації та створення математичної моделі. Визначена технічна структура автоматизованої системи для їх реалізації