Model-based Optimization of Microwave Heating of Bioproducts

The main drawbacks of microwave heating of bioproducts (e.g. foods) are associated with its nonuniform heating patterns. The objective of this work was to derive optimal operating policies for microwave combination ovens in order to achieve better uniformity of temperature and/or quality. The corresponding optimal control problems were stated considering the microwave power and the oven temperature as the control variables. These problems were efficiently solved using a hybrid (stochastic-deterministic) optimization method. Results are presented for several case studies involving different geometries, showing that it is possible to achieve a quite uniform quality distribution inside cylindrical or spherical loads. INTRODUCTION Microwave processing of bioproducts (foods and biological materials in general) offers a number of well-known advantages, namely faster and more efficient heating. As a consequence, microwave ovens are very popular for domestic applications, and the industrial usage for operations like drying, pasteurization and sterilization is increasing. However, several problems often arise due to the uneven pattern of microwave heating: unsatisfactory (non-homogeneous) quality of the final product, insufficient microbiological destruction in cold areas, and safety hazards due to over-heating. There is a clear need to optimize these operations in order to reduce these problems. Modern process systems engineering methods, i.e. model-based optimization and control, can be used to obtain and implement optimal operation policies for these processes. Many research efforts have been dedicated to the mathematical modeling and simulation of microwave processing. In contrast, there is a lack of studies regarding its model-based optimization, probably due to the complexity of the process models. In this work, we present efficient and reliable numerical methods which can successfully solve these challenging optimization problems. DYNAMIC OPTIMIZATION PROBLEMS The dynamic optimization (open loop optimal control) of microwave processing in combined microwave-convection ovens is considered here. In particular, we have formulated and studied the following two classes of optimal control problems: i. maximum temperature uniformity at a given final time. ii. maximum uniformity of the final product quality (measured using C-values [1]) where the control variables are the microwave power and the temperature of the air inside the oven. The optimal control problem (ii) is probably the most interesting, since achieving an homogeneous quality is Presented at 7 International Conference on Microwave and High Frequency Heating. 13-17 September 1999, Valencia (Spain) the main issue both at industrial and domestic levels. A simplified statement (due to space restrictions) of this class of optimal control problems for a cylindrical load (coordinates r, z) is the following: Find the microwave power { } t P , the oven temperature { } t Toven and the process time f t to minimize [ ] } t ; z , r { C max J f Tref = (1) subject to the following constraints: Œ Minimum desired C-value to be achieved: [ ] SET min , Zref f Zref C } t ; z , r { C min ≥ (2) Œ Maximum allowed temperature at the end of the process: [ ] SET max f food T } t ; z , r { T max ≤ (3) Œ The system dynamic model (partial and ordinary differential and algebraic equality constraints), describing all the relevant transport phenomena at the microscopic level. The C-value is defined as the equivalent number of minutes the product would have to spend at a reference temperature (usually T ref=100°C) to achieve a given effect on the final product quality. Mathematically: dt C t Z / ) T T ( Z ref ref ref ∫ − =