Mathematical modeling and optimization of transiant thermoelectric cooling process

Detailed theoretical and experimental studies of thermoelectric cooling, as well as its optimization carried out mainly for the steady state operation of the cooling modules. The process of transient cooling insufficiently studied. However, deeper cooling than under stationary conditions may occur in transient modes when optimization. Optimization problems of transient thermoelectric cooling are problems of optimal control of objects with distributed parameters. The article suggests a generalized mathematical model of transient cooling. This model takes into account the main physical factors that affect the process. The problem of optimal control of transient mode of operation of the thermoelectric cooler with an arbitrary number of stages is formulated. It is proposed a method of solving it. The method consists in sampling the object and moving the object with lumped parameters, which is used to optimize the Pontryagin maximum principle. The article gives examples of computer modeling of optimal process control functions of transient thermoelectric cooling. These functions can be used in the construction and auto-calibration PI and PID controllers for the automatic process control of transient cooling in the thermoelectric devices for different purposes.