Precision control of thermal field in solid sample

Abstract

The research and development results on the con- trol system design governing by the thermal field into the solid sample are given. The design is based on the following steps: 1) definition of model for thermal field dynamics, 2) prior (in first approximation) spectral decomposition of the field, 3) identifica- tion of field and sample parameters, 4) improved spectral de- composition. Computer simulation and implementation of the control system was performed for 1D sample. The efficiency and high accuracy of control system and control algorithms are demonstrated in details. I. INTRODUCTION The design of systems for control of the fields in distrib- uted samples (e.g., thermal or deformations field, form of wave front etc.) when external perturbations take place is a very complicated problem (even for linear systems). The root is that the system under control has infinite number degrees of freedom while real system can have under the control only finite number of degrees of freedom. So there is a competi- tion between high accuracy of a control and excessive com- plexity . The finding of this problem solution is under the de- tail investigation in this paper. To that end the theoretical modeling, computer simulation and implementation in ex- perimental device of the control over distributed sample have been done and definite recommendations for precision con- trol system design are proposed. A number of methods of analysis, control modeling and engineering implementations were developed for design of control of distributed samples. For example in paper (1) plasmotronic dynamics is investigated. Distributed system is approximated by finite-dimensional system for which regula- tor was synthesized that is helped to decrease transition time up to 3…4 times. In the paper (2) method was proposed for control of distributed systems under the uncertain environ- ment by using so called sliding mode. The specific problem of this kind is the design of control over the space-distributed thermal field when only finite number of heaters concentrated near some space points are in use. In the paper (3) review of physical models and engineering solutions for methods of wave front compensation in optical systems is given. There are many other methods were developed for different kinds of application. But nevertheless the problem of control systems design over the fields is still far from its termination. In our investigation the system for automatic compensation of external thermal disturbances in solid sample is studied which serves for precision control of temperature drops over the sample. This system was named as Control System for Thermo-Gradient Stabilization (CSTGS). Decomposition of the thermal field have been done on the base of harmonics method or in the other terms spectral method (4). The advantages of the spectral method over the finite-difference method are marked out in the papers (5), (6). Parameters of the model (parametric identification) may be calculated (ideal identification) by analysis of model prop- erties. But the most appropriate parametric identification are given by experimental measurements. It is shown in our pa- per that only by this way it is possible to achieve high effec- tiveness and high accuracy of control. In what follows we will refer to experimental realization of CSTGS that was specially designed for the purposes of inves- tigations of the control theory problems mentioned above.