DYNAMIC OBSERVER METHOD BASED ON MODIFIED GREEN'S FUNCTIONS FOR ROBUST AND MORE STABLE INVERSE ALGORITHMS

摘要

This work presents a modified procedure to use the concept of dynamic observers based on Green's functions to solve inverse problems. The original method can be divided in two distinct steps: ⅰ) obtaining a transfer function model G_H and; ⅱ) obtaining heat transfer functions G_Q and G_N and building an identification algorithm. The transfer function model, G_H, is obtained from the equivalent dynamic systems theory using Green's functions. The modification presented here proposes two different improvements in the original technique: ⅰ) A different method of obtaining the transfer function model, G_H, using analytical functions instead of numerical procedures, and ⅱ) Definition of a new concept of G_H to allow the use of more than one response temperature. Obtaining the heat transfer functions represents an important role in the observer method and is crucial to allow the technique to be directly applied to two or three-dimensional heat conduction problems. The idea of defining the new G_H function is to improve the robustness and stability of the algorithm. A new dynamic equivalent system for the thermal model is then defined in order to allow the use of two or more temperature measurements. Heat transfer function, G_H can be obtained numerically or analytically using Green's function method. The great advantage of deriving G_H analytically is to simplify the procedure and minimize the estimative errors.