Study On Solution To IHCP Problems By Asymptotical Observer

In this paper the inverse heat conduction problem (IHCP), which arose from estimating the temperature of the blast furnace, was discussed and solved by designing a dynamic asymptotical observer.First we introduced the problem and its significance, and simplified the 3-dimenisional blast furnace model to one-dimensional IHCP. Then we gave an overview of the known methods about IHCP. With an example we showed the difficulty of studying IHCP: IHCP is an ill-posed problem, that is to say, the small errors in initial data will lead to a large errors in the solution. We also introduced Beck's future sequential method, and its application at solving the first kind Volterra integral equations. In section 3, the theory about asymptotical observer of linear system was introduced. Then it was generalized by Huang J.W. to observe the finite dimensional unknown input of the system. In section 4, a linear system was derived from the partial differential equation, and the IHCP was rewritten as the problem to estimate the unknown input of the linear system. With the result of the above section, the observability was checked, and the observer was designed to estimate the solution of the IHCP. The error analysis showed that the estimated solution could be exact gradually. In section 5, simulation showed the effectiveness of our method.