MOTION PLANNING FOR THE HEAT EQUATION WITH RADIATION BOUNDARY CONDITIONS BASED ON FINITE DIFFERENCE SEMI-DISCRETIZATIONS

In this contribution, motion planning for the temperature distribution in a 1-dimensional slab with radiation boundary conditions is considered. For this, the infinite-dimensional model of the slab is spatially discretized using finite differences. It is shown that the discretized finite-dimensional model is flat and hence serves as a basis for a feedforward control design. For the heat equation with constant parameters, it is shown that the obtained feedforward control converges to the feedforward control for the infinite-dimensional problem in the limit as the discretization step size tends to zero. For the heat equation with temperature dependent parameters, simulation results illustrate the convergence behavior.