Proper Orthogonal Decomposition Based Modeling and Experimental Implementation of a Neurocontroller for a Heat Diffusion System
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Experimental implementation of a dual neural network based optimal controller for a heat diffusion system is presented. Using the technique of proper orthogonal decomposition (POD), a set of problem-oriented basis functions are designed taking the experimental data as snap shot solutions. Using these basis functions in Galerkin projection, a reduced-order analogous lumped parameter model of the distributed parameter system is developed. This model is then used in an analogous lumped parameter problem. A dual neural network structure called adaptive critics is used to obtain optimal neurocontrollers for this system. In this structure, one set of neural networks captures the relationship between the states and the control, whereas the other set captures the relationship between the states and the costates. The lumped parameter control is then mapped back to the spatial dimension, using the same basis functions, which results in a feedback control. The controllers are implemented at discrete actuator locations. Modeling aspects of the heat diffusion system from experimental data are discussed. Experimental results to reach desired final temperature profiles are presented.