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Nonlinear robust control of parabolic distributed parameter systems by means of radial basis function neural networks and singular value

In this paper, a nonlinear robust control law for quasi linear parabolic distributed parameter systems is developed. Firstly, the singular value decomposition method is applied to dissociate the temporal from the spatial behavior of the system. The produced empirical eigenfunctions are used as basis functions in a reduced-order model that captures the dominant behavior of the distributed system. Then, a radial-basis-function neural network is developed to estimate the responses of the temporal coefficients, based on past values of the process input variables. A state-space representation of the neural network that includes the distance of the controlled variables from their set points is constructed next. The nonlinear state-space model is finally incorporated in the context of a robust control law of guaranteed stability. The implementation of the method in a two-dimensional tubular-reactor example illustrates that the control law tracks successfully set point changes despite the model error.