On the application of singular perturbation techniques to nuclear engineering control problems

With the help of a linear state regulator problem for the control of xenon-induced spatial flux oscillations in a nuclear reactor, it is shown that model simplifications may cause the system equations look like singularly perturbed. An example illustrates that an attempt to transform the system equations to standard singular perturbation form also transforms the performance index and raises the possibility of cheap control, which is physically not possible with mechanical control systems in a nuclear reactor. Another example demonstrates that the stiffness of the system equations dramatically improves by making the model less approximate. Care must, therefore, be exercises while applying singular perturbation techniques to problems which are ill-conditioned as a result of model simplification