We would appreciate some plots. Learning curves of recurrent NN working as a plant are interesting. For harmonic oscillator your RNN should not contain any hidden layers - only 1 input and 1 output node and 2 delays at each of them. Activation function should be linear. If your code is correct, this configuration will match oscillator perfectly. The question is how much time does it take to adapt.

Does FANN support regularization? I think this will make your controller more stable. Try to use more advanced algorithms then gradient descent for adaptation. They will increase convergence speed. For example, look at fminunc function at Matlab.