Design of experiments with models that are nonlinear in their parameters is available using either the DOE menu or the JMP Starter DOE category.
Nonlinear designs offer both advantages and disadvantages compared to designs for linear models.
On the positive side, predictions using a well chosen model are likely to be good over a wider range of factor settings. It is also possible to model response surfaces with more curvature and with asymptotic behavior.
On the negative side, the researcher needs a greater understanding of both the system and of the nonlinear design tool.