I have 84 data sets (n=3) corresponding to 28 conditions (sample composition and temperature) and have fit my data set to the following nonlinear model using MATLAB nonlinear curve fitting:

$$y = \bigg[\frac{A}{1+\exp(-B\cdot(x-C))}\bigg]+D\cdot x$$

where the $y$ is mass [g] and $x$ is time [s].

How can I statistically and simultaneously compare my model parameters across all my conditions (i.e. A from condition 1 is statistically different from condition 2)? My first thought was to do an ANOVA+Tukey, but I do not know if this is valid with a nonlinear model parameter as the response.