I obtained the transfer function for an electrical system from experimental data (left plot). Thereby, I can calculate the output voltage response for a given voltage input, using TransferFunctionModel and OutputResponse in the time domain (right plot):
My question is, how can I use the obtained TransferFunctionModel to find the right voltage input pulse for a desired output voltage? I know from this publication, that for simple RC networks there is an analytical solution for this task, see for example Fig. 4(b) therein. As I'm not aware of an analytical solution for an arbitrary transfer function I was wondering if I could numerically solve for the required input (blue curve from above) if I want my output response to follow a specific function (green curve from above), e.g., Sin[x]^2.
I'm thinking that I might need to parametrize my possible input function somehow and then use Solve or NSolve to find the right parameters. However, I expect the required input to be of complex shape, i.e., not simply proportional to Sin[x]^2 like the blue curve above, and, thus, not sure how to parametrize it.
I really would appreciate comments or suggestions on how to proceed.