System identification for control design

Hi everybody,

I actually do not have a good knowledge of control theory but I have the task to control a controller for a given complex model implementation in Simulink, but with no knowledge about the mathematical representation. Now I was told to do system identification from expriment data to get a mathematical representation of the system. Due to lack of knowledge I read many literatur but still could not find a reasonably explanation for my problem:

My question is: How good has the model to fit for control design purposes?

I tried to obtain a linear model that describes the dynamic of the system vaguely. The problem is that the output of the system is inverse proportional to the input of the system. Now the identified model fits with about 30% to 60% to different validation sets obtained by the given model according to System Identification Toolbox. The input is always positive and the output, too.

With the identified model I was able to obtain fitting parameters for a PID controller that works for the already given model. But when I look at the output of the controller the output is negative. In contrary feeding the positive values from the validation sets now lead to negative outputs although the outputs should be positive.

My first question is: Why does the identified model now give negative outputs for the same positive values of the validation data different from obtaining the results from System Identification Toolbox?

Second question: Although the identified model does not reflect the system well, is it still possible to use it to obtain parameters for PID controller since the parameters I obtained with this model was fitting to the already given model implementation?

I know that my description is very vague but maybe there is someone who can help me. This task really overstrains me and I am not able to find suitable literatur for good understanding of such particular systems.