The most important obstacle for this type of controller design is caused by the fact that most plants contain true integrators between the control signal and the output signal. As the plant integrates the control signal, the inverse plant has no choice but to differentiate the output signal.
This problem can be solved by assigning at least as many open integrators to the ideal (model) plant as there are open integrators in the true (physical) plant. In that case, a cascade of the ideal plant with the inverse physical plant model doesn't contain any surplus differentiators.
Dymola offers an elegant way for implementing this controller design. To this end, it suffices to have access to models of the ideal and the real plant. Dymola allows to connect the outputs of these two plants with each other, while declaring the input of the real plant an output of the model. Dymola makes use of symbolic formula manipulations in the translation of the object-oriented model description down to the simulation code. These formula manipulations symbolically invert the real plant model, and in addition, get rid of the surplus differentiators. This can be accomplished in a fully automatic fashion, and works even for most non-linear systems. The only condition to be satisfied is that all of the non-linearities in the original plant model are themselves invertible.
Now there is a second problem. The control found in this fashion is an open-loop control structure, not a closed-loop control structure. This is undesirable. Yet, FIR can be used to convert the open-loop control into a closed-loop fuzzy control structure. We use the open-loop control structure to record system responses for a set of different representative control actions. We record the input signal, the output signal, and the optimal control signal. Subsequently, we identify a FIR model that "predicts" future values of the control signal as a function of the input signal, the output signal, earlier values of these two signals, as well as earlier values of the control signal. This FIR model represents a closed-loop fuzzy controller.