So I have been trying to come up with a mock process control for a hypothetical system. The system itself is pretty simple: the pressure of a chamber is measured by a pressure sensor and fed to a PI Controller which controls a nozzle. Controlling the opening of the nozzle regulates the pressure within the chamber.
So I derived the closed loop transfer function for pressure control. This was simple enough and easy to model in simulink. However, I am not interested in controlling the pressure. I want to control a property of the material that is produced by this process. This property is crystallinity. I cannot measure the crystallinity directly or fast enough to implement in a feedback loop. But I do have a polynomial correlation between pressure and crystallinity. Assume this correlation is: a*pressure^2+b*pressure+c = crystallinity.
So I have something like this: yout = {Overall Transfer Function}*SetPoint. Using the polynomial correlation I want to do something like this: a*yout^2 + b*yout + c. I don't know how to model a function like this in simulink. So I tried my own approach; I plotted the above function in the laplace domain and derived a polynomial fit for the curve. Then I found the inverse laplace of the polynomial fit in order to observe the time domain response.
However, the inverse laplace transformation of that fit is simply a string of dirac delta functions and plotting this yields a straight line.
So, first of all, is my general approach to this problem correct? Is there something fundamentally wrong with my attempt at plotting the laplace domain response and transferring that to time domain?
What is the easiest way to obtain a time domain response with this unusual transfer function?
