I have a system composed by k-thermocouple + metal handpiece, the thermocouple is drowned into the handpiece. If I manage to estimate a transfer function of the system so-made, for example trough several step and ramp response, is it possible to get an approximation of the real temperature? If I briefly recall the system theory, we have that: y(s)=x(s)h(s), where
- h(s) is the transfer function
- y(s) is the output ( the read temperature)
- x(s) is the input ( the real temperature)
As a student, I'm used to manage the "unknown" as the output y(s)...but in this case, I know the output (because I read it from the thermocouple) and I know the transfer function (because I've characterized the system), what I need is the input.
Mathematically speaking the answer is easy: x(t)=inverseLT(y(s)/h(s)) , but practically how can I obtain this? With a real-time measuring system, for example microcontrollers? The first step is to convert the h(s) into the equivalent discrete time h(z), of course, but then? I need to find the frequency response? And so, the final question: why do I need the response of the system when sinusoidal inputs are applied if the system will never experience such inputs in real life usage?