Chapter 8. Measuring the Transfer Function
If we have a good theoretical model for the system under consideration, then we can derive the transfer function directly from the model by calculating the Laplace transform of the differential equation that describes the system dynamics. More often than not, however, there won’t be a good analytical model. In those cases, we will have to measure the transfer function in a process known as system identification. Even if we have a good model, we will still need to perform some measurements to “fit” the model’s parameters.
There are basically two different questions we need to ask.
- Static input/output relation:
If an input change of a certain size is applied, what’s the size and direction of the ultimate change in process output?
- Dynamic process response:
If an input change is applied suddenly, how long does it take for the system to respond?
These are the basic questions we want to answer through observations. The answer to the first one is captured in the static process characteristic, the answer to the second in the dynamic process reaction curve or plant signature.
All measurements are done in an open-loop arrangement, and without a controller:
In that way, we can adjust the input in an arbitrary fashion as desired, so that we observe only the response of the system or plant alone.
Static Input/Output Relation: The Process Characteristic