What are the requirements for a transfer function to track a

What are the requirements for a transfer function to track a time dependent reference?

Solution

The transfer function always has to be stable.

If the input time is a step function (constant value) only a zero type system can follow it
If the input time is a ramp a zero system can follow it, first type system can follow it, second type system can\'t
If the input time is a parable a zero and first system cant follow it, second type system can follow it

If you keeping upgrading the grade of the input signal you must upgrade the pure integrator in FT
zero type system= 0 integrator
first type system= 1 integrator
second type system= 2 integrator