In order to design a physically realizable controller for the first-order process, there must be a denominator polynomial in the controller. Define a first-order filter as the following transfer function,
where λ is a filter tuning parameter that has units of time. We see shortly that we can think of λ as a desired time constant for the output response; if a faster response is desired, then λ is decreased. Now, let the controller be designed in the following fashion to make q(s) proper.
which yields the following controller for a first-order process,
Equation ( ...