Question: An example of ringing occurs when a digital proportional-only controller is applied to a process that is so fast that it reaches steady state within one execution period, ?t. The following calculations, which are simple enough to be carried out by hand, will help explain ringing.
(a) Calculate several steps of the response of a control system with a steady-state process with Kp = 1.0(θ = τ = 0) and a proportional only controller, Kc = 0.8. Assume that the system is initially at steady state and a set point change of 5 units is made.
(b) Repeat the calculation for an integral-only controller. Find a value of the parameter (Kc?t/ Ti) by trial and error that gives good dynamic performance for the controlled and manipulated variables.
(c) Generalize the results in (a) and (b) and give a tuning rule for integral only, digital control of a fast process.