Reduced gain pi/pid controllers for foptd/soptd processes under load disturbance

In practical applications, an engineer is sometimes expected to execute the step test for tuning the controller without waiting much for the steady-state or a low level of disturbances. Hence, knowing that the initial settings may not be quite reliable, he/she detunes the controller by reducing its gain as a precaution against possible poor behaviour of the closed-loop system. It is up to their experience to choose by how much to detune. Therefore, the development of a practically oriented approach that would assist the engineer to choose the degree of gain reduction is the goal of this paper. The approach assumes that process parameters are determined by the least-squares approximation of the step response. Accuracy of the approximation is evaluated by a relative approximation error involving integrals of the error and the process response itself. The SIMC tuning rules are applied to choose the initial controller settings. The approach relies on detecting by simulation the worst case that may happen when the step response is triggered at any time. Detuning nomograms specify by how much to reduce the initial gain for PI-FOPTD and PID-SOPTD designs, given the relative approximation error. Two long-lasting lab experiments involving temperature control identify a plant, verify the load disturbance model through multiple step tests and demonstrate usage of the approach in the closed-loop system.