Uncovering Disturbance Observer and Ultra-Local Plant Models in Series PI Controllers

Abstract

The paper settles two major liabilities and asymmetries of the theory of automatic control to the design of simple system controllers. It shows the most frequently used series proportional integral (PI) controllers as disturbance reconstruction and compensation-based structures and solves their designs using two types of linear system models. Beginning with the example of a simple integrator controlled by a P controller, it shows that constant input disturbances can be reconstructed by evaluating steady state values of the controller output. Thereby, the nearly steady state controller output can be simply achieved by using a low-pass filter with a time constant significantly longer than the time constant of stabilized processes. This disturbance observer (DOB) functionality can be demonstrated as being kept by series PI controllers designed by the pole assignment method. The DOB design can also be extended to first-order systems with internal feedback. However, there, the reconstructed disturbances depend both on the controller and the plant output steady state values. Because this feature is missing in industrial PI controllers, it indicates their connections with simpler, ultra-local (integral) linear system models. The interpretation of PI controllers as DOB-based structures allows a systematic consistent classification of all existing disturbance compensation structures and simplifies their comparisons with other modern and postmodern DOB-based alternatives. Given the breadth of use, improved understanding of PI control functionality also represents an important step to their optimal implementation and to research of innovative modifications, as illustrated by facilitating the flexible use of the new functional capabilities offered by embedded controls. By enhancing “the birth” of new solutions, it is then possible to better satisfy the permanently growing requirements of practice.