On tuning of ADRC with competing design indices: a quantitative study

Controller optimization has mostly been done by minimizing a certain single cost function. In practice, however, engineers must contend with multiple and conflicting considerations, denoted as design indices (DIs) in this paper. Failure to account for such complexity and nuances is detrimental to the applications of any advanced control methods. This paper addresses this challenge heads on, in the context of active disturbance rejection controller (ADRC) and with four competing DIs: stability margins, tracking, disturbance rejection, and noise suppression. To this end, the lower bound for the bandwidth of the extended state observer is first established for guaranteed closed-loop stability. Then, one by one, the mathematical formula is meticulously derived, connecting each DI to the set of controller parameters. To our best knowledge, this has not been done in the context of ADRC. Such formulas allow engineers to see quantitatively how the change of each tuning parameter would impact all of the DIs, thus making the guesswork obsolete. An example is given to show how such analytical methods can help engineers quickly determine controller parameters in a practical scenario.