Control of a process with unmeasured disturbances that change its steady-state gain sign

Because the sign of the steady-state gain of an industrial NOx reduction unit changes according to the magnitude of the main external disturbance (hydrogen flow rate), designing an appropriate controller is particularly challenging. To address this issue, theoretical analysis suggested that a simple linear controller can provide adequate control for this process. Interestingly, tuning of this controller deviates from well known guidelines of linear control theory, which dictate that closed-loop stability is maintained by sluggish enough control of a stable linear process. It turns out, that for this nonlinear process, controller tuning must be neither too sluggish nor too aggressive, in an intermediate range suggested by a variant of the small-gain theorem proven here for corresponding nonlinear operators. The operator-based analysis was confirmed via computer simulation on a simple first-principles model, calibrated on real plant data. It is expected that control performance and robustness may improve if a number of ideas suggested in the text are explored further.

► Large disturbances may change the steady-state gain sign of a NOx reduction unit, making controller design challenging.
► Controller design guidelines were developed using nonlinear operator theory, found to have distinct advantages over robust linear control theory for this system.
► An appropriately tuned PI controller was found to be adequate.
► The PI controller was tested via computer simulations.
► Adaptive control schemes may improve closed-loop performance and robustness.