TY - JOUR

T1 - Bias of anticipated non-parametric closed-loop frequency response for controller gain re-tuning

AU - Steinert, Agnes

AU - Steffensen, Rasmus

AU - Holzapfel, Florian

N1 - Publisher Copyright:
© 2023

PY - 2023/5

Y1 - 2023/5

N2 - In data-driven controller re-tuning, when requirements exist for the closed-loop frequency response, it is essential that the estimated closed-loop frequency response for a new controller parameter set, correctly reflects the respective true closed-loop. To quantify the difference between the true and estimated frequency response, this paper presents the bias of the non-parametric closed-loop frequency response estimate for the closed-loop system with updated controller parameters. It is calculated for the case where the estimate of the closed-loop frequency response of the system with an initial controller is used, to estimate the new closed-loop frequency response with an updated controller. Such estimates are useful in the process of gain re-tuning based on closed-loop experiments, where new controller parameters are calculated to satisfy requirements for the closed-loop frequency response. It is shown that the estimate appears similar in structure to the indirect non-parametric plant estimate, and hence the bias is reduced with an increasing excitation-to-noise-ratio for the closed-loop experiment. It is also seen that the bias tends to zero when the change in the controller parameters tends to zero or the feed-forward is increased sufficiently. Simulation results demonstrate the concept for a flight-test-based gain re-tuning of a pitch rate controller for an aircraft.

AB - In data-driven controller re-tuning, when requirements exist for the closed-loop frequency response, it is essential that the estimated closed-loop frequency response for a new controller parameter set, correctly reflects the respective true closed-loop. To quantify the difference between the true and estimated frequency response, this paper presents the bias of the non-parametric closed-loop frequency response estimate for the closed-loop system with updated controller parameters. It is calculated for the case where the estimate of the closed-loop frequency response of the system with an initial controller is used, to estimate the new closed-loop frequency response with an updated controller. Such estimates are useful in the process of gain re-tuning based on closed-loop experiments, where new controller parameters are calculated to satisfy requirements for the closed-loop frequency response. It is shown that the estimate appears similar in structure to the indirect non-parametric plant estimate, and hence the bias is reduced with an increasing excitation-to-noise-ratio for the closed-loop experiment. It is also seen that the bias tends to zero when the change in the controller parameters tends to zero or the feed-forward is increased sufficiently. Simulation results demonstrate the concept for a flight-test-based gain re-tuning of a pitch rate controller for an aircraft.

KW - Autotuning

KW - Closed-loop identification

KW - Frequency domain

KW - Statistical analysis

KW - System identification

UR - http://www.scopus.com/inward/record.url?scp=85148687583&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2023.110881

DO - 10.1016/j.automatica.2023.110881

M3 - Article

AN - SCOPUS:85148687583

SN - 0005-1098

VL - 151

JO - Automatica

JF - Automatica

M1 - 110881

ER -