TY - GEN

T1 - Robust rejection of sinusoids in stable nonlinearly perturbed unmodelled linear systems

T2 - 2011 American Control Conference, ACC 2011

AU - Natarajan, Vivek

AU - Bentsman, Joseph

PY - 2011/9/29

Y1 - 2011/9/29

N2 - Assuming no knowledge of closed-loop dynamics other than being that of a stable nonlinearly perturbed linear system and the forward path gain at the frequency of interest being known and non-zero, a control approach is proposed that rejects a sinusoidal disturbance of known frequency from the system output. The approach consists in partitioning the feedback path of a stable closed-loop system into two weighted paths and inserting between them a loop containing an internal model based filter. The approach is supported by two theorems ascertaining internal stability, that guarantee the rejection of the unwanted sinusoid under the augmentation proposed, with no closed-loop stability loss. The efficacy of the approach is demonstrated through simulations on a model of a servo system consisting of a beam with an electro-hydraulic actuator attached at one end and a mass at the other, and through experiments on the corresponding physical testbed. Robustness of the approach is briefly discussed. A relative non-intrusiveness of the augmentation procedure, a virtual lack of a modeling necessity, and simplicity of estimating the unaugmented forward path gain via experiment on the stable closed-loop system make the approach proposed well suited for industrial use.

AB - Assuming no knowledge of closed-loop dynamics other than being that of a stable nonlinearly perturbed linear system and the forward path gain at the frequency of interest being known and non-zero, a control approach is proposed that rejects a sinusoidal disturbance of known frequency from the system output. The approach consists in partitioning the feedback path of a stable closed-loop system into two weighted paths and inserting between them a loop containing an internal model based filter. The approach is supported by two theorems ascertaining internal stability, that guarantee the rejection of the unwanted sinusoid under the augmentation proposed, with no closed-loop stability loss. The efficacy of the approach is demonstrated through simulations on a model of a servo system consisting of a beam with an electro-hydraulic actuator attached at one end and a mass at the other, and through experiments on the corresponding physical testbed. Robustness of the approach is briefly discussed. A relative non-intrusiveness of the augmentation procedure, a virtual lack of a modeling necessity, and simplicity of estimating the unaugmented forward path gain via experiment on the stable closed-loop system make the approach proposed well suited for industrial use.

KW - Internal model principle

KW - Periodic response

KW - Perturbed linear system

KW - Small gain theorem

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M3 - Conference contribution

AN - SCOPUS:80053148135

SN - 9781457700804

T3 - Proceedings of the American Control Conference

SP - 3289

EP - 3294

BT - Proceedings of the 2011 American Control Conference, ACC 2011

Y2 - 29 June 2011 through 1 July 2011

ER -