A dynamic feedback control strategy for control loops with time-varying delay

Abstract

Dynamic systems of nth order with time-varying delay in the control loop are examined in this paper. The infinite-dimensional pure delay problem is approximated using a jth-order Padé approximation. Although the approximation provides a well-matched finite-dimensional configuration, it poses a new challenge in terms of unstable internal dynamics for the resulted non-minimum phase system. Such a non-minimum phase characteristic limits the closed-loop system bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the unstable internal dynamics of the system is captured and a new dynamic compensator is proposed to stabilise it in a systematic framework. A dynamic controller is developed, which provides the overall system stability against unmatched perturbation and meets the desired tracking error dynamics. The proposed approach is then applied to fuelling control in gasoline engines addressing the varying transport delay of the oxygen-sensor measurement in the exhaust. The developed methodology is finally validated on a Ford F-150 SI lean-burn engine model with large time-varying delay in the control loop.

Keywords:

• time-varying delay
• feedback control
• dynamic compensator
• non-minimum phase systems

Notes

1. The relative degree of a linear system is the difference between the degree of the denominator and numerator of the transfer function.

Additional information

Funding

This work was supported by NPRP grant from the Qatar National Research Fund (a member of Qatar Foundation) [grant number 08-398-2-160].