Parameter-Varying Loop-Shaping for Delayed Air-Fuel Ratio Control in Lean-Burn SI Engines

Dynamic systems with time-varying delay in the control input are studied in the present paper. The delay is considered as a varying parameter and Padé approximation is applied to transfer the infinite-dimensional delay problem into a finite-dimensional paradigm represented in the form of a non-minimum phase system (NMP). Inherited delay characteristics are now represented through unstable internal dynamics for the NMP system, which poses restrictions on the achievable control bandwidth thereby resulting in an imperfect tracking performance and poor stability condition. Presented in this paper, is a methodical parameter-varying loop-shaping control design approach, which simultaneously satisfy a variety of control requirements and offer an insight into the limitations posed by the NMP representation. The suggested method is then applied to fueling control in lean-burn gasoline engines addressing the varying transport and combustion delay. The developed approach is validated with experimental data on a Ford F-150 truck SI lean-burn engine with large time-varying delay in the control loop and the closed-loop system responses are presented to demonstrate disturbance rejection, measurement noise attenuation, and robustness properties against delay estimation errors.