Adaptive backstepping controller for uncertain systems with unknown input time-delay. Application to SI engines

In this paper, we study the equilibrium regulation of potentially unstable linear systems with an unknown input time-delay and unknown parameters in the plant. We extend recent results from the literature where such systems are treated using a backstepping approach applied to a distributed parameters system representation of the delay. We develop a local result, robust to delay errors and apply it for the control of the Air-Fuel Ratio in Spark Ignition engines. A proof of convergence is established for this particular example. Experimental results stress the relevance of the proposed control algorithm.