Controlling nonlinear systems through time delays: An automotive perspective

The paper considers the problem of controlling systems with time delay. Two examples from engine powertrain control are selected to illustrate different effects of time delay on the performance of the closed loop system. In the first example, the air-to-fuel ratio is measured with delay. A plot of an envelope for parameters of a PI controller shows the gain reduction imposed by the time delay. In the second example, the delayed term satisfies the matching condition in a nonlinear model of a turbocharged diesel engine. Input-output linearization and the Razumikhin Theorem are used to claim stability of the feedback system. In this case, gain reduction is not needed to preserve stability.