Time-varying controller based on flatness for nonlinear anti-lock brake system

It is shown that by the use of flatness the problem of pole placement, which consists in imposing closed-loop system dynamics, can be related to track desired trajectories in the finite-dimensional linear time-invariant case. Polynomial two-degree-of-freedom controller can then be designed with the use of an exact observer and without resolving the Bézout's equation. In this paper, an extension of these developments is proposed in the linear time-varying (LTV) framework. The proposed approach is illustrated with the control of nonlinear model of an anti-lock brake system. The time-varying controller obtained from the LTV model ensures the trajectory tracking of the nonlinear model.