Nonlinear state feedback control of second-order nonminimum-phase nonlinear systems

The present work addresses the problem of synthesizing nonlinear state feedback controllers for second-order nonminimum-phase nonlinear systems. The concept of a first-order nonlinear all-pass is first introduced. A class of static state feedback control laws is then developed that makes the closed-loop system equivalent, under an appropriate coordinate transformation, to a nonlinear first-order all-pass in series with a linear first-order lag. A particular control law from this class is calculated that results in ISE-optimal response. The performance of the proposed methodology in set point tracking is evaluated through numerical simulations in a CSTR example.