On Nonlinear Systems with Poorly Behaved Zero Dynamics

The design of controllers for nonlinear, nonminimum-phase systems is very challenging and is currently considered to be one of the most difficult theoretical control problems. Most control algorithms for nonlinear processes perform a linearization making use of an inverse of the system. In the linear case, the system can be factored into the minimum-phase and the nonminimum-phase parts and only the first one is inverted for purpose of control design. A similar scheme for nonlinear systems is still under investigation. The present work adresses the problem of synthesizing nonlinear state feedback controllers for nonlinear, nonminimum-phase processes in three different ways. The first approach consists of a partial linearization which preserves stability by using an approximate stable/anti-stable factorization. The second technique can be viewed as an inner-outer factorization based approach. And, finally, in the single-output case, it is shown (through an example) that stabilization of the internal dynamics of a nonmininum-phase system can be achieved by using an additional input if this is feasible in practice. In this case, the manipulated variables have different roles, i.e., one is chosen such as to input/output feedback linearize the system and the second is used to locally stabilize the resulting nonminimum-phase internal dynamics.