Feedback Passivation as a Tool in Controller Design for Nonlinear Systems

Mrdjan Jankovic, University of California, Santa Barbara

We examine the use of feedback passivation, i.e. rendering a system passive via feedback, to design feedback control for nonlinear systems. The method is illustrated on a model of a rotational proof mass actuator (TORA System). The crucial task in the design is to find a Lyapunov function for a stable system representing zero-dynamics with respect to an appropriately chosen output. This problem has been resolved for a class of cascade systems which are obtained as an interconnection of a stable and exponentially stable parts. The systematic method for construction of Lyapunov functions has led to a recursive controller design procedure for a very general class of upper-triangular (feedforward) systems. These results are illustrated in two examples: the "nonlinear benchmark problem" and the third order cubic chain of integrators.