A general canonical form for feedback passivity of nonlinear systems

In this article projection operators are used for obtaining a natural canonical form, for non-linear single-input single-output systems, which clearly exhibits the conservative, the dissipative and the locally destabilizing forces present in the drift vector field of a given system, for which a storage function is known. When the system's natural 'energy management' structure is revealed, a suitable state-dependent input coordinate transformation makes the system passive or strictly output passive. A direct application of the 'energy shaping plus damping injection' controller design method, which is a well known controller design option for passive systems, may then be attempted. A bioreactor controller design example is presented, for illustrative purposes, which includes computer simulations.