Stabilization of food-chain systems using a port-controlled Hamiltonian description

We consider the problem of output-feedback stabilization of a class of food-chain systems. The design methodology builds upon some developments on passivity-based stabilization of port-controlled Hamiltonian (PCH) systems reported in Ortega et al. (1999) and Maschke et al. (1998). We first write the system dynamics in PCH form, with the Hamiltonian function being the total mass. Then, following the design procedure, we modify the Hamiltonian function to assign a minimum at the desired equilibrium. Finally, to obtain an output feedback scheme, we inject positive damping into the system. We should underscore that, even though, adding positive damping is rather unusual in control applications, here it is naturally suggested by the design methodology. Some simulation results are presented to illustrate the properties of the controller