Generalized Nonlinear Stabilizing Controllers for Hamiltonian-Passive Systems With Switching Devices

A generalized nonlinear control scheme suitable to regulate any state variable at any desired reference value, for a class of nonlinear Hamiltonian-passive systems that includes switching power devices, is presented. The proposed controller acts as a special nonlinear oscillator, uses as feedback only the state variable that has to be regulated, renders the Hamiltonian-passive structure of the entire system, and regulates the nonlinear system to any nonzero desired equilibrium independently from its parameters and characteristics. Particularly, it is proven that under some common assumptions, the system states consisting of the controller states plus the original system states, are bounded for constant or piecewise constant external inputs. Under the same assumptions, it is established and proven that for these systems there exists a general, bounded, differentiable, nonincreasing storage function. Thus, LaSalle´s invariance principle can be directly applied to prove convergence to the desired equilibrium. Although this storage function can be really constructed as a suitably switching function, its explicit derivation is not necessary for the controller design; it is only needed to guess that such a storage function exists. This constitutes the main contribution of this brief since, in order to implement the proposed controller, one has simply to check whether some initial assumptions are satisfied. The simulation and experimental results conducted for the case of a dc-dc boost converter system with resistance-inductance load verify the proposed design approach.