A port-Hamiltonian approach to exponential stabilisation and disturbance rejection of a DC-DC buck converter with a nonlinear load

Abstract

In this paper we present a passivity-based control (PBC) design for stabilisation of a DC-DC buck converter subject to nonlinear loads and matched and unmatched disturbances. We propose a stabilising dynamic controller that also implements integral action in the closed-loop system to reject constant disturbances. We show that the desired equilibrium in closed loop is exponentially stable and that it is input-to-state-stable with respect to matched and unmatched disturbances. The controller is designed within the framework of port-Hamiltonian theory, which allows us to ensure stability and robust closed-loop properties. We also characterise, in terms of the Volt-Ampere functions, the class of nonlinear loads that the controller can handle. The resulting controller is a classical interconnection and damping assignment PBC with integral action. An advantage of our design process is that we solve the so-called matching equation by construction; thus, we avoid the need of solving partial differential equations (PDEs). The performance of the control system is assessed via numerical simulations of the closed loop under several disturbance scenarios.