Border Collisions and Chattering in State Feedback Controlled Boost Converters

Abstract

Digital state feedback controllers are frequently used in DC-DC converters when high/optimal performance is required. In this paper we investigate the nonlinear behavior of such systems when the feedback control law is a discontinuous function of the location of the state vector in the state space. It is shown that the well known problem of chattering that appears in these controllers (e.g. in Model Predictive Control - MPC) is due to a border collision between the fixed point of the nominal period one orbit and the borders that define the areas that the specific gains are utilized, and forces the converter to exhibit high current ripple that can deteriorate the system’s performance. The exact switched dynamical model of the system is described along with the three switching manifolds in the state space and through that a detailed analysis of the border collision that causes the chattering and the high current ripple is presented. Finally, a methodology is proposed that can lead to a design procedure that completely avoids this problem. The latter can be taken into account when advanced controllers are employed in order to guarantee the optimal behavior of the system.