Controller Design and Analysis for a Two-Cell DC-DC converter in the Presence of Saturation

In this work, a zero static error proportional controller for a two-cell DC-DC buck converter is synthesized and analyzed. Under a traditional proportional control scheme, the system presents a constant error of the current supplying the output load. As the proportional feedback gain is increased, the average static error decreases. However, sub-harmonic oscillations and chaotic behavior emerge beyond successive bifurcations. To achieve zero current and zero voltage static error, we suggest a modification of the traditional proportional controller. By optimizing the feedback gain, the settling time is also decreased. Then, using nonlinear analysis and Lyapunov stability theory, we prove that zero static error is achieved even in presence of duty cycle saturation. Numerical simulations are presented to confirm our theoretical results.