Damping-Shaped Voltage Control of PWM Buck Converters: A Modal Co-Design Framework with Energetic Performance Assessment

Modern power electronic converters increasingly require control strategies capable not only of voltage regulation but also of energetic stress management under switched operation. In order to address these requirements, the energetic implications associated with different modal philosophies, polynomial synthesis criteria, and integral structures deserve further investigation. This paper proposes a study of a Damping-Shaped Voltage Control framework for PWM buck converters based on Butterworth, Chebyshev, and Bessel polynomial structures, along with single- and double-integrator state-feedback formulations. In this approach, both the passive filter synthesis and control structure are intentionally derived from the same polynomial family, motivated by preserving modal coherence between energetic storage dynamics and control action. The proposed methodology integrates a multifaceted process, including normalized filter synthesis, damping-shaped pole allocation, and switched-model evaluation. This comprehensive approach encompasses the PWM operation, duty-cycle saturation, and dynamic disturbances. Furthermore, an energy-oriented figure of merit was formulated to quantify voltage regulation, capacitor RMS current, energy storage deviation, and control effort. The damping-shaping formulation systematically modified the energetic performance of the closed-loop system, thereby revealing a correlation among modal damping, energetic smoothness, and control effort. The results presented here extend the scope of classical polynomial synthesis in order to encompass an energetically oriented control perspective for power electronic converters.