Mathematical Modeling and <i>µ</i>-Synthesis-Based Robust Control of Boost DC-DC Converters Using MATLAB

This paper presents a robust control framework for Boost Direct Current to Direct Current (DC-DC) converters based on µ-synthesis in MATLAB. The approach explicitly models structured parameter uncertainties, including the capacitor Equivalent Series Resistance (ESR) and load variations, and tailors the weighting filters to balance tracking performance, control effort, and noise attenuation. In simulations, the µ-controller achieves zero overshoot, settling time ≈ 1.2 ms, and steady-state error < 0.01 V, while a tuned Proportional-Integral-Derivative (PID) baseline exhibits ~12% overshoot, settling time ≈ 2.5 ms, and ≈ 0.45 V steady-state error under the same uncertainty set. Robust stability is certified by µ-bounds below unity across the design frequency band, and robust performance margins meet the specification. Novelty and contributions: explicit inclusion of capacitor ESR as a structured uncertainty in the modeling and synthesis loop; an implementation-oriented workflow (linearization → weighting design → D-K iteration → realization) with reproducible MATLAB code; and a quantitative benchmark versus a classical PID baseline under identical operating scenarios. The results support the deployment of the proposed controller in renewable and automotive applications that require resilience to parameter variations and fast transients.