Disturbance observer-based voltage harmonic suppression in three-phase standalone inverters using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg"> <mml:msub> <mml:mi mathvariant="script">H</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> approach and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"> <mml:mi mathvariant="script">D</mml:mi> </mml:math> -stability theory

The objective of this work is to develop a systematic and analytically grounded approach for designing a proportional multi-resonant (PMR) controller for three-phase standalone voltage source inverters, capable of maintaining high-quality output voltage under various loading conditions. This objective is achieved through a composite control strategy that combines a disturbance observer with a state-feedback controller. The disturbance observer is designed using the H ∞ approach combined with D -stability theory, allowing the observer synthesis problem to be formulated as a Linear Matrix Inequality (LMI) for optimal gain computation. An important feature of the proposed composite control scheme is that it simplifies to a PMR controller, which facilitates practical implementation. The main difference between the proposed PMR controller and conventional PMR controllers lies in the featured design methodology. The proposed approach introduces a systematic and analytically grounded framework for tuning the controller gains, offering practitioners a structured and alternative method for the design of PMR controllers. Experimental results confirm the effectiveness of the proposed approach, achieving a voltage total harmonic distortion below 8 % for both linear and nonlinear load conditions, while maintaining stable and fast transient performance under load variations and parameter uncertainties.