Progressively improved LMIs for achieving high-performance robust control of DC–DC converters with low-cost microcontrollers

Linear matrix inequalities are recognized by the control community as powerful tools for robust control design. However, its full potential for ensuring high performance and robustness in experimental applications – particularly in DC–DC converters – remains underexplored. The present work aims to investigate progressively improved linear matrix inequalities for designing robust controllers for output voltage regulation in DC–DC buck converters subject to interval parametric uncertainties. The proposed robust controller is developed in the discrete-time domain, considering delay and a polytopic model for the parametric uncertainties, along with constraints on closed-loop poles and in the control gains norm. This results in a strategy capable of achieving high performance in practice, and with a theoretical certification of robust stability based on Lyapunov functions. The proposal is experimentally validated on a physical prototype of a DC–DC buck converter with a low-cost microcontroller, demonstrating superior performance when compared to both a linear quadratic regulator and a state feedback controller optimized through metaheuristics. Finally, the elimination of a current sensor, via a state observer, is proposed, demonstrating robust stability and performance of the augmented system under uncertain and time-varying parameters.