Robust ℋ 2 control applied to boost converters: design, experimental validation and performance analysis

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Abstract
This study proposes a design procedure and experimental validation for a robust ℋ2 state feedback controller applied to a DC–DC boost converter modelled as a linear system affected by time-varying parameters lying in known intervals. The parameters considered as time-varying are the input voltage, the load resistance and the operating point duty cycle. A polytopic representation of the system is derived and the controller is designed by means of a convex optimisation problem based on linear matrix inequalities. The conventional ℋ2 controller is extended to cope with alpha-stability and robust linear quadratic regulator design, providing different strategies to trade-off the magnitude of the control gains and the response of the closed-loop system. Tight correspondences between numerical simulations and the experimental results prove the viability of the application of this technique for this kind of plant. Finally, a robust performance analysis illustrates the capacity of the closed-loop system to reject energy bounded disturbances, with interpretation for the cases of time-varying and time-invariant parameters.