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Modified Bounded Real Lemma for Structured Robust Control of Fifth-Order DC-DC Converter
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DOI：10.1109/JESTIE.2025.3647209.png)
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Abstract
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The reported charge-pump-based double-input dc-dc converter topology is buck type, but its range of bucking is restricted. With an aim to evolve buck type of double-input topology with a wider bucking range, a fifth-order MIMO converter is evolved in this article. A novel approach is developed to design the structured robust proportional-integral-derivative controller for this fifth-order MIMO dc-dc converter system. The proposed controller design methodology is based on solving the nonlinear bounded real lemma wherein the matrix inequality involved is bilinear in nature and inherently nonconvex, thereby precluding the guarantee of solution existence. To alleviate associated nonlinearity, an augmented matrix is formulated, which includes the system dynamics and augmented states representing the impact of disturbance or uncertainties in the system. It also extends the feasible set of linear matrix inequality as the augmented states introduce an additional degree of freedom and hence the controller will be less conservative. The inclusion of additional auxiliary terms ((B-cl,B-d)B-T(cl,d,) P-2) leads to a reduced value of gamma, signifying enhanced disturbance rejection capability and improved stability margins. To demonstrate the efficacy of the proposed approach, an extensive comparative analysis is conducted across critical performance metrics, including robust stability, gain and phase margins, and structured singular value. The controller synthesized is experimentally validated using a 150 W prototype setup, thereby affirming the practical efficacy and robustness of the developed control design framework.
Keywords:
DC-DC power converters
Inductors
Design methodology
MIMO
Uncertain systems
Robust stability
Matrix converters
Linear matrix inequalities
Steady-state
Stability analysis
Bounded real-lemma (BRL)
disk margin
double-input converter
fifth-order dc-dc converter
Gershgorin bands
linear fractional transformation (LFT)
linear matrix inequality (LMI)
proportional-integral-derivative (PID) controller
structured singular value (SSV)
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