The regulation of output voltage and equivalent distribution of phase currents of multi-phase converters which have non-minimum phase characteristic are still challenges, especially in the presence of uncertainties in real parameters, duty cycle, input voltage, and load disturbances. However, in classical third-order integral-lead (Type-III) controller design methodologies, the controller is synthesized considering only the nominal performance conditions. This paper proposes a structured $H_{\infty }$ synthesis framework based on an optimization methodology to the design of a robust Type-III controller for interleaved boost converters. The structured $H_{\infty }$ control approach is adapted for optimization of Type-III feedback and feedforward controllers in two-degree-of-freedom (2-DOF) control system configuration. The robust stability of the closed-loop interleaved boost converter system against model uncertainties is ensured via the classical $\mu$-analysis technique. Numerical comparisons are made among the classical, i.e. unstructured or full order, $H_{\infty }$-based controller design method, a dual-loop PI controller, and proposed 1-DOF and 2-DOF structured controller synthesis approaches on an interleaved boost converter model. Simulation results verify the effectiveness and advantages of the proposed approach from the viewpoint of the output voltage regulation under different disturbance points.

具有非最小相位特性的多相转换器的输出电压调节和相电流等效分布仍然是一个挑战，尤其是在实际参数、占空比、输入电压和负载扰动存在不确定性的情况下。然而，在经典的三阶积分超前 (Type-III) 控制器设计方法中，仅考虑标称性能条件来综合控制器。本文提出了一种结构化的$H_{\infty }$基于优化方法的综合框架设计用于交错式升压转换器的鲁棒 III 型控制器。结构化的$H_{\infty }$控制方法适用于优化二自由度 (2-DOF) 控制系统配置中的类型 III 反馈和前馈控制器。闭环交错式升压转换器系统对模型不确定性的鲁棒稳定性是通过经典的$\mu$——分析技术。在经典的，即非结构化或全序之间进行数值比较，$H_{\infty }$基于控制器设计方法、双环 PI 控制器，以及在交错升压转换器模型上提出的 1-DOF 和 2-DOF 结构化控制器综合方法。仿真结果从不同扰动点下的输出电压调节角度验证了所提出方法的有效性和优势。