基于 Bode 图解法的改进频域框架分数阶 PI 控制器设计方法

Improved fractional-order PI controller design method for frequency domain frames based on Bode graphical method

摘要

为了有效减少求解分数阶 PI 控制器参数的计算量，基于 Bode 图解法，提出一种改进频域框架分数阶 PI 控制器设计方法。将改进频域框架法引入中频段，求取改进频域框架法的三角形面积最小；根据截止频率、相角穿越频率约束公式，确定改进频域框架范围；考虑多种约束条件，引入拉格朗日乘数方程，计算比例系数和积分系数，求取在某一改进频域框架内的最优比例系数和积分系数；通过仿真算例验证设计方法的可行性与有效性。结果表明：改进频域框架分数阶 PI 控制器设计满足系统的稳定性要求，有较好的鲁棒性。该设计方法具有计算简单、精确度高和取值范围直观等优点。

Abstract

To effectively reduce the computational complexity of determining the parameters of a frac-tional-order PI controller, this paper proposes a design method based on an improved frequency-domain graphical framework, building on Bode diagram analysis. The method introduces the improved frequen-cy-domain framework into the mid-frequency range, optimizing by minimizing the triangular area of the framework. The cutoff frequency and phase crossover frequency constraints are used to determine the boundaries of the improved framework. Consider multiple constraints, Lagrange multiplier equations are employed to calculate the proportional and integral gains, yielding the optimal values within the defined frequency-domain framework. Simulation examples are provided to validate the feasibility and effectiveness of the design approach. The results demonstrate that the proposed fractional-order PI controller meets system stability requirements and exhibits strong robustness. This method is simple, precise, and provides a clear range for parameter selection, making it highly intuitive.

关键词

分数阶 / PI 控制器 / Bode 图解法 / 最优控制 / 频域框架

Key words

fractional-order / PI controller / Bode graphical method / optimal control / frequency domain framework

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基金资助

黑龙江省高校基本科研项目(2022TSTD-04)