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首页> 外文期刊>Automatica >An incremental harmonic balance-based approach for harmonic analysis of closed-loop systems with Prandtl-Ishlinskii operator
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An incremental harmonic balance-based approach for harmonic analysis of closed-loop systems with Prandtl-Ishlinskii operator

机译：基于谐波分析的基于谐波余量的Prandtl-Ishlinskii运算符

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Analyzing hysteretic systems presents a significant challenge due to the memory effect of hysteresis. In this paper we present an incremental harmonic balance (IHB)-based approach to compute the steady-state response of a closed-loop system with hysteresis under a sinusoidal excitation, where the hysteresis element is modeled by the Prandtl-Ishlinskii (PI) operator. While the describing function method (DFM) can be used to obtain an approximate solution for the closed-loop system based on first-order harmonics, the proposed IHB-based approach iteratively calculates the harmonic components of the hysteretic system up to an arbitrary order. The main challenge is the harmonic calculation of the periodic output of the PI operator for a multi-harmonic input. In order to address this problem, an alternative definition of the play operator is utilized as the hysteron for the PI operator. By using the alternative definition, a set of switching time instants, when the play operator enters or exits the boundary region, are determined by a bisection method. The calculation of the incremental harmonic components is finally reformulated as a linear matrix equality that can be solved efficiently. As an illustration, numerical results for a system involving a proportional-integral feedback controller are presented to demonstrate the advantage of the IHB-based approach over the DFM in approximating the harmonic response of the hysteretic system. (C) 2017 Elsevier Ltd. All rights reserved.
机译：分析滞后系统由于滞后的记忆效应而提出了重大挑战。在本文中，我们提出了一种增量谐波平衡（IHB）的方法，用于计算闭环系统的恒定循环系统在正弦激励下的稳态响应，其中滞后元件由Prandtl-Ishlinskii（PI）操作员建模。虽然描述功能方法（DFM）可用于基于一阶谐波获得闭环系统的近似解，所提出的基于IHB的方法迭代地计算滞后系统的谐波分量，直到任意顺序。主要挑战是对多谐波输入的PI运算符的周期性输出的谐波计算。为了解决这个问题，播放运算符的替代定义用作PI运算符的HUSTERON。通过使用替代定义，当播放操作员进入或退出边界区域时，一组切换时间瞬间由二分法确定。最终将增量谐波分量的计算最终重新重新重新重新重新重整为可以有效求解的线性矩阵平等。作为图示，提出了一种涉及比例积分反馈控制器的系统的数值结果，以展示基于IHB的方法在近似滞后系统的谐波响应时的优点。 （c）2017 Elsevier Ltd.保留所有权利。

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