论文标题
使用分数演算概括混合积分器增益系统
Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus
论文作者
论文摘要
混合积分增益系统（HIGS）最近在控制精确运动系统的控制中引起了很多关注。 HIGS是一种非线性低通滤波器，其线性对应物具有52度相优势。该属性使我们避免了通常与线性控制器相关的局限性，例如水床效应和Bode的相位增益关系。在本文中，我们通过用分数阶的一个替换相关的整数积分器来概括了HIG，以使相位铅从0度（线性低通滤波器）调整到52度（HIGS）。为了在频域中分析此滤波器，使用输出信号的傅立叶扩展获得了提出的滤波器（即分数希格）的描述功能。此外，该广义的HIG在控制双积分系统的PID结构中实现，以验证所提出的过滤器在时域中的性能，在时间域中，将分数变量从零更改为一个，该输出因非线性控制系统的响应而变化。
The Hybrid Integral Gain Systems (HIGS) has recently gained a lot of attention in the control of precision motion systems. HIGS is a nonlinear low pass filter with a 52 degree phase advantage over its linear counterpart. This property allows us to avoid the limitations typically associated with linear controllers like the waterbed effect and bode's phase gain relation. In this paper, we generalize HIGS via replacing the involved integer order integrator with a fractional order one to adapt the phase lead from 0 degree (linear low pass filter) to 52 degree (HIGS). To analyze this filter in the frequency domain, the describing function of the proposed filter, i.e., the fractional-order HIGS, is obtained using the Fourier expansion of the output signal. In addition, this generalized HIGS is implemented in a PID structure controlling a double integrator system to validate the performance of the proposed filter in the time domain, in which changing the fractional variable from zero to one, the output varies from the response of a nonlinear control system to a linear one.
