基于速度反馈分数阶PID控制的达芬振子的主共振

发布时间：2018-04-24 10:04

本文选题：分数阶比例-积分-微分控制 + 达芬振子　；参考：《力学学报》2016年02期

【摘要】：与传统整数阶比例-积分-微分(PID)控制器相比,分数阶比例-积分-微分控制器由于增加了两个控制参数,因此能够更灵活地控制受控对象.研究了基于速度反馈分数阶比例-积分-微分控制的达芬振子的主共振,利用平均法获得了系统的近似解析解.研究发现分数阶比例-积分-微分控制器的比例环节以等效线性阻尼的形式影响系统的共振振幅,积分环节以等效线性阻尼和等效线性刚度的形式影响系统的动力学特性,微分环节以等效线性阻尼和等效质量的形式影响系统的动力学特性.建立了主共振幅频响应方程的解析表达式和稳定性判断准则,并对主共振幅频响应的近似解析解和数值解进行了比较,二者吻合良好,验证了求解过程和近似解析解的正确性.分析了分数阶比例-积分-微分控制器的比例环节系数、积分环节系数、微分环节系数以及分数阶阶次变化时,对系统主共振幅频响应的影响.对分数阶比例-积分-微分控制器与传统整数阶比例-积分-微分控制器的控制效果进行了对比,发现当控制器各个环节的系数相同时,基于速度反馈的分数阶比例-积分-微分控制对达芬振子主共振的控制效果要优于传统整数阶比例-积分-微分控制.
[Abstract]:Compared with the traditional integer order proportional integral differential (PID) controller, the fractional order proportional integral differential controller can control the controlled object more flexibly because of the increase of two control parameters. The main resonance of the Dafen oscillator based on the fractional proportional integral differential control based on the velocity feedback is studied and the system is obtained by means of the mean method. It is found that the proportional link of fractional order integral differential controller affects the resonance amplitude of the system by the form of equivalent linear damping. The integral link affects the dynamic characteristics of the system by the form of equivalent linear damping and equivalent linear stiffness, and the differential link is influenced by the equivalent linear damping and the equivalent mass form. The analytic expression of the amplitude frequency response equation of the main resonance and the criterion for judging the stability are established, and the approximate analytical solution and the numerical solution of the amplitude frequency response of the main resonance are compared. The two ones are in good agreement, and the correctness of the solving process and the approximate analytical solution are verified. The ratio of the fractional proportion integral differential controller is analyzed. The effect of the link coefficient, integral link coefficient, differential link coefficient and fractional order change on the amplitude frequency response of the main resonance of the system. The control effect of the fractional proportional integral differential controller and the traditional integer order proportional integral differential controller is compared. The speed feedback Fractional Order Integro differential control is superior to the traditional integer order proportional integral derivative control for the main resonance of the Duffing oscillator.

【作者单位】：石家庄铁道大学机械工程学院;
【基金】：国家自然科学基金(11372198) 河北省高等学校创新团队领军人才计划(LJRC018) 河北省高等学校高层次人才科学研究项目(GCC2014053) 河北省高层次人才资助项目(A201401001)资助项目
【分类号】：O328

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