| 引用本文: | 王一光,陈兴林,李晓杰.基于PMLM的PDμ运动控制器的设计研究.[J].国防科技大学学报,2014,36(1):142-147.[点击复制] |
| WANG Yiguang,CHEN Xinglin,LI Xiaojie.A PDμ motion controller design method for PMLM[J].Journal of National University of Defense Technology,2014,36(1):142-147[点击复制] |
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| 基于PMLM的PDμ运动控制器的设计研究 |
| 王一光1, 陈兴林1, 李晓杰2 |
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(1.哈尔滨工业大学 航天学院，黑龙江 哈尔滨 150001;2.哈尔滨工程大学 自动化学院，黑龙江 哈尔滨 150001)
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| 摘要: |
| 近年来随着非整数阶微积分理论的不断完善，使分数阶微积分在控制方面的应用受到越来越多的关注。特别是分数阶PIλDμ控制，在很多领域中得到了应用。针对运动控制系统中经常采用的比例微分控制器，提出了一种分数阶PDμ控制器的设计和整定方法。由于所设计系统的相角裕度与超调量有确定的对应关系，所以通过对相角变化率的设计可以使系统相角在剪切频率附近保持稳定，从而减小系统开环增益波动对超调量的影响。以给定的剪切频率ωc和相角裕度γm作为设计指标，由系统相频特性方程和相角变化率方程可以确定PDμ控制器的微分阶次μ和微分系数Kd，通过剪切频率点的幅频特性方程可以确定比例系数Kp。将方法应用于一个直线运动控制试验台，通过与整数阶ITAE最优控制方法进行的对比仿真和试验验证了方法的有效性和优越性。由试验结果可以看出，在保证系统设计指标的前提下所设计的PDμ控制器对于系统参数波动引起的超调量的变化具有很好的抑制作用。 |
| 关键词: 分数阶微积分 分数阶控制器 PDμ控制器 运动控制 |
| DOI：10.11887/j.cn.201401025 |
| 投稿日期：2013-05-15 |
| 基金项目:国家科技重大专项资助项目（2009ZX02207）；国家重点基础研究发展计划项目（973-10007.07-LB7） |
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| A PDμ motion controller design method for PMLM |
| WANG Yiguang1, CHEN Xinglin1, LI Xiaojie2 |
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(1.School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;2.College of Automation, Harbin Engineering University, Harbin 150001, China)
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| Abstract: |
| Recently, with the improvement of non-integer order calculus theory, fractional order calculus receives more and more attentions in the application of controlling. Especially, the fractional order PIλDμ controlling is applied in many fields. For the traditional PD controller which is usually used in motion control system, a kind of designing and tuning method of PDμ controller is proposed. Since there is explicit corresponding relation between phase margin and overshoot of the designed system, by designing the rate of change of phase the system’s phase can be made stable around cut off frequency and the influence of open loop gain’s variations on the overshoot can be reduced. Cut-off frequency ωc and phase margin γm given are considered as design specifications in this method. PDμ’s derivation order μ and derivation coefficient Kd can be derived from system’s phase equation and rate of change equation. Proportional coefficient Kp can be obtained from the magnitude equation on the cut off frequency. Finally, this method is applied to a linear motion control experiment platform. By simulations and experiments comparing with integer order ITAE-optimal method, the effectiveness and excellence of this method is verified. From the results, it can be noticed that the controlling system designed in this method has a good inhibition effect on the overshoot variations caused by the fluctuations of the system parameters on the premise of meeting the design specifications. |
| Keywords: fractional calculus fractional order controller PDμ controller motion control |
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