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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (8): 1497-1504    DOI: 10.3785/j.issn.1008-973X.2020.08.007
机械工程     
基于H∞理论的滚珠丝杠进给系统滑模控制
李剑(),汤文成*()
东南大学 机械工程学院，江苏 南京 211189
Sliding mode control for ball screw drives based on H∞ theory
Jian LI(),Wen-cheng TANG*()
School of Mechanical Engineering, Southeast University, Nanjing 211189, China
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摘要：

针对滚珠丝杠进给系统的动态特性，建立参数不确定的数学模型. 为了消除参数不确定的影响，设计满足H∞性能的积分滑模控制器. 针对存在的未知干扰，设计指数干扰观测器进行补偿. 分析结果表明，本研究的控制方法具有L2增益性能. 利用该方法在滚珠丝杠实验台上进行轨迹跟踪实验. 实验结果表明，当使用设计的控制器时，最大跟踪误差为16.85 μm；当使用设计的控制器加上指数干扰观测器时，最大跟踪误差为10.18 μm；在工作台增加25 kg质量块后，当使用设计的控制器加上干扰观测器时，最大跟踪误差为15.61 μm. 实验结果说明所设计的控制器具有较好的性能，并且干扰观测器能够提高控制精度. 与传统的比例-比例积分控制器的对比结果说明本研究的控制方法有较好的综合性能.
关键词： 滚珠丝杠;  滑模控制;  H∞理论;  不确定系统;  指数干扰观测器    
Abstract:

A mathematical model with uncertain parameters was established considering the dynamic characteristics of ball screw drives. A sliding mode controller with H∞ performance was designed to eliminate the influence of uncertainties. An exponential disturbance observer was designed to compensate the unknown disturbances of the system. The analyses prove that the control method has L2 gain performance. The trajectory tracking experiments were carried out on the experiment platform of ball screw drives. Results show that the maximum tracking error is 16.85 μm by using H∞ sliding mode controller and 10.18 μm by using H∞ sliding mode controller with the designed observer. After adding a 25 kg mass block on the table, the maximum tracking error is 15.61 μm by using the proposed controller with the designed observer. Results prove that the controller has good performance. The designed observer can improve the control performance. The proposed control method has good performance by comparison with a traditional proportion-proportion integral controller.
Key words: ball screw    sliding mode control    H∞ theory    uncertain system    exponential disturbance observer
收稿日期: 2019-07-15 出版日期: 2020-08-28
CLC:  TP 273  
基金资助: 国家自然科学基金资助项目（51675100）；国家科技重大专项资助项目（2016ZX04004008-002）
通讯作者: 汤文成     E-mail: hellolij@163.com;tangwc@seu.edu.cn
作者简介: 李剑（1994—），男，硕士生，从事先进控制理论研究. orcid.org/0000-0001-9553-3317. E-mail： hellolij@163.com
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引用本文:

李剑,汤文成. 基于H∞理论的滚珠丝杠进给系统滑模控制[J]. 浙江大学学报(工学版), 2020, 54(8): 1497-1504.

Jian LI,Wen-cheng TANG. Sliding mode control for ball screw drives based on H∞ theory. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1497-1504.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.08.007    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I8/1497

图 1  滚珠丝杠实验台
图 2  二自由度模型
图 3  工作台频率响应特性
图 4  HISMC控制系统框图
${ { {m_{\rm{1} } } } / {\left( { {\rm{V} } \cdot { {\rm{s} }^{\rm{2} } } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${ { {m_{\rm{2} } } } / {\left( { {\rm{V} } \cdot { {\rm{s} }^{\rm{2} } } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${c / {\left( { {\rm{V} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${ { {b_{\rm{1} } } } / {\left( { {\rm{V} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${ { {b_{\rm{2} } } } / {\left( { {\rm{V} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${k / {\left( { {\rm{V} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$
1.3016 0.1484 5.3550 ${\rm{8} }{\rm{.085\;4} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }$ 1.6103 ${\rm{4} }{\rm{.181\;4} } \times {\rm{1} }{ {\rm{0} }^{\rm{4} } }$
表 1  二自由度模型参数
图 5  轨迹跟踪实验参考轨迹
图 6  P-PI+VFF+AFF 轨迹跟踪实验结果
图 7  HISMC和EDO 轨迹跟踪实验结果
图 8  P-PI+VFF+AFF，HISMC和HISMC+EDO 轨迹跟踪实验结果对比
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