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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (8): 1497-1504    DOI: 10.3785/j.issn.1008-973X.2020.08.007
    
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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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     
Received: 15 July 2019      Published: 28 August 2020
CLC:  TP 273  
Corresponding Authors: Wen-cheng TANG     E-mail: hellolij@163.com;tangwc@seu.edu.cn
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Cite this article:

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.

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


基于H∞理论的滚珠丝杠进给系统滑模控制

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 
Fig.1 Ball screw drive experimental setup
Fig.2 Two degrees of freedom model
Fig.3 Frequency response functions of table
Fig.4 Block diagram of HISMC
${ { {m_{\rm{1} } } } / {\left( { {\rm{V} } \cdot { {\rm{s} }^{\rm{2} } } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${ { {m_{\rm{2} } } } / {\left( { {\rm{V} } \cdot { {\rm{s} }^{\rm{2} } } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${c / {\left( { {\rm{V} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${ { {b_{\rm{1} } } } / {\left( { {\rm{V} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${ { {b_{\rm{2} } } } / {\left( { {\rm{V} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$ ${k / {\left( { {\rm{V} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }} \right)} }$
1.3016 0.1484 5.3550 ${\rm{8} }{\rm{.085\;4} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }$ 1.6103 ${\rm{4} }{\rm{.181\;4} } \times {\rm{1} }{ {\rm{0} }^{\rm{4} } }$
Tab.1 Two degrees of freedom model parameters
Fig.5 Reference trajectory of trajectory tracking experiment
Fig.6 P-PI+VFF+AFF trajectory tracking experiment results
Fig.7 HISMC and EDO trajectory tracking experiment results
Fig.8 Comparison of trajectory tracking experiment results between P-PI+VFF+AFF, HISMC and HISMC+EDO
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