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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 (5): 940-946    DOI: 10.3785/j.issn.1008-973X.2020.05.011
机械工程     
轴向受压梁非线性随机最优电压有界控制
胡凯明1,2(),李华2,*()
1. 中国计量大学 机电工程学院，浙江 杭州 310018
2. 浙江大学 航空航天学院，浙江 杭州 310027
Nonlinear stochastic optimal voltage bounded control for axial compressed beam
Kai-ming HU1,2(),Hua LI2,*()
1. College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China
2. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
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摘要：

针对轴向受压细长结构容易在外界扰动下产生低频大幅振动的问题，基于几何非线性理论、压电耦合场理论和拉格朗日方程，推导表面贴附压电作动片的轴向受压梁的机电能量表达式，建立轴向受压梁的非线性随机振动压电主动控制模型；考虑压电作动器工作电压的限制因素，利用随机平均法和动态规划方程导出改进型的非线性随机最优电压有界控制策略. 该策略包括无界最优电压和bang-bang控制电压，因而较bang-bang电压控制律具有更好的连续性. 对简支轴向受压梁在多种情况下的非线性随机振动最优控制进行数值仿真，与bang-bang电压控制律进行比较，结果表明本研究导出的改进型电压控制律所需的压电作动器控制电压大幅下降，而振动控制效果略有降低.
关键词： 压电结构;  轴向受压梁;  非线性随机动力学;  最优控制;  电压有界    
Abstract:

The electromechanical energy expressions of axial compressed beam with surface attached piezoelectric actuators were derived, and then a nonlinear stochastic vibration active control model of axial compressed beam was developed, based on the geometric nonlinear theory, multi-physics coupling theory of piezoelectric materials and Lagrange's equation. The purpose is to deal with the low-frequency nonlinear stochastic vibration of the axial compressed slim structures which is easily led by the external disturbance. A modified nonlinear stochastic optimal voltage bounded control strategy was derived by the stochastic average method and dynamical programming equation, in consideration of the voltage limitation of piezoelectric actuators. This voltage control strategy consists of unbounded optimal voltage control and bang-bang voltage control, so that has a better continuity than bang-bang voltage control strategy. The derived optimal voltage bounded control strategy were applied to control the nonlinear stochastic vibration of an axial compressed simply supported beam. Numerical results of various parameters cases show that the required control voltage of piezoelectric actuators is lower than that of bang-bang voltage control, with slight loss of vibration control effectiveness.
Key words: piezoelectric structure    axial compressed beam    nonlinear stochastic dynamics    optimal control    bounded voltage
收稿日期: 2019-05-01 出版日期: 2020-05-05
CLC:  O 324  
基金资助: 国家自然科学基金重点资助项目（11432012）
通讯作者: 李华     E-mail: kaiminghu@cjlu.edu.cn;lhlihua@zju.edu.cn
作者简介: 胡凯明（1985—），男，讲师，博士，从事智能材料结构及振动控制研究. orcid.org/0000-0003-0043-8291. E-mail： kaiminghu@cjlu.edu.cn
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引用本文:

胡凯明,李华. 轴向受压梁非线性随机最优电压有界控制[J]. 浙江大学学报(工学版), 2020, 54(5): 940-946.

Kai-ming HU,Hua LI. Nonlinear stochastic optimal voltage bounded control for axial compressed beam. Journal of ZheJiang University (Engineering Science), 2020, 54(5): 940-946.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.05.011    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I5/940

图 1  表面贴附压电作动片的轴向受压梁
参数部件 L/m b/m h/mm ρ/(g?cm?3) E/GPa d31/(pC?N?1)
梁 1.00 0.01 4.0 2.7 70 ?
压电作动器 0.02 0.01 0.5 7.8 61 ?300
表 1  梁及压电作动器的模型参数
图 2  轴向受压梁的非线性幅频响应
图 3  2种电压控制律下的受压简支梁位移响应与控制电压样本
图 4  2种电压控制律下的控制效果和电压控制效率随激励强度的变化
图 5  2种电压控制律下控制效果和电压控制效率随电压限幅的变化
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