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工程设计学报
Chinese Journal of Engineering Design  2014, Vol. 21 Issue (5): 456-468    DOI: 10.3785/j.issn. 1006-754X.2014.05.009
    
Design of an optimal control method based on the dynamic performance space
LI Wen-juan1， CHEN Xiao-xuan1， GONG Li-jiao2， CHEN Xu-dong3
1. College of Chemistry and Chemical Engineering， Shihezi University， Shihezi 832000， China;
2. College of Machinery and Electrical Engineering， Shihezi University， Shihezi 832003， China;
3. Printing Engineering Department， Anhui Press and Publication Vocational College， Hefei 230601， China
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Abstract  Same zeroes and poles located at different locations of the root locus plane will exhibit different dynamic performance, which shows that the system performance has nothing to do with the zeroes or poles themselves and is completely determined by their location. The relationship between root locus coordinates and dynamic performance indices were established beginning with the root locus plane in classical control theory and then with the aid of the “field theory” concept in mathematical analysis, which took the positioning accuracy and stability as the descriptive quantities of the system's dynamic performance. Through drawing the equioscillation and equiprecision curves in the root locus plane, the system dynamic performance space was built up. The real pole, complex conjugate zero, and complex conjugate pole of the sixthorder linear tracking system were globally optimized by using this dynamic performance space. Sensitivity, complementary sensitivity, and dynamic response results showed that the optimal control method can solve the discrepancy between system accuracy and positioning time delay, and meet the exact track requirements with an effect much better than that of a PID controller.

Key words： root locus plane      dynamic performance space      equioscillation line      equiprecision line     
Received: 15 May 2014      Published: 28 October 2014
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LI Wen-Juan
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Cite this article:

LI Wen-juan， CHEN Xiao-xuan， GONG Li-jiao， CHEN Xu-dong. Design of an optimal control method based on the dynamic performance space. Chinese Journal of Engineering Design, 2014, 21(5): 456-468.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn. 1006-754X.2014.05.009     OR     https://www.zjujournals.com/gcsjxb/Y2014/V21/I5/456


基于动态性能空间的优化控制方法设计

相同零点、极点在根轨迹平面的不同位置表现出不同的动态性能，表明系统性能与零点或极点本身无关，完全由其所处的位置决定.从经典控制理论的根轨迹平面出发，借助数理分析中的“场论”概念，以定位精度和控制稳定性作为系统动态性能的描述量，尝试建立动态性能指标与根轨迹平面坐标之间的函数对应关系；并据此通过在根轨迹平面绘制等振荡线和等精度线，实现动态性能空间的构建.应用该动态性能空间，对六阶线性跟踪系统的实数极点和复共轭零点、极点进行全局优化.灵敏度、补灵敏度函数及动态响应结果显示：该优化设计方法可以较好地解决系统定位精度与控制稳定性之间的矛盾，满足精确动态跟踪要求，效果远优于PID控制器.

关键词： 根轨迹平面,  动态性能空间,  等振荡线,  等精度线 
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