TY - GEN
T1 - On the Angles of Root Loci Branches that Arrive or Depart from Breakaway Points
AU - Zhu, Bing
AU - Lin, Yan
AU - Zuo, Zongyu
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - In most textbooks on principles of automatic control, very limited content is given on the angles of arrival or departure from breakaway points of root loci. Sometimes, for simplicity of description, the angles of arrival or departure from breakaway points are given by 180l apart, where l denotes the number of branches of root loci that meet at the breakaway point; however, no detailed proof is given for this result. In this paper, detailed proof is provided for the angles apart of the root loci branches from the breakaway point. It is proved that, the result is valid with strictly positive real open loop transfer function in both cases of unit negative feedback and unit positive feedback. The proof is based on the property of angles of departure or arrival and the angle condition of the root locus itself. Several examples are given to support the proposed proof. The proposed results can be lectured to students for better understanding and more precise plot of root locus.
AB - In most textbooks on principles of automatic control, very limited content is given on the angles of arrival or departure from breakaway points of root loci. Sometimes, for simplicity of description, the angles of arrival or departure from breakaway points are given by 180l apart, where l denotes the number of branches of root loci that meet at the breakaway point; however, no detailed proof is given for this result. In this paper, detailed proof is provided for the angles apart of the root loci branches from the breakaway point. It is proved that, the result is valid with strictly positive real open loop transfer function in both cases of unit negative feedback and unit positive feedback. The proof is based on the property of angles of departure or arrival and the angle condition of the root locus itself. Several examples are given to support the proposed proof. The proposed results can be lectured to students for better understanding and more precise plot of root locus.
KW - Control Theory
KW - angles apart of the root loci branches
KW - breakaway points
KW - control education
KW - root locus
UR - https://www.scopus.com/pages/publications/85075802108
U2 - 10.1109/ICCA.2019.8899934
DO - 10.1109/ICCA.2019.8899934
M3 - 会议稿件
AN - SCOPUS:85075802108
T3 - IEEE International Conference on Control and Automation, ICCA
SP - 928
EP - 933
BT - 2019 IEEE 15th International Conference on Control and Automation, ICCA 2019
PB - IEEE Computer Society
T2 - 15th IEEE International Conference on Control and Automation, ICCA 2019
Y2 - 16 July 2019 through 19 July 2019
ER -