TY - GEN
T1 - Frequency domain approach to computing loop phase margins of multivariable systems
AU - Ye, Zhen
AU - Wang, Qing Guo
AU - Hang, Chang Chieh
AU - Zhang, Yu
AU - Zhang, Yong
PY - 2008
Y1 - 2008
N2 - The loop phase margins of multivariable control systems are defined as the allowable individual loop phase perturbations within which stability of the closed-loop system is guaranteed. This paper presents a frequency domain approach to accurately computing these phase margins for multivariable systems. With the help of unitary mapping between two complex vector space, the MIMO phase margin problem is converted using the Nyquist stability analysis to the problem of some simple constrained optimization, which is then solved numerically with the Lagrange multiplier and Newton-Raphson iteration algorithm. The proposed approach can provide exact margins and thus improves the LMI results reported before, which could be conservative.
AB - The loop phase margins of multivariable control systems are defined as the allowable individual loop phase perturbations within which stability of the closed-loop system is guaranteed. This paper presents a frequency domain approach to accurately computing these phase margins for multivariable systems. With the help of unitary mapping between two complex vector space, the MIMO phase margin problem is converted using the Nyquist stability analysis to the problem of some simple constrained optimization, which is then solved numerically with the Lagrange multiplier and Newton-Raphson iteration algorithm. The proposed approach can provide exact margins and thus improves the LMI results reported before, which could be conservative.
KW - N-dimensional systems
KW - Robustness analysis
KW - Static optimization problems
UR - http://www.scopus.com/inward/record.url?scp=79961019262&partnerID=8YFLogxK
U2 - 10.3182/20080706-5-KR-1001.0034
DO - 10.3182/20080706-5-KR-1001.0034
M3 - Conference contribution
AN - SCOPUS:79961019262
SN - 9783902661005
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
BT - Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC
T2 - 17th World Congress, International Federation of Automatic Control, IFAC
Y2 - 6 July 2008 through 11 July 2008
ER -