TY - GEN
T1 - A Singular Perturbation approach for time-domain assessment of Phase Margin
AU - Zhu, J. Jim
AU - Yang, Xiaojing
AU - Hodel, A. Scottedward
PY - 2010
Y1 - 2010
N2 - This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter ε. First, a bijective relationship between the Singular Perturbation Margin (SPM) εmax and the PM of the nominal (slow) system is established with an approximation error on the order of ε2. In proving this result, relationships between the singular perturbation parameter ε, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.
AB - This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter ε. First, a bijective relationship between the Singular Perturbation Margin (SPM) εmax and the PM of the nominal (slow) system is established with an approximation error on the order of ε2. In proving this result, relationships between the singular perturbation parameter ε, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.
UR - https://www.scopus.com/pages/publications/77957760403
U2 - 10.1109/acc.2010.5530798
DO - 10.1109/acc.2010.5530798
M3 - 会议稿件
AN - SCOPUS:77957760403
SN - 9781424474264
T3 - Proceedings of the 2010 American Control Conference, ACC 2010
SP - 315
EP - 322
BT - Proceedings of the 2010 American Control Conference, ACC 2010
PB - IEEE Computer Society
ER -