On overshoot and nonminimum phase zeros

It is widely known that real nonminimum phase zeros lead to step response undershoot, and that the size of the undershoot necessarily tends to infinity as the settling time tends to zero. In this note, we show that the presence of two or more real nonminimum phase zeros can lead to step response ove...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2006-08, Vol.51 (8), p.1378-1382
Main Authors: Stewart, J., Davison, D.E.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer science
control theory
systems
Control systems
Control theory. Systems
Councils
Degrees of freedom
Exact sciences and technology
H infinity control
Infinity
Lower bounds
Mathematical analysis
Miscellaneous
Nonminimum phase zeros
Open loop systems
Output feedback
overshoot
Settling
Stability
State feedback
State-space methods
Step response
Transfer functions
Transient response
undershoot
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Summary:It is widely known that real nonminimum phase zeros lead to step response undershoot, and that the size of the undershoot necessarily tends to infinity as the settling time tends to zero. In this note, we show that the presence of two or more real nonminimum phase zeros can lead to step response overshoot in addition to undershoot. A lower bound on the overshoot is derived, and it is shown that the overshoot, like the undershoot, necessarily tends to infinity as the settling time tends to zero. The results are derived for single-input-single-output linear time-invariant continuous-time systems, and apply to both open-loop control and general two degree-of-freedom closed-loop control
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2006.878745