threekingtiger
Member level 1
In control theory, the relationship between step transient response and frequency response has been elaborated specifically, especially for 1st order and 2nd order systems.
However, for linear, time-invariant, high-order systems having a dominant pair of complex congjugate closed loop poles, some relationship is too vague. For instance, some author claims that in terms of the open-loop frequency response, the damped natural freqency ωd in the transient response is somewhere between the gain crossover frequency(ω@unity gain) and phase crossover frequency(ω@-180°). Could anybody explain the reason for the location of ωd ?
However, for linear, time-invariant, high-order systems having a dominant pair of complex congjugate closed loop poles, some relationship is too vague. For instance, some author claims that in terms of the open-loop frequency response, the damped natural freqency ωd in the transient response is somewhere between the gain crossover frequency(ω@unity gain) and phase crossover frequency(ω@-180°). Could anybody explain the reason for the location of ωd ?