How Transfer Function Zeros Affect Transient Response – Quick Concepts in Control 2

Zeros and their pull
Transient response unfolds
Poles, coefficients.

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The effect of transfer function zeros on system transient response is investigated. Two transfer functions with the same poles but different zeros are shown to have different transient responses. The functions are generalized and analyzed in the time and frequency domain. It is shown mathematically and graphically how zeros can interact with poles and scale coefficients in the time domain frequency response terms. The derivation proceeds from frequency to time domain and back to frequency domain, offering multiple perspectives on the effect of zeros.

Errata:
4/24/2024 There is an error when partial fraction is applied to H1(s) (time 1:01), the term (1-a) is 1 a is not present in the decomposition. This error was not present in the code so the visualizations do not change. Thanks @1jymelgar