- #1
CraigH
- 222
- 1
Mistake 1.
In the lecture slides from my university it says that:
"The response of a stable first-order transfer function to a unit sine wave input is:"
[itex]Y(s)=\frac{1}{s+a}*\frac{\omega}{s^2+\omega^2}[/itex]
Isn't this missing an [itex]a[/itex] in the numerator since the standard form of a first order transfer function is:
[itex]H(s) = \frac{1}{\tau s +1} = \frac{a}{s+a}[/itex]
where [itex]\tau=1/a[/itex]
and the laplace transform of the sine wave input is:
[itex]\frac{\omega}{s^2+\omega^2}[/itex]
Mistake 2.
The lecture slides also say that:
"The response of a stable second-order transfer function to a unit sine wave input is:"
[itex]Y(s)=\frac{1}{s^2+2\zeta\omega_n+\omega_n^2}*\frac{\omega}{s^2+\omega^2}[/itex]
Similarly, isn't this missing an [itex]\omega_n^2[/itex] in the numerator as the standard form of a second order transfer function is:
[itex]H(s) = \frac{\omega_n^2}{s^2+2 \zeta \omega_n s + \omega_n^2}[/itex]
In the lecture slides from my university it says that:
"The response of a stable first-order transfer function to a unit sine wave input is:"
[itex]Y(s)=\frac{1}{s+a}*\frac{\omega}{s^2+\omega^2}[/itex]
Isn't this missing an [itex]a[/itex] in the numerator since the standard form of a first order transfer function is:
[itex]H(s) = \frac{1}{\tau s +1} = \frac{a}{s+a}[/itex]
where [itex]\tau=1/a[/itex]
and the laplace transform of the sine wave input is:
[itex]\frac{\omega}{s^2+\omega^2}[/itex]
Mistake 2.
The lecture slides also say that:
"The response of a stable second-order transfer function to a unit sine wave input is:"
[itex]Y(s)=\frac{1}{s^2+2\zeta\omega_n+\omega_n^2}*\frac{\omega}{s^2+\omega^2}[/itex]
Similarly, isn't this missing an [itex]\omega_n^2[/itex] in the numerator as the standard form of a second order transfer function is:
[itex]H(s) = \frac{\omega_n^2}{s^2+2 \zeta \omega_n s + \omega_n^2}[/itex]
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