consider the following transfer functions: $$ G(s)=\frac{1}{\tau s+1}G_0 \quad \tau_{min}<\tau<\tau_{max} $$ show that this system equal to model with additive perturbation as follow $$ G(s)=G_1(s)+W(s)\Delta \qquad ||\Delta||\le1 $$ $\Delta$ is perturbation and where $$ W(s)=-\frac{r_{\tau}\tau_ms}{(1+\tau_m s)^2}\qquad G_1(s)=\frac{G_0}{(1+\tau_m s)} $$ in this $$ \tau_m=\frac{\tau_{max}+\tau_{min}}{2}\quad r_{\tau}=\frac{\tau_{max}-\tau_{min}}{\tau_{max}+\tau_{min}} $$ and
3
-
$\begingroup$ @AJN I edited the question. thank you for your attention $\endgroup$– u1997Nov 28, 2021 at 5:38
-
$\begingroup$ Is there any assumption on $G_0$ ? Like its order or if it a proper transfer function etc. ? I think that there probly exists some assumption that order of $G_0$ denominator is one more than $G_0$ numerator. $\endgroup$– AJNNov 28, 2021 at 16:55
-
$\begingroup$ yes, $G_0$ is a proper transfer function. $\endgroup$– u1997Nov 28, 2021 at 19:04
Add a comment
|