Solution Found!
In order to obtain a low-cost lithium-ion battery charger,
Chapter 6, Problem 60(choose chapter or problem)
In order to obtain a low-cost lithium-ion battery charger, the feedback loop of Figure P6.3 is used, where \(G(s)=G_c(s) P(s)\). The following transfer functions have been derived for G(s) (Tsang, 2009):
\(\begin{gathered} P(s)=\frac{R_1 R_2 C_1 C_2 s^2+\left(R_1 C_1+R_2 C_1+R_2 C_2\right) s+1}{C_1\left(1+R_2 C_2\right) s} \\ G_c(s)=K_p+\frac{K_I}{s} \end{gathered}\)
If \(R_1=0.15 \Omega ; R_2=0.44 \Omega ; C_1=7200 \mathrm{~F}\); and \(C_2=170 \mathrm{~F}\), use the Routh-Hurwitz criteria to find the range of positive \(K_P\) and \(K_I\) for which the system is closed-loop stable.
Questions & Answers
QUESTION:
In order to obtain a low-cost lithium-ion battery charger, the feedback loop of Figure P6.3 is used, where \(G(s)=G_c(s) P(s)\). The following transfer functions have been derived for G(s) (Tsang, 2009):
\(\begin{gathered} P(s)=\frac{R_1 R_2 C_1 C_2 s^2+\left(R_1 C_1+R_2 C_1+R_2 C_2\right) s+1}{C_1\left(1+R_2 C_2\right) s} \\ G_c(s)=K_p+\frac{K_I}{s} \end{gathered}\)
If \(R_1=0.15 \Omega ; R_2=0.44 \Omega ; C_1=7200 \mathrm{~F}\); and \(C_2=170 \mathrm{~F}\), use the Routh-Hurwitz criteria to find the range of positive \(K_P\) and \(K_I\) for which the system is closed-loop stable.
ANSWER:Step 1 of 4
Open loop transfer function of 
where,
and
