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):

If R₁ = 0.15Ω; R₂ = 0.44Ω; C₁ = 7200F; and C₂ = 170F, use the Routh Hurwitz criteria to find the range of positive K_P and K_I for which the system is closed-loop stable.

R,R2C,C, + (R;C, + R2C1 + R2C2)s+ 1 P(s) = C(1 +R2C2)s KI G.(s) = K, + %3D