The signal R splits into two parallel blocks G₂ = 11 and G₃ = 1. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 6. Find the overall gain T = C/R.
The signal R splits into two parallel blocks G₂ = 9 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 10. Find the overall gain T = C/R.
The plant G(s) = 4/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 5 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.
The plant G(s) = K/((s + 3)(s + 9)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).
A proportional controller K drives the plant G(s) = 1/(s + 10) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.01.
Reduce the block diagram with G₁ = 5/(s + 1), G₂ = 1/(s + 8), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).
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