The signal R splits into two parallel blocks G₂ = 12 and G₃ = 4. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 8. Find the overall gain T = C/R.
In the block diagram the forward path has the gains G₁ = 14 and G₂ = 4 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.
The plant G(s) = K/(s(s + 14)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).
The plant G(s) = K/((s + 7)(s + 12)) 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) = 3/(s + 4) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.075.
A proportional controller K drives the plant G(s) = 6/(s + 2) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.3.
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