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 = 2. Find the overall gain T = C/R.
A plant G(s) = 7/(s + 8) is placed in a unity negative feedback loop. Find the closed-loop pole p.
A plant G(s) = 32/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. Find the time constant τ of the closed loop.
The plant G(s) = K/(s(s + 8)) 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) = 5/(s + 4) 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 0.625.
The plant G(s) = K/((s + 5)(s + 6)(s + 8)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.
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