The signal R splits into two parallel blocks G₂ = 15 and G₃ = 9. 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.
In the block diagram the forward path has the gains G₁ = 4 and G₂ = 9 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.
A plant G(s) = 32/(s + 4) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. A step of size 1 is applied at R. Find the steady-state output css.
A plant G(s) = 13/(s + 5) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.
A proportional controller K = 14 drives the plant G(s) = 6/(s + 4) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 2 and a disturbance step of size 0.5 are applied together. Find the steady-state output css.
The plant G(s) = K/(s(s + 7)(s + 9)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.
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