The signal R splits into two parallel blocks G₂ = 15 and G₃ = 2. 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.
An amplifier with gain G = 10 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.
A plant G(s) = 18/(s + 6) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.
The plant G(s) = 2/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 6 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.
The plant G(s) = K/(s(s + 3)(s + 4)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.
The plant G(s) = 20/(s(s + 3)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.
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