Block diagrams worksheet with answers

The signal R splits into two parallel blocks G₂ = 15 and G₃ = 8. 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.

A plant G(s) = 6/(s + 7) is placed in a unity negative feedback loop. A step of size 10 is applied at R. Find the steady-state output c_ss.

The plant G(s) = K/((s + 7)(s + 11)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

A unity negative feedback loop has G(s) = 10(s + 5)/((s + 7)(s + 9)). A step of size 10 is applied at the reference. Find the steady-state error e_ss.

Reduce the block diagram with G₁ = 4/(s + 1), G₂ = 3/(s + 2), 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).

A proportional controller K drives the plant G(s) = 7/(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 1.75.