Project ForgeA control configuration has R(s)→[sum +/−]→Kc1=0.5→U1(s)→[sum +/−]→Kc2→U2(s)→(s+2)/(s−4)→Y(s), with Y(s) fed back with unity gain to BOTH summing junctions. The system is stable when Kc2 is
- A3/4
- B1
- C5/4
- 3/2
Explanation
With both summers subtracting Y: U1=Kc1(R−Y), U2=Kc2(U1−Y), Y=Gp·U2. Substituting: Y[1+Gp·Kc2(Kc1+1)]=Gp·Kc2·Kc1·R. Characteristic equation: (s−4)+1.5Kc2(s+2)=0, i.e. (1+1.5Kc2)s+(3Kc2−4)=0. For a stable (negative) root, both coefficients must share the same sign; since (1+1.5Kc2)>0 always, we need 3Kc2−4>0 ⟹ Kc2>4/3≈1.33. Only Kc2=3/2 among the options satisfies this (stabilizing the open-loop-unstable process, which has a pole at s=4).
Source: GATE CH 2010 (2010)
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