It is desired to design a compensator to stabilize the syste

It is desired to design a compensator to stabilize the system shown in Fig. P7.37. The only means available is a constant multiplier K which can be inserted in the feedback loop as shown. Sketch the root-locus plot and then use Routh\'s criterion to determine the gain K such that the roots of the characteristic equation tie on The imaginary axis The vertical axis at - 3

Solution

The closed loot Transfer Function for the circuit is C(s)/K(s) = K*G/[1+K*G], where G is the expression shown

Hence The characteristic eqn is 1+K*G =0

Substituting, the denominator becomes s^2 +s*(K-2) +3*K+10=0

The roots can be found from the quadratic formula, the main point to note:

1.)for imaginary roots ( lying on the imaginary axis , ) K-2 =0 hence K=2

2) To lie on the vertical axis at -3, this happens when K=0 , ie the roots are 1+/- 3i