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1. For the characteristic polynomials given below construct the Routh array and determine the stability of the system. Also determine the number of roots lying on the right half of s-plane, left half of s-plane and on imaginary axis.
a) 9s5- 20s4+ 10s3- s2- 9s -10 = 0
b) s6+ s5 + 3s4+ 3s3+ 3s2+ 2s +1 = 0
2. Determine the range of K for stability of a unity feedback system whose open loop transfer function is given by Eq. 1.
G = k/s(s+1)(s+2)
3. For the unity feedback system shown in Fig. 1, construct Routh array to determine the value of ‘K' and ‘a' so that the system oscillates at a frequency of 2 rad/sec. Use MATLAB to verify the obtained result.
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