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Consider a sixth order system with characteristic equation:..

 

Control System Stability Solution

Question

Consider a sixth order system with characteristic equation:

s6 + 2s5 + 8s4 + 12s3 + 20s2 + 16s + 16 = 0

The control system is:

  • A. Stable
  • B. Unstable
  • C. Limitedly stable
  • D. Oscillatory unstable

Solution

Step 1: Form the Routh Table

s6 182016
s5 212160
s4 21216
s3 000

Step 2: Handle Zero Row

Since the entire row becomes zero, form the auxiliary equation from the row above:

2s4 + 12s2 + 16 = 0

Simplifying:

s4 + 6s2 + 8 = 0

Step 3: Solve Auxiliary Equation

s2 = -2, -4

Therefore:

s = ±j√2, ±j2

Step 4:

  • No roots in the right half-plane
  • Pure imaginary roots exist

Final Answer

The system is marginally stable (limitedly stable).

Correct Option: C. Limitedly stable

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