Test Stability using Routh Stability Method

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SUMMARY

The discussion centers on analyzing the stability of a control system represented by the transfer function G(s)H(s) = 1/(s²(s+α)). The equation 1 + G(s)H(s) = 0 leads to the characteristic polynomial s³ + αs² + 1 = 0. It is established that the absence of the s¹ term indicates at least one root in the right half-plane (RHP), confirming system instability. Additionally, the discussion highlights the need to determine the value of α for achieving critical stability.

PREREQUISITES
  • Understanding of control systems and stability analysis
  • Familiarity with transfer functions and characteristic equations
  • Knowledge of Routh-Hurwitz stability criterion
  • Basic algebra and polynomial root analysis
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  • Study the Routh-Hurwitz stability criterion in detail
  • Learn how to derive characteristic equations from transfer functions
  • Research methods for determining critical stability values in control systems
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mym786
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Homework Statement



For a control system that has G(s)H(s) = \frac{1}{s^{2}*(s+\alpha)}

Homework Equations



1 + G(s)H(s) = 0

The Attempt at a Solution



Exam question i messed up . I really need to know the answer.
 
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mym786 said:

Homework Statement



For a control system that has G(s)H(s) = \frac{1}{s^{2}*(s+\alpha)}


Homework Equations



1 + G(s)H(s) = 0

The Attempt at a Solution



Exam question i messed up . I really need to know the answer.

i + G(s)H(s) = 0 means:
s^3+\alpha s^2 + 1 = 0
Since the polynomial is incomplete (there is no term in s^1) there is at least one root in the RHP and the system is unstable. No need to use Routh algorithm.
 
I forgot one more thing. It also says find the value of \alpha for which the system can be classified in the critically stable state.
 

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