Routh-Hurwitz Stability Criterion: Solving Feedback Control Systems Homework

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SUMMARY

The discussion centers on applying the Routh-Hurwitz Stability Criterion to solve feedback control systems homework problems. The first question involves constructing the Routh Array, ensuring the first row contains all positive coefficients, leading to a maximum gain (Kmax) of 1. For the second question, participants suggest forming an auxiliary equation using the coefficients from the s^2 line, which yields two imaginary roots representing the oscillation frequency when K equals 1.

PREREQUISITES
  • Understanding of the Routh-Hurwitz Stability Criterion
  • Familiarity with constructing the Routh Array
  • Knowledge of auxiliary equations in control theory
  • Ability to solve characteristic equations for stability analysis
NEXT STEPS
  • Study the derivation and application of the Routh-Hurwitz Stability Criterion
  • Learn how to construct and interpret the Routh Array
  • Explore the concept of auxiliary equations in control systems
  • Investigate the implications of imaginary roots in system stability
USEFUL FOR

Students and professionals in control engineering, particularly those tackling stability analysis in feedback control systems using the Routh-Hurwitz Criterion.

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Homework Statement



http://img24.imageshack.us/img24/9028/72841137.jpg

Homework Equations



Routh-Hurwitz Stability Criterion

The Attempt at a Solution



For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough

How would I approach the second question though? Any starters would be sincerely appreciated.
 
Last edited by a moderator:
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l46kok said:

Homework Statement



http://img24.imageshack.us/img24/9028/72841137.jpg

Homework Equations



Routh-Hurwitz Stability Criterion

The Attempt at a Solution



For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough

How would I approach the second question though? Any starters would be sincerely appreciated.

You got the value K = 1 by making the line s^1 equal to zero. Now, you form an auxiliary equation with the coefficients of the s^2 line. The roots of the auxiliary equation are also roots of the characteristic equation. Solve it and you get two imaginary roots, whose module is the oscillation frequency when K = 1.
 
Last edited by a moderator:

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