Determine the range of K that keeps the system stable

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SUMMARY

The discussion focuses on determining the range of gain K for the control system G(s) = K(s+4)/s(s+1)(s+2) to maintain stability and induce oscillation. The Routh-Hurwitz criterion is utilized to analyze stability, with the first part successfully solved by constructing the Routh-Hurwitz table. The participants express confusion regarding the conditions for oscillation and the calculation of oscillation frequency, indicating a need for clarification on these concepts within the context of unity feedback systems.

PREREQUISITES
  • Understanding of control system dynamics
  • Familiarity with Routh-Hurwitz stability criterion
  • Knowledge of unity feedback systems
  • Basic concepts of oscillation in control theory
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  • Study the Routh-Hurwitz stability criterion in detail
  • Learn about the conditions for oscillation in control systems
  • Explore methods for calculating oscillation frequency in feedback systems
  • Review block diagram representations of control systems
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Control system engineers, students studying feedback systems, and anyone interested in stability analysis and oscillation behavior in control theory.

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Homework Statement



i meet problem below in control system :

G(s)= K(s+4)/s(s+1)(s+2) its a unity feedback system.

1. determine the range of K that keeps the system stable.
2. determine the range of K that makes the system oscillate
3. calculate the frequency of oscillation when the system oscillate

Homework Equations



characteristic equation for stability Routh Hurwitz Creation


The Attempt at a Solution



i have solved the first by determine the range of K by using Routh Hurwitz Table. But, i m very confused when it comes to find the range of K that makes system oscillate. even, i don't understand the term for oscillate. conclusion number 2 and 3 is very confusing.
 
Physics news on Phys.org
Is G(s) the forward gain with unity feedback? Good idea is to draw us a block diagram.
 

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