Maximum amplitude of second order system

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SUMMARY

The discussion focuses on determining the maximum amplitude of a second-order system by analyzing the derivative of the denominator in the transfer function. Participants emphasize the importance of setting the derivative equal to zero to find critical points, which may include local minima and maxima. The final step involves substituting the optimal value of r back into the transfer function's magnitude |H(jω)| for simplification. This theoretical approach is crucial for understanding system behavior in control theory.

PREREQUISITES
  • Understanding of second-order system dynamics
  • Familiarity with transfer functions and their properties
  • Knowledge of calculus, specifically derivatives
  • Basic concepts of control theory
NEXT STEPS
  • Study the derivation of transfer functions for second-order systems
  • Learn about local extrema in calculus and their significance in system analysis
  • Explore the implications of |H(jω)| in frequency response analysis
  • Investigate the role of damping ratio and natural frequency in system performance
USEFUL FOR

Control engineers, system analysts, and students studying control theory who seek to deepen their understanding of second-order system behavior and amplitude analysis.

MMCS
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See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
 

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MMCS said:
See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
Okay, so far so good. :smile:

But you just sort of stopped. Is there a particular question that you had?

You've already found the derivative of the denominator. Set the derivative equal to 0 and solve for r. You'll find that there are two or three values of r that make the derivative go to 0, but not all of them are necessarily local minimums (there could be local maximums).

Once you find the appropriate expression for r that makes the denominator a minimum, plug that back into |H(jω)| and simplify. :wink:
 

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