Can You Change the Damping Ratio of a Second Order Linear System Easily?

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SUMMARY

The discussion focuses on modifying the damping ratio of a second-order linear system, particularly in the context of robotic arms. It is established that while one can change system variables to adjust both damping and natural frequencies, achieving a direct adjustment of the damping ratio alone is challenging. The conversation emphasizes that altering the natural frequency will inherently affect the damping ratio, making it difficult to isolate changes to just one parameter.

PREREQUISITES
  • Understanding of second-order linear systems
  • Familiarity with damping ratios and natural frequencies
  • Basic knowledge of control systems and dynamics
  • Experience with robotic arm mechanics
NEXT STEPS
  • Research methods for adjusting damping ratios in control systems
  • Explore the relationship between natural frequency and damping ratio in second-order systems
  • Learn about PID controllers and their impact on system dynamics
  • Investigate simulation tools for modeling robotic arm dynamics
USEFUL FOR

Control engineers, roboticists, and anyone involved in the design and optimization of dynamic systems, particularly those working with second-order linear systems.

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How to change the damping ratio of dynamical system if it is say for example robotic arm? Can it be changed directly or one need to change natural freqvancy? by which it will automatically change.
 
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assuming a second order linear system, the system equations make it pretty clear.

https://en.wikipedia.org/wiki/Damping

You can change any system variable, or multiple variables to get different damping and natural frequencies.

If you want one knob to just change only the damping ratio, that is difficult for a 2nd order linear system.
 
Most likely this can only be answered by an "old timer". I am making measurements on an uA709 op amp (metal can). I would like to calculate the frequency rolloff curves (I can measure them). I assume the compensation is via the miller effect. To do the calculations I would need to know the gain of the transistors and the effective resistance seen at the compensation terminals, not including the values I put there. Anyone know those values?

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