2nd order System steady state error

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SUMMARY

The forum discussion centers on determining the values of K and α in a second-order system's closed-loop transfer function to ensure that the input R(s) = 1/s² results in no steady-state error. The hint specifies that the system is not a unit feedback system, which is crucial for solving the problem correctly. A participant mistakenly transformed the system into a unit feedback configuration, leading to confusion regarding the equations needed to solve for K and α. The correct approach involves using the closed-loop transfer function to calculate the steady-state error.

PREREQUISITES
  • Understanding of closed-loop transfer functions in control systems
  • Familiarity with steady-state error analysis
  • Knowledge of second-order system dynamics
  • Experience with feedback system configurations
NEXT STEPS
  • Study the derivation of steady-state error formulas for different input types
  • Learn about the implications of feedback types on system stability and performance
  • Explore the design of control systems using MATLAB's Control System Toolbox
  • Investigate the effects of gain (K) and pole placement on system response
USEFUL FOR

Control engineers, students studying control theory, and anyone involved in designing or analyzing feedback control systems will benefit from this discussion.

silentwf
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Homework Statement


The system's closed loop transfer function is given below, find K and \alpha such that the input R(s) = 1/s^2 has no steady state error. (Hint: the system is not a unit feedback system)
[PLAIN]http://img829.imageshack.us/img829/9899/problempr.png

Homework Equations


not sure how many there are.


The Attempt at a Solution


So I made the system into a unit feedback system despite its hint...and it turned out..strange.
Another thing i don't understand is, with the conditions that the questions, i only get one equation to solve for k and \alpha, are there any others that i might be overlooking?


[PLAIN]http://img692.imageshack.us/img692/3111/solj.png
 
Last edited by a moderator:
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silentwf said:

Homework Statement


The system's closed loop transfer function is given below, find K and \alpha such that the input R(s) = 1/s^2 has no steady state error. (Hint: the system is not a unit feedback system)
[PLAIN]http://img829.imageshack.us/img829/9899/problempr.png

Homework Equations


not sure how many there are.


The Attempt at a Solution


So I made the system into a unit feedback system despite its hint...and it turned out..strange.
Another thing i don't understand is, with the conditions that the questions, i only get one equation to solve for k and \alpha, are there any others that i might be overlooking?


[PLAIN]http://img692.imageshack.us/img692/3111/solj.png[/QUOTE]

You used the wrong expression for the steady state error. You should have used the closed loop function and not the open loop G.
 
Last edited by a moderator:

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