2nd order System steady state error

In summary: You need to use the closed loop function to find K and \alpha such that the input R(s) = 1/s^2 will have no steady state error.
  • #1
silentwf
37
0

Homework Statement


The system's closed loop transfer function is given below, find K and [tex]\alpha[/tex] such that the input [tex]R(s) = 1/s^2[/tex] 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 [tex]\alpha[/tex], 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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  • #2
silentwf said:

Homework Statement


The system's closed loop transfer function is given below, find K and [tex]\alpha[/tex] such that the input [tex]R(s) = 1/s^2[/tex] 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 [tex]\alpha[/tex], 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:

1. What is a 2nd order system steady state error?

A 2nd order system steady state error refers to the error that remains when a system has reached a stable state. It is the difference between the desired output and the actual output of a system after it has been subjected to a constant input for a long period of time.

2. How is the steady state error of a 2nd order system calculated?

The steady state error of a 2nd order system can be calculated by taking the difference between the input and output signals at steady state. It can also be calculated using the final value theorem.

3. What factors can affect the steady state error of a 2nd order system?

The steady state error of a 2nd order system can be affected by factors such as the system's natural frequency, damping ratio, and the type of input signal being applied.

4. How can the steady state error of a 2nd order system be minimized?

The steady state error of a 2nd order system can be minimized by adjusting the system's parameters such as the natural frequency and damping ratio. It can also be reduced by implementing a feedback control system.

5. Can the steady state error of a 2nd order system be completely eliminated?

No, it is not possible to completely eliminate the steady state error of a 2nd order system. It can only be reduced to a certain extent based on the system's parameters and input signal. However, with proper control and tuning, it can be kept within acceptable limits.

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