Find the range of K for stability

In summary, the question is asking for the range of K to make the closed loop system stable. The closed loop transfer function is Gcl=Gol/(1-LG) with LG= - Gol*K. To find the range of K, we set the denominator of Gcl to be greater than zero, which results in K>1/2. However, this answer may not be accurate without more information about the block diagram and values of Gol and K.
  • #1
jdoe10
3
0

Homework Statement


Find the range of K for the closed loop system to be stable.
##G_{OL}(s) = \frac{10}{s-5}##

Homework Equations

The Attempt at a Solution


##G_{CL}(s) = \frac{KGol}{1+Gol}##
##G_{CL}(s) = \frac{10K}{s-5+10K}##
##-5+10K>0##
##K>\frac{1}{2}##
is this correct?
 
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  • #2
No - the quation for Gcl is not correct (assuming Gol is the open-loop gain and K is the negative feedback factor).
We have Gcl=Gol/(1-LG)
with Loop Gain LG= - Gol*K.
 
  • #3
In this context I am guessing that K is the amplifier block before the open loop gain that can be adjusted, also known as the DC gain of the controller. I am guessing Gol is really the open loop gain of the plant.
 
  • #4
Jdoe10, can you provide us with a block diagram or more information?
 
  • #5
jdoe10 - please, please, be so kind and give us the chance (necessary information) to answer your question.
 

Related to Find the range of K for stability

1. What does "range of K for stability" mean?

"Range of K for stability" refers to the values of the variable K in a mathematical equation or model that will result in a stable outcome. In other words, it is the range of values that will not cause the system to become unstable or unpredictable.

2. Why is it important to find the range of K for stability?

It is important to find the range of K for stability because it allows us to determine the conditions under which a system will remain stable and predictable. This information is crucial in fields such as engineering, physics, and chemistry, where stability is essential for the proper functioning of systems and processes.

3. How can the range of K for stability be calculated?

The range of K for stability can be calculated through various methods, depending on the specific equation or model being used. In general, it involves analyzing the behavior of the system at different values of K and determining the threshold at which it becomes unstable. This can be done through mathematical calculations or simulations.

4. Are there any limitations to finding the range of K for stability?

Yes, there may be limitations to finding the range of K for stability. In some cases, the system may exhibit chaotic behavior, making it difficult to determine a specific range of K for stability. Additionally, the accuracy of the results may depend on the assumptions and simplifications made in the model or equation being used.

5. Can the range of K for stability be applied to any system?

The concept of finding the range of K for stability can be applied to many different systems, as long as they can be described by mathematical equations or models. However, the specific methods and calculations used may vary depending on the complexity of the system and the variables involved.

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