# Determine the range of K that keeps the system stable

• alagez
In summary, the conversation is about a control system with a transfer function of G(s)=K(s+4)/s(s+1)(s+2) and the task of determining the range of K for stability and oscillation, as well as calculating the frequency of oscillation. The Routh Hurwitz Table is used to solve for the stability range of K, but there is confusion about finding the range for oscillation and understanding the term itself. A suggestion is made to draw a block diagram to clarify the situation.
alagez

## Homework Statement

i meet problem below in control system :

G(s)= K(s+4)/s(s+1)(s+2) its a unity feedback system.

1. determine the range of K that keeps the system stable.
2. determine the range of K that makes the system oscillate
3. calculate the frequency of oscillation when the system oscillate

## Homework Equations

characteristic equation for stability Routh Hurwitz Creation

## The Attempt at a Solution

i have solved the first by determine the range of K by using Routh Hurwitz Table. But, i m very confused when it comes to find the range of K that makes system oscillate. even, i don't understand the term for oscillate. conclusion number 2 and 3 is very confusing.

Is G(s) the forward gain with unity feedback? Good idea is to draw us a block diagram.

## 1. What is the definition of stability in a scientific context?

Stability refers to the ability of a system to maintain a steady state or equilibrium despite external disturbances or fluctuations.

## 2. How is the range of K determined in a stable system?

The range of K is determined by analyzing the system's transfer function, which represents the relationship between the input and output of the system. The stability criteria, such as Routh-Hurwitz or Nyquist stability criteria, are then applied to determine the range of values for K that will keep the system stable.

## 3. What factors can affect the stability of a system?

The stability of a system can be affected by various factors such as the system's components, external disturbances, changes in system parameters or operating conditions, and the type of control used.

## 4. How does the range of K affect the performance of a stable system?

The range of K can significantly impact the performance of a stable system. If the value of K is too low, the system may be too slow to respond to changes. On the other hand, if K is too high, the system may become unstable and exhibit oscillations or overshoots in its response.

## 5. Are there any general guidelines for selecting the range of K for a stable system?

There are no specific guidelines for selecting the range of K, as it depends on the specific system and its requirements. However, it is generally recommended to choose a value of K that provides a good balance between system response time and stability. Additionally, the range of K may need to be adjusted if there are changes in the system's parameters or operating conditions.

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