Why Does Integral Control Affect Transient Response But Not Root Locus Plot?

In summary, adding integral control to a root locus plot with a zero at the origin can result in a pole at the origin. This can cause a change in the transient response, but may not be reflected in the root locus plot. Additionally, having a zero at the origin can lead to a closed-loop pole at the origin, making it difficult to meet settling time requirements. It is unclear if there is a way to achieve both a zero at the origin and meeting settling time requirements.
  • #1
susmatt
5
0
I have a zero at the origin of my root locus plot. I understand that I need integral control to have zero steady-state error. I have 2 questions about this.

1. When I add integral control like this, Kp (1/(Ti*s)) where Ti is from Z-N first method and Kp=1, I get a pole at the origin. I don't don't see any change in the root locus plot by changing Ti, but I do see change in the transient response. Why is this?

2. When I add the integral control and there's a zero at the origin, I have a CL pole at the origin. This means I'm not able to achieve my settling time requirements. Is there a way to achieve both when there's a zero at the origin?
 
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  • #2
Can you rewrite the question a bit more clearly, I am not sure what some of your terms are. For example, what is Ti? Also, what is Z-N first method?
 

Related to Why Does Integral Control Affect Transient Response But Not Root Locus Plot?

1. What is control theory?

Control theory is a branch of mathematics and engineering that deals with the analysis and design of systems to achieve desired behaviors. It involves understanding how systems behave, identifying control objectives, and designing control strategies to achieve those objectives.

2. What are the main components of a control system?

The main components of a control system are the input, the plant, the output, and the controller. The input is the signal that is fed into the system, the plant is the system being controlled, the output is the desired behavior or response, and the controller is the device or algorithm responsible for adjusting the plant to achieve the desired behavior.

3. What are the types of control systems?

There are two main types of control systems: open-loop and closed-loop (also known as feedback) systems. In an open-loop system, the controller does not use any feedback information from the output to adjust the plant. In a closed-loop system, the output is compared to the desired behavior and the controller uses this information to adjust the plant accordingly.

4. What is the difference between linear and nonlinear control systems?

A linear control system is one in which the relationship between the input and the output is described by a linear equation. This means that the output is directly proportional to the input, and changing the input by a certain amount will result in a corresponding change in the output. In contrast, a nonlinear control system is one in which the relationship between the input and the output is not described by a linear equation. This means that the output may not be directly proportional to the input, and changing the input may result in a non-proportional change in the output.

5. How is control theory used in real-world applications?

Control theory has numerous applications in various fields, such as engineering, economics, and biology. It is used to design and improve systems, such as aircraft autopilot systems, industrial processes, and traffic control systems. It is also used in modeling and analyzing complex systems, such as the stock market and the human body, to understand their behaviors and predict their responses to different inputs.

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