Response of a system (Control theory)

In summary, the conversation discussed the difficulties in understanding the response of a system when it has oscillations. It was mentioned that the maximum elongation can be calculated using a formula that includes the damped coefficient and final value. However, there was uncertainty on what to do if the final value is 0.
  • #1
Domenico94
130
6
Hi everyone. I'm studying for the exam of control theory, and now I'm having an hard time with the response of a system, in particular when we have oscillations.
Suppose you have a system, with a transfer function, say, G(S), in the form:

G(S) = 1
-------------------
(s ^2 + 2a*w (s) + w^2)

Then, if we have oscillations, we can calculate the maximum elongation (in percentage), over final value, with the formula

S = (final value)* 100 * e ^ ((-pi * a)/sqrt(1 - a^2)),
in which a is the damped coefficient.
The problem is, if the final value is 0, what should I do there? Thank you for your help
 
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  • #2
Anyone?
 

1. What is a system in control theory?

A system in control theory refers to a collection of interrelated parts that work together to achieve a specific goal. In this context, the system can be a physical, biological, or social entity that can be controlled or manipulated.

2. What is the purpose of studying the response of a system in control theory?

The main purpose of studying the response of a system in control theory is to understand and analyze how the system behaves when subjected to different inputs or disturbances. This allows us to design and implement control strategies to achieve desired outcomes and improve the system's performance.

3. What factors can affect the response of a system in control theory?

The response of a system in control theory can be affected by various factors such as the system's design, the control input, external disturbances, and the system's environment. These factors can influence the system's stability, speed of response, and accuracy.

4. How is the response of a system measured in control theory?

The response of a system in control theory is typically measured using different performance metrics, such as rise time, settling time, and steady-state error. These metrics provide quantitative measures of the system's behavior and help evaluate the effectiveness of the control strategies.

5. What are some common control techniques used to improve the response of a system?

Some common control techniques used to improve the response of a system in control theory include proportional-integral-derivative (PID) control, feedforward control, and model predictive control. These techniques aim to adjust the control input based on the system's response to achieve a desired performance or track a reference signal.

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