Process Control (transfer function) problem

In summary, a "Process Control (transfer function) problem" involves the analysis and design of control systems using transfer functions, which represent the relationship between the input and output of a system in the frequency domain. This problem typically includes identifying system dynamics, stability, and performance characteristics, often requiring the application of mathematical techniques such as Laplace transforms and feedback control principles to optimize system behavior and response.
  • #1
guiromero
18
0
TL;DR Summary: transfer function

Hello,

I have a doubt on this exercise from my post graduation course:
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The transfer funtion of a series RL circuit is given by:

1706903438830.png

Determine the answer y(t) for an entry signal given by x(t) = u(t) V:

1706903562428.png

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From the Laplace table, I find the closest association would be e-at, for F(s) = 1/s+a. Then the answer would be "d", but I'm not sure if this association is correct, because F(s) is not exactly 1/s+a, it's more likely a/s+a, where a = R/L.

Could someone give me a clear answer?

Thanks a lot!
 
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  • #2
1) Use parentheses. If you mean 1/(s+a), then write 1/(s+a), not 1/s + a. Correct all those errors.
2) Define u(t).
3) Compare the y(t) values at ##t=0## and ##t=\infty## of the optional answers with what you would expect from a first order lag transformation, H(s). That should rule out practically all the wrong answers.
 

FAQ: Process Control (transfer function) problem

What is a transfer function in process control?

A transfer function in process control is a mathematical representation of the relationship between the input and output of a system. It is typically expressed in the Laplace transform domain and provides a concise way to model the dynamic behavior of linear time-invariant systems.

How do you derive a transfer function from a differential equation?

To derive a transfer function from a differential equation, you first take the Laplace transform of the differential equation, assuming zero initial conditions. Then, you solve for the output variable in terms of the input variable. The ratio of the Laplace transform of the output to the Laplace transform of the input gives you the transfer function.

What is the significance of poles and zeros in a transfer function?

Poles and zeros of a transfer function significantly influence the system's behavior. Poles are the values of the Laplace variable (s) that make the denominator of the transfer function zero, and they determine the system's stability and transient response. Zeros are the values of s that make the numerator zero, and they affect the system's frequency response and transient characteristics.

How can you use a transfer function to analyze system stability?

You can analyze system stability using a transfer function by examining the locations of its poles in the complex plane. If all poles have negative real parts, the system is stable. If any pole has a positive real part, the system is unstable. Poles on the imaginary axis indicate marginal stability, which requires further analysis.

What are common methods for obtaining a transfer function experimentally?

Common methods for obtaining a transfer function experimentally include the step response method, frequency response method, and system identification techniques. In the step response method, you apply a step input to the system and record the output. In the frequency response method, you apply sinusoidal inputs at various frequencies and measure the output. System identification techniques use statistical methods to model the system based on input-output data.

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