Sinusoidal response to sinusoidal input (Process control)

  • #1
guiromero
18
0
Homework Statement
The sinusoidal response is a common response type in first-order industrial process control systems. This response is characterized by the oscillation that occurs in the controlled variable around its steady state value, when a sinusoidal input is applied to the system. Which of the following correctly describes one of the main characteristics of the sinusoidal response in first-order systems?


a) The amplitude of the sinusoidal response is not affected by the frequency of the sinusoidal input.
b) The amplitude of the sinusoidal response increases as the frequency of the sinusoidal input increases.
c) The amplitude of the sinusoidal response decreases as the frequency of the sinusoidal input increases.
d) The phase of the sinusoidal response is directly proportional to the frequency of the sinusoidal input.
e )The phase of the sinusoidal response is inversely proportional to the frequency of the sinusoidal input.
Relevant Equations
G(s) = K/(Ts + 1) (basic first orde transfer function)
This a homeawork from my graduate course. I know that a sinusoidal input affects both the amplitude and phase of the response, but I don't know how it does.

I'd be really glad if someone could help.

Thanks
 
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  • #2
It might help to be a little more precise in the statements. If you mean 1/(Ts+1), then write that, not 1/Ts +1. If you mean first order LAG, then write that. If you mean amplitude GAIN, then write that. If you mean phase SHIFT, then right that.
That being said, how do you think that a first order lag would respond to faster frequencies? A lag is slow to respond. That should help you to rule out a lot of the incorrect answers.
We can not give answers to homework-type problems and can only give guidance and hints for your work. So I don't think that I can say more.
 
Last edited:
  • #3
That was great! Thanks a lot!
 

FAQ: Sinusoidal response to sinusoidal input (Process control)

What is a sinusoidal response in process control?

A sinusoidal response in process control refers to the behavior of a system when it is subjected to a sinusoidal input signal. This type of input is a continuous wave that oscillates smoothly and periodically. The response of the system to this input helps in understanding the dynamic characteristics of the system, such as its frequency response, gain, and phase shift.

Why is sinusoidal input used to analyze process control systems?

Sinusoidal input is used to analyze process control systems because it allows for a straightforward assessment of the system's frequency response. By applying a sinusoidal input at different frequencies, one can determine how the system amplifies or attenuates signals and how it shifts their phase. This information is crucial for designing and tuning controllers to ensure stability and desired performance.

What is the significance of gain and phase shift in sinusoidal response analysis?

Gain and phase shift are critical parameters in sinusoidal response analysis. Gain measures how much the amplitude of the output signal is amplified or attenuated compared to the input signal. Phase shift indicates the time delay between the input and output signals. Together, these parameters provide insights into the system's behavior and help in designing control strategies that can effectively manage the process dynamics.

How do you determine the frequency response of a system using sinusoidal input?

To determine the frequency response of a system using sinusoidal input, one typically applies sinusoidal signals of varying frequencies to the system and measures the corresponding output. By plotting the gain and phase shift of the output signal against the input frequency, one can create a Bode plot, which visually represents the system's frequency response. This plot helps in understanding how the system reacts to different frequencies and is essential for control system design.

What are the practical applications of sinusoidal response analysis in process control?

Sinusoidal response analysis has several practical applications in process control, including the design and tuning of PID controllers, stability analysis, and system identification. By understanding how a system responds to sinusoidal inputs, engineers can develop control strategies that ensure stability, optimize performance, and enhance the robustness of the control system against disturbances and uncertainties.

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