Control problem. Transfer function of an electrical system

In summary, the conversation discusses finding a transfer function for an electrical system and correcting a previous answer. The correct transfer function is found to be UR(s)/U(s)=1/(s+2). The conversation also includes a set up for the transfer function and a discussion about Kirchhoff's laws. One participant questions a specific fraction in the set up, which is clarified by the other participant.
  • #1
rowardHoark
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[URL]http://img28.mediafire.com/bacfa47633147eefb0c3433511d3f1415g.jpg[/URL]

1. Electrical system given. Find a transfer function. Correct answer UR(s)/U(s)=1/(s+2)

2. My attempt
Use Kirchhoff's voltage law u(t)-i(t)*R1-UR(t)=0; u(t)=i(t)R1+uR(t); apply Laplace Transform (L.T.) U(s)=I(s)R1+UR(s)

i(t)=i1(t)+i2(t)=1/L*[tex]\int[/tex]uR(t) dt+uR(t)/R2; take a L.T. assuming zero initial conditions I(s)=1/(L*s)*UR(s)+UR(s)/R2=UR(s)[1/(L*s)+1/R2]; since L=R1=R2=1 I(s)=UR(s)*(1/s+1); UR(s)=I(s)/(1/s+1)

H(s)=HR(s)/U(s)=[I(s)/(1/s+1)]/[I(s)R1+UR(s)]=[I(s)/(1/s+1)]/[I(s)+I(s)/(1/s+1)]=[1/(1/s+1)]/[1+1/(1/s+1)]=s/(1+2s)

Where am I making a mistake?
 
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  • #2
I'm not going to look through your nonlatex work but I'll post a set up that should be correct.

[tex]\frac{u_R(t)-u(t)}{R_1}+\frac{u_R(t)}{sL}+\frac{u_R(t)}{R_2}=0[/tex]
 
  • #3
xcvxcvvc said:
I'm not going to look through your nonlatex work but I'll post a set up that should be correct.

[tex]\frac{u_R(t)-u(t)}{R_1}+\frac{u_R(t)}{sL}+\frac{u_R(t)}{R_2}=0[/tex]

I am assuming you are using the Kirchhoff's current law?

I agree with everything, except the frac [tex]\frac{u_R(t)}{sL}[/tex].Can you, please explain, how does this results in current? How can you have a time domain function in the numerator and a frequency variable in the denominator?
 

FAQ: Control problem. Transfer function of an electrical system

What is a control problem in an electrical system?

A control problem in an electrical system refers to the issue of maintaining a desired output or response from the system, despite disturbances or changes in the input. This involves designing a control system that can adjust and regulate the output of the system based on the input and external factors.

What is the purpose of a transfer function in an electrical system?

The transfer function of an electrical system is a mathematical representation of the relationship between the input and output of the system. It allows engineers to analyze and design control systems to achieve the desired response from the system. Essentially, it describes how the system responds to different inputs.

How is a transfer function determined for an electrical system?

A transfer function is typically determined through mathematical modeling and analysis of the system. This involves identifying the components of the system, such as resistors, capacitors, and inductors, and determining their individual transfer functions. The overall transfer function of the system is then derived from these individual functions.

Can the transfer function of an electrical system change over time?

Yes, the transfer function of an electrical system can change over time due to various factors such as component aging, temperature changes, or external disturbances. This is why it is important to regularly monitor and tune control systems to ensure they are still functioning properly.

How is the stability of an electrical system determined using the transfer function?

The stability of an electrical system can be determined by analyzing the poles and zeros of the transfer function. If all the poles of the transfer function are in the left half of the complex plane, then the system is stable. If any poles are in the right half of the complex plane, the system is unstable and may exhibit oscillations or even become uncontrollable.

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