What Do Unit Step and Unit Impulse Mean in Systems Control?

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SUMMARY

The unit step function, denoted as u(t), represents a sudden change in input from 0 volts to E volts in systems control, effectively modeling a switch being turned on. Conversely, the unit impulse function, δ(t), models a brief voltage application, where the switch is activated for a time T much shorter than the system's time constants, resulting in an input of E*T*δ(t) volts. Both functions serve as critical inputs in control systems, allowing for the analysis of system responses to sudden changes.

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  • Understanding of control systems theory
  • Familiarity with mathematical functions, specifically the unit step and unit impulse functions
  • Basic knowledge of electrical circuits and voltage concepts
  • Experience with system response analysis
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Homework Statement


Hi,can someone explain to me through real world examples what the unit step and unit impulse means in systems control?How are they related to the system's input? Thank you.

Homework Equations


δ(t) = unit umpulse
u(t) = unit step

The Attempt at a Solution

 
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Well, for one thing they ARE system inputs.

If you have a network with a battery as input, and you throw a switch which changes the input to your network from 0 volts to E volts, then your system input is E*u(t).

δ(t) is more complex. Picture a voltage E again, but this time throw the switch on and off for a very short time T. By 'very short' I mean much shorter than the shortest time constant in your network. Then the input to your network is E*T*δ(t) volts.
 

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