Which of the following indicates that a system is stable?

Practice Questions

Q1
Which of the following indicates that a system is stable?
  1. All poles of the transfer function are in the right half of the s-plane.
  2. All poles of the transfer function are in the left half of the s-plane.
  3. Poles are on the imaginary axis.
  4. Poles are complex with positive real parts.

Questions & Step-by-Step Solutions

Which of the following indicates that a system is stable?
  • Step 1: Understand what a system is in control theory. A system can be anything that takes input and produces output, like a car or a robot.
  • Step 2: Learn about the transfer function. The transfer function is a mathematical representation that describes how the output of a system responds to its input.
  • Step 3: Know what poles are. Poles are specific values in the transfer function that help determine the behavior of the system.
  • Step 4: Identify the s-plane. The s-plane is a graph where the horizontal axis represents the real part of the poles and the vertical axis represents the imaginary part.
  • Step 5: Understand the left half of the s-plane. The left half of the s-plane is where the real part of the poles is negative.
  • Step 6: Determine stability. A system is stable if all its poles are located in the left half of the s-plane, meaning they all have negative real parts.
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