- #1
truva
- 18
- 1
Laplace transform includes exp(-st) and s=σ+jω. σ is negative in the left side and hence exp(-st) goes to infinity. It is not stable. Where am I wrong?
omkar13 said:σ is negative.So,exp(-σt) will tend to 0 as t tends to ∞.Also according to the function for which you want to find LT,limits are imposed on s for stabilty.You cannot directly think of the equation without function.
omkar13 said:IF S IS POSITIVE IT MEANS THAT σ IS ALSO POSITIVE.
The s-plane is a mathematical representation of a system's transfer function in the Laplace domain. It is used in control systems engineering to analyze the stability of a system. The s-plane allows us to see the behavior of a system over a range of frequencies and identify any unstable regions.
In the s-plane, the left side represents the stable region and the right side represents the unstable region. The stability of a system is determined by the location of its poles (or roots) in the s-plane. If all the poles are located in the left side of the s-plane, the system is stable. If any poles are in the right side, the system is unstable.
The left side of the s-plane is stable because it represents the region where the transfer function has a negative real part. This means that the response of the system will decay over time and will not grow without bound. In other words, the input to the system will not be amplified, ensuring stability.
No, a system cannot be stable if it has poles on the imaginary axis of the s-plane. This is because poles on the imaginary axis represent oscillatory behavior, which can lead to instability. Therefore, for a system to be stable, all its poles must be on the left side of the s-plane.
The location of poles in the s-plane is directly related to the stability of a system. For a system to be stable, all its poles must be in the left side of the s-plane. If any poles are in the right side, the system is unstable. Additionally, the distance of the poles from the imaginary axis also affects the stability of a system, with closer poles indicating a faster response and potentially leading to instability.