Root Locus is a graphical method used in control system analysis to show how the closed-loop poles of a system move in the complex plane as the system gain varies from zero to infinity. It is based on the characteristic equation and helps engineers study system stability, transient response, damping, natural frequency, and the effect of controller gain. By examining the root-locus plot, suitable gain values can be selected to achieve desired performance while maintaining system stability.
Root Locus Interactive Simulation
Demonstration:
Root Locus is a graphical method used in control system analysis to show how
the closed-loop poles of a system move in the complex plane as the system gain
K varies from zero to infinity.
This simulation uses the open-loop transfer function:
This simulation uses the open-loop transfer function:
G(s)H(s) = 1 / [s(s + 2)(s + 4)]
Characteristic equation:
1 + K G(s)H(s) = 0
s³ + 6s² + 8s + K = 0
Characteristic equation:
1 + K G(s)H(s) = 0
s³ + 6s² + 8s + K = 0
Root Locus Plot
K = 8.0
Closed-loop poles
Calculating…
Damping Ratio
—
Natural Frequency
—
Stable