Angle and Magnitude Condition
Angle and Magnitude conditions are important conditions for the construction of root locus.
The closed-loop transfer function for the given block diagram is
Closed Loop
C(s) / R(s) = G(s) / 1 + G(s) H(s)
Characteristic equation for above transfer function is
1 + G(s) H(s) =0
G(s) H(s) = -1
Here G(s) H(s) is complex part and it can be written in terms of magnitude and angle part
Angle Condition
Phase angle of G(s) H(s) is
∠G(s)H(s) = tan-1 ( 0 / -1 ) = (2 n + 1 ) π , where n = 0, 1, 2, ……… (1)
Phase of open loop transfer function is odd multiple of 1800 at angle condition point.
Magnitude Condition
|G(s)H(s)|= 1 ……… (2)
Magnitude of open loop transfer function becomes 1 at Magnitude condition Point.
Equation 1 and 2 is also known as EVAN ‘ S CONDITION .
The value of s is roots of characteristic equation is if it satisfy both Angle and Magnitude condition.
Construction of Root Locus
The Root Locus is the Technique to identify the roots of Characteristics Equations Within a Transfer Function. It Follows the Process of Plotting the roots on a graph, Showcasing their Variations across Different Parametric Values. In this article, we will be going through What is Root Locus?, Angle and Magnitude Conditions, Construction Rules of Root Locus, and At last we will solve the Examples.
Table of Content
- What is Root Locus?
- Angle and Magnitude Condition
- Construction Rules of Root Locus
- Effects of adding Open Loop Poles and Zeros on Root Locus
- Solved Example
- Application
- FAQs on Root Locus in Control System