Root Locus Analysis 2 Hany Ferdinando Dept of
- Slides: 16
Root Locus Analysis (2) Hany Ferdinando Dept. of Electrical Eng. Petra Christian University
General Overview Ø This section explain the root locus plot for positive feedback system instead of negative feedback Ø All rules use the opposite of the ones used in the negative feedback
Standardization R(s) + G(s) C(s) + H(s) 1 – G(s)H(s) = 0 Find Characteristic Equation!!
How to make it? 1. 2. 3. 4. 5. 6. 7. Start from the characteristic equation Locate the poles and zeros on the s plane Determine the root loci on the real axis Determine the asymptotes of the root loci Find the breakaway and break-in points Determines the angle of departure (angle of arrival) from complex poles (zeros) Find the points where the root loci may cross the imaginary axis
Example (1) 1. Start from the characteristic equation
Example (2) 2. Locate the poles and zeros on the s plane
Example (3) 3. Determine the root loci on the real axis
Example (4 a) 4. Determine the asymptotes of the root loci
Example (4 b) 4. Determine the asymptotes of the root loci
Example (5) From the characteristic equation, find then calculate… s = -0. 8 and s = -2. 35± 0. 77 j 5. Find the breakaway and break-in point
Example (6) qpole = 0 – sum from pole + sum from zero qzero = 0 – sum from zero + sum from pole qpole = 0 – 27 – 90 + 45 = -72 6. Determine the angle from complex pole/zero
Example (7) Do this part by substituting jw for all s in the characteristic equation K = - w 2+8 and - w 2 = -10/3 The root locus does not cross the jw axis 7. Find the points where the root loci may cross the imaginary axis
Example (8)
Plot in negative feedback
Root Locus in Matlab Function rlocus(num, den) draws the Root Locus of a system. Another version in state space is rlocus(A, B, C, D) The characteristic equation For positive feedback use rlocus(-num, den) to plot the Root Locus in complex plane
Next… Design of a compensator is the topic for the next meeting… See you there!
- Root locus plotter
- What is root locus in control system
- Root locus break in and break away points
- Root locus departure angle
- Root locus
- Construction of root loci
- Properties of root locus
- Locus rule
- Lag lead compensator in control system
- Root locus definition
- ]fd t,k
- Root locus drawer
- Lag lead compensator in control system
- Root-locus techniques
- Root-locus techniques
- Cicatricis
- Ventajas del socialismo