Control Systems · Digital lecture note
Lecture 11 – Root Locus (continued)
Kontrol Sistemleri – Root Locus (devam)
- Course
- Control Systems (ELEC322)
- Semester
- Semester 6 · Spring 2023–24
- Format
- PDF · 9 pages · 0.3 MB · handwriting-style LaTeX
- Language
- Turkish
- Original note
- Control-Systems-lecture-11.pdf
Open the PDF (0.3 MB)LaTeX source (.tex)Original handwritten note
What is in this note?
Section headings of the note (in Turkish):
- Root locus
- 5 - Complex conjugate poles
- Step 6 Intersection with the jω axis
Text of the note
Show as plain text (Turkish; formulas and drawings are not included)
5 - Complex conjugate poles
Departure angle from poles?
arrival angle '' zeros
Step 6 Intersection with the jω axis
I) in the characteristic
II) characteristic eq
if one of the components of the first column is zero
make one full row zero!
So Step 7- Find the location of root locus of the complex poles!
Method I) do numerical trial & error to discover the locations of ` s ' which satisfy the phase condition
Method II) Substitute s as s=σ+jω in the characteristic equation and mathematically find the phase condition.
: magnitudes of individual complex function in numerator and denominator
for large s values
The characteristic equ.
Intersection with jω axis
checking the magnitude condition at
n = number of poles =2
break in point:
Departure angles from complex poles
for the complex conjugate pair the department angle is 145^°