Root Locus Method Root Locus Method Root locus
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![Root Locus Method Root Locus Method](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-2.jpg)
![Root Locus Method • Root locus is a graphical presentation of the closed-loop poles Root Locus Method • Root locus is a graphical presentation of the closed-loop poles](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-3.jpg)
![Control System Problem Definition (1) • The poles of the open-loop transfer function are Control System Problem Definition (1) • The poles of the open-loop transfer function are](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-4.jpg)
![Control System Problem Definition • Example Control System Problem Definition • Example](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-5.jpg)
![Control System Problem Definition (5) • Example Pole Plot Root Locus Plot The root Control System Problem Definition (5) • Example Pole Plot Root Locus Plot The root](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-6.jpg)
![Root Locus Properties (1) Closed Loop Transfer Function A Closed loop pole, s, exists Root Locus Properties (1) Closed Loop Transfer Function A Closed loop pole, s, exists](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-7.jpg)
![Root Locus Properties (2) Root Locus Properties (2)](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-8.jpg)
![Root Locus Properties (3) Root Locus Properties (3)](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-9.jpg)
![A Root Locus Plot Asymptote: a branch goes to or comes from infinity Break-away A Root Locus Plot Asymptote: a branch goes to or comes from infinity Break-away](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-10.jpg)
![Sketching Root Locus By Dr. Enas Ismail Sketching Root Locus By Dr. Enas Ismail](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-11.jpg)
- Slides: 11
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![Root Locus Method Root Locus Method](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-2.jpg)
Root Locus Method
![Root Locus Method Root locus is a graphical presentation of the closedloop poles Root Locus Method • Root locus is a graphical presentation of the closed-loop poles](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-3.jpg)
Root Locus Method • Root locus is a graphical presentation of the closed-loop poles as a system parameter is Varied. • Root locus is a powerful method of analysis and design for stability and transient response. • Root locus is a graphical technique that gives us the qualitative description of a control system’s performance that we are looking for. • With Root locus method, gains and other system parameters were designed to yield a desired transient response for systems of order higher than 2.
![Control System Problem Definition 1 The poles of the openloop transfer function are Control System Problem Definition (1) • The poles of the open-loop transfer function are](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-4.jpg)
Control System Problem Definition (1) • The poles of the open-loop transfer function are easily found (typically, they are known by inspection and do not change with changes in system gain), Open Loop Transfer Function Closed Loop Transfer Function • The poles of the closed-loop transfer function are more difficult to find (typically, they cannot be found without factoring the closed-loop system’s characteristic polynomial, the denominator of the closed-loop transfer function), and further, the closed-loop poles change with changes in system gain.
![Control System Problem Definition Example Control System Problem Definition • Example](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-5.jpg)
Control System Problem Definition • Example
![Control System Problem Definition 5 Example Pole Plot Root Locus Plot The root Control System Problem Definition (5) • Example Pole Plot Root Locus Plot The root](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-6.jpg)
Control System Problem Definition (5) • Example Pole Plot Root Locus Plot The root locus will allow us to make that association and will become an important technique in the analysis and design of higher-order systems.
![Root Locus Properties 1 Closed Loop Transfer Function A Closed loop pole s exists Root Locus Properties (1) Closed Loop Transfer Function A Closed loop pole, s, exists](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-7.jpg)
Root Locus Properties (1) Closed Loop Transfer Function A Closed loop pole, s, exists when the characteristic polynomial in the denominator becomes zero, A pole of the closed-loop system causes the angle to be an odd multiple of 180.
![Root Locus Properties 2 Root Locus Properties (2)](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-8.jpg)
Root Locus Properties (2)
![Root Locus Properties 3 Root Locus Properties (3)](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-9.jpg)
Root Locus Properties (3)
![A Root Locus Plot Asymptote a branch goes to or comes from infinity Breakaway A Root Locus Plot Asymptote: a branch goes to or comes from infinity Break-away](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-10.jpg)
A Root Locus Plot Asymptote: a branch goes to or comes from infinity Break-away point Branch/Locus Break-in point
![Sketching Root Locus By Dr Enas Ismail Sketching Root Locus By Dr. Enas Ismail](https://slidetodoc.com/presentation_image_h2/0ca59f5c790fb437112eb34db9d845b0/image-11.jpg)
Sketching Root Locus By Dr. Enas Ismail