Control Systems – Lecture 12 – Positive feedback root locus, lead/lag compensators

Lecture 12 – Positive feedback root locus, lead/lag compensators

Kontrol Sistemleri – Positive feedback root locus, lead/lag compensators

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Positive Feedback architecture

(2) Departure angles from complex poles

arrival '' to complex zero

departure angle = 360 +Σ phase of c.c pole w.r.t. other poles

-Σ phase of c.c pole w.r.t. other zeros

Positive feedback system

To find characteristic equation

if its negative feedback

specific `` k '' which renders the system unstable

4 seperate roots of ch.e.q.

Its unuseless itself so we have to add a pole

by adding poles the locus plot move to right, systems get more unstable. (lag compensator)

System get more unstable - slower! ( t_s )

More accurate by adding integrator

lag compensation, The output angle is less than input

pulls the root locus plot to the left

more sensitive to noise

The output angle is more than the input angle

its leading output

lead laging compensator

Series/parallel compensation

Lead compensator: zero is closer to jω axis

if α>1 ⇒ lag compensator

Lead lag compensator

Dominant pole =-3+2j → lead compensator

Steady state error =10% (step input) → lag compensator

k give dominant pole

Lecture 12 – Positive feedback root locus, lead/lag compensators

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