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Nichols Chart çi ye?

Nichols Chart (ji bo yasayış Nichols Plot) wekheya ekranê ye ku bi karî yên signal processing û control system design bikar în e ji bo taybetandina stabîlîyey û pêşgotina feqencyek dawiyên feedback system. Nichols chart li ser navê wan bûyer, Nathaniel B. Nichols.

Nichols Chart çawa werke?

Lokên M-circles da ku tevahîn magnitude constant hene û lokên N-circles da ku tevahîn phase angle constant hene an jî komponentên esasî yên ji bo dizayn krdina Nichols chart ne.

M û N circles constant în G (jω) plane dikarin bi karî yên analiz û dizayn krdina control systems bikar bîn.

Berdî lê, M û N circles constant în gain phase plane taybetandin ji bo dizayn û analiz krdina systeman diçin, ji ber ku wê grafikên agahdar ên bide.

Gain phase plane wekheya ekranê ye ku di ordinate (axis vertical) de gain in decibels heye û di abscissa (axis horizontal) de phase angle heye.

M û N contours în rectangular coordinates hatine transform kirin ji M û N circles în G (jω) plane.

Di G (jω) plane de pointek ji M loci constant hatine transfer kirin bi karî yên vektora directed ji origin ên G (jω) plane ji bo pointek ji M circle û hatine mapekirin length in dB û angle in degree.

Pointek critical în G (jω) plane hatine peyda kirin ji pointek zero decibels û -180o în gain phase plane. Plotek M û N circles în gain phase plane nikarînin Nichols chart (ji bo Nichols plot).

Compensators dikarin bigihîn bi karî yên Nichols plot.

Taybetandina DC motor dikare bi karî yên Nichols plot bikar în e. Ji bo signal processing û control system design bikar în e.

Nyquist plot related în complex plane nîşan dide ku cîhek transfer function û frequency variation of magnitude related ne. Dikarin gain û phase ji bo frequency taybetî bînin.

Angle of the positive real axis determines the phase and the distance from the origin of the complex plane determines the gain. There are some advantages of Nichols’ plot in control system engineering.

They are:

• Gain û phase margins dikarin sade û grafîkî hatine taybetand.

• Closed loop frequency response hatine girtin ji open loop frequency response.

• Gain of the system dikare adjusted be suitable values bikar în e.

• Nichols chart provides frequency domain specifications.

There are also some drawbacks to the Nichols plot. Using a Nichols plot is difficult for small changes in gain.

Constant M û N circles în Nichols chart hatine deform kirin be squashed circles.

The complete Nichols chart extends for the phase angle of G (jω) from 0 to -360o. The region of ∠G(jω) is used for the analysis of systems between -90o to -270o. These curves repeat after every 180o interval.

If the open loop T.F of unity feedback system G(s) is expressed as

Closed loop T.F is

Substituting s = jω in the above eq. frequency functions are,

and

Eliminating G(jω) from the above two eq.

and

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