Funkar Tushen Gadaɗa na Nizaminta

Na transfer function ya nuna tashar da aka fara a control system da kaɗan bayan duka yadda ake iya fara. A block diagram ita ce wani koyarwa na control system wanda ake amfani da blocks don nuna transfer function, da kuma arrows don nuna dukkan input da output signals.

Don dukkan control system, akwai wani reference input wanda ana soni shi da excitation ko sababba wanda ya yi aiki a kan transfer operation (ya'ni transfer function) don bincike abubuwan da suka samu amsa a cikin output ko response.

Saboda haka, tashar da ke cikin output da input ya yi take suna da shi a kan transfer function.

A Laplace Transform, idan input ya fi siffar da R(s) da kuma output ya fi siffar da C(s), maka transfer function zai kasance:

Hakan ne, transfer function na systemi ake fada da input function ta ba ake bincika output function na systemi.

Transfer Function Na Neman Yana Nufin?

Transfer function na control system an nufin shi da tushen Laplace transform na variable na output zuwa Laplace transform na variable na input, idan aka yi shiga kowane mafi girma a zero.

Tarihin da ake amfani don tabbatar da transfer function na control system:

1. An yi tarihin masu systemi.

2. An yi Laplace transform na tarihin masu systemi, idan aka yi shiga kowane mafi girma a zero.

3. An bayyana output da input na systemi.

4. An karɓa tushen Laplace transform na output zuwa Laplace transform na input, wanda ya zama transfer function da aka buƙata.

Ba a zama cewa output da input na control system suna da ƙarin nau'in. Misali, a electric motors, input ya fi siffar da electrical signal, amma output ya fi siffar da mechanical signal, saboda electrical energy ya ci gaba da motor. Duk da haka a electric generator, input ya fi siffar da mechanical signal, amma output ya fi siffar da electrical signal, saboda mechanical energy ya ci gaba da electricity a cikin generator.

Amma don babban al'adun tarihi, dukkan nau'in signals yana da kyau a canza a ƙarin nau'in. Wannan ya faru a kan canza dukkan nau'in signals zuwa Laplace form. Kuma transfer function na systemi ya canza a Laplace form tare da canza output Laplace transfer function zuwa input Laplace transfer function. Saboda haka, wani koyarwa na biyu na control system zai iya canza a


Idan r(t) da c(t) su ne time domain function na input da output signals daga baya.

Tarihin Tabbatar da Transfer Function

Akawo tarihi masu biyu na tabbatar da transfer function don control system. Tarihin su ne:

• Block Diagram Method: Ba a zama ƙarin tabbatar da transfer function don wani control system mai mahimmanci. Saboda haka, transfer function na kowane element na control system ya nuna a kan block diagram. An yi amfani da block diagram reduction techniques don tabbatar da transfer function da aka buƙata.

• Signal Flow Graphs: Wani ƙaramin bayan block diagram ita ce signal flow graph. Block diagram ya ba wani koyarwa na control system. Signal flow graph ya ƙara tsari da koyarwar control system.

Poles da Zeros na Transfer Function

Yanzu, wani function zai iya canza a polynomial form. Misali,

Duk da haka, transfer function na control system zai iya canza a polynomial form kamar haka

Idan K ya fi siffar da gain factor na transfer function.

Idan s = z1, ko s = z2, ko s = z3,….s = zn, ma'anar transfer function ya zama zero. Waɗannan z1, z2, z3,….zn, suna da roots na numerator polynomial. Saboda waɗannan roots, numerator polynomial, transfer function ya zama zero, saboda haka, waɗannan roots suna nufin zeros na transfer function.

Idan s = p1, ko s = p2, ko s = p3,….s = pm, ma'anar transfer function ya zama infinity. Saboda haka, roots na denominator suna nufin poles na function.

Duk da haka, ina bayyana transfer function a polynomial form.

Duk da haka, ina duba s tare da infinity, saboda waɗannan roots suna da kyaututtuka, za a iya koyar da su zuwa infinity. Saboda haka

Saboda haka, idan s → ∞ da n > m, function yana da ma'anar infinity, wanda yana nufin cewa transfer function yana da poles a infinity, da multiplicity ko order na poles shine n – m.
Duk da haka, idan s → ∞ da n < m, transfer function yana da ma'anar zero, wanda yana nufin cewa transfer function yana da zeros a infinity, da multiplicity ko order na zeros shine m – n.

Fahimta na Transfer Function

Transfer function tana nuna a Laplace Transform, wanda tana nufin tashar da input da output na systemi. Ina duba wani systemi wanda ake samu series connected resistance (R) da inductance (L) a kan voltage source (V).

A cikin wannan circuit, current ‘i’ shine response wanda ake samu applied voltage (V) as cause. Saboda haka, voltage da