Kudancin Nyquist da Dukkan Yadda: Me kana? (Daga Misalai a Matlab)
Me Da Nyquist Stability Criterion?
Nyquist stability criterion (ko Nyquist criteria) ita ce koyar tushen da ake amfani da ita a sayar sauki don in gano ingantaccen tsarin daidaita. Saboda Nyquist stability criteria yana nuna kawai Nyquist plot na cikin tsari mai girma, zan iya amfani da shi bace ba a tabbataccen poles da zeros na ciki ko kasa na cikin tsarin.
Saboda haka, Nyquist criteria zan iya amfani da shi a kan tsari da ake bayyana da funtunoyi da ba suka da duka (kamar tsari da wasu dalilai). Tare da Bode plots, zan iya amfani da transfer functions da singularities a kan babban hagu.
Nyquist Stability Criterion zan iya nufin:
Z = N + P
Me:
Z = adadin roots of 1+G(s)H(s) a kan gabashin s-plane (Ana ce zero of characteristics equation)
N = adadin encirclement of critical point 1+j0 a kan gyakkyauwa
P = adadin poles of open loop transfer function (OLTF) [i.e. G(s)H(s)] a kan gabashin s-plane.
Yadda za a iya nuna (i.e. Z=N+P) yana da muhimmanci zuwa duk waɗannan tsari ba su ci gaba ko abinci.
A nan muna so ku fada wannan criterion tare da misalai na Nyquist stability criterion.
Misalai Na Nyquist Stability Criterion
Misali 1 Na Nyquist Criterion
Za a duba open-loop transfer function (OLTF) kamar 
. Ana yin da amsa ko ana yi. Kadan da mutum ke amsa wanda aka amsa saboda pole akwai a +2. Amma, lafiya ya ne a kan denominator na closed-loop transfer function.
Idan kowane root na denominator na closed-loop transfer function (ko kuma characteristics equation) akwai a kan gabashin s-plane, maka amsa yana buƙatar abinci. Saboda haka, a nan, pole a +2 zan iya buƙatar abinci, amma amsa yana iya zama lafiya. A nan Nyquist plot yana da muhimmanci don in gano lafiya.
Kamar yadda ake nuna ta a Nyquist theory Z=N+P (don waɗannan tsari, ko cewa lafiya ko abinci).
Don amsa lafiya, Z=0, i.e. Ba a yi roots of characteristics equation a kan gabashin s-plane.
Saboda haka, don amsa lafiya N = –P.
Nyquist plot na amsa yana nuna kamar yadda ake nuna a kan cikin:
Nyquist Plot Matlab Code
s = tf('s')
G1 = 120 / ((s-2)*(s+6)*(s+8))
nyquist(G1, 'red')
Daga cikin diagram, Nyquist plot yana encircle point –1+j0 (ko kuma critical point) maimakon a gyakkyauwa. Saboda haka N= –1, a OLTF, pole (a +2) akwai a kan gabashin s-plane, saboda haka P =1. Za a iya nuna N= –P, saboda haka amsa yana lafiya.
Idan za a nuna roots of characteristics equation, za a iya nuna –10.3, –0.86±j1.24. (i.e. amsa yana lafiya), and Z=0. Wanda ake magana, idan roots of characteristics equation zan iya nuna, don haka muna iya nuna lafiya daga baya, wanda nyanyu da Nyquist plot. Amsa ta amsa, lokacin da softwares ba suka da damu, a nan Nyquist plot yana da muhimmanci.
Misali 2 Na Nyquist Criterion
Na gode a matsayin misali: 
Nyquist plot yana nuna kamar yadda ake nuna a kan cikin:
