root-locus-basic · python · pygal · anyplot.ai-5.0-5.0-4.0-4.0-3.0-3.0-2.0-2.0-1.0-1.00.00.01.01.02.02.03.03.04.04.05.05.0-6.0-6.0-5.0-5.0-4.0-4.0-3.0-3.0-2.0-2.0-1.0-1.00.00.01.01.02.02.03.03.04.04.0root-locus-basic · python · pygal · anyplot.aiReal Axis (σ)Imaginary Axis (jω)0.0: 0.01212.3384615384614942.5-0.0: 0.01209.0143076923075942.5-0.0: 0.01205.6901538461539942.5-0.1: 0.01202.3659999999998942.5-0.1: 0.01199.041846153846942.5-0.1: 0.01195.7176923076922942.5-0.1: 0.01192.3935384615384942.5-0.1: 0.01189.0693846153847942.5-0.1: 0.01185.7452307692306942.5-0.2: 0.01182.421076923077942.5-0.2: 0.01179.2924615384616942.5-0.2: 0.01175.9683076923077942.5-0.2: 0.01172.6441538461536942.5-0.2: 0.01169.32942.5-0.2: 0.01165.995846153846942.5-0.3: 0.01162.6716923076922942.5-0.3: 0.01159.3475384615385942.5-0.3: 0.01156.0233846153844942.5-0.3: 0.01152.6992307692308942.5-0.3: 0.01149.375076923077942.5-0.3: 0.01146.050923076923942.5-0.4: 0.01142.7267692307694942.5-0.4: 0.01139.4026153846153942.5-0.4: 0.01136.0784615384616942.5-0.4: 0.01132.7543076923077942.5-0.4: 0.01129.4301538461539942.5-0.4: 0.01126.106942.5-0.5: 0.01122.7818461538461942.5-0.5: 0.01119.4576923076922942.5-0.5: 0.01116.1335384615384942.5-0.5: 0.01113.0049230769232942.5-0.5: 0.01109.680769230769942.5-0.5: 0.01106.3566153846155942.5-0.6: 0.01103.0324615384616942.5-0.6: 0.01099.7083076923077942.5-0.6: 0.01096.3841538461538942.5-0.6: 0.01093.06942.5-0.6: 0.01089.735846153846942.5-0.6: 0.01086.4116923076922942.5-0.7: 0.01083.0875384615383942.5-0.7: 0.01079.7633846153844942.5-0.7: 0.01076.4392307692306942.5-0.7: 0.01073.115076923077942.5-0.7: 0.01069.790923076923942.5-0.7: 0.01066.4667692307694942.5-0.8: 0.01063.1426153846153942.5-0.8: 0.01059.8184615384614942.5-0.8: 0.01056.4943076923078942.5-0.8: 0.01053.1701538461539942.5-0.8: 0.01049.8459999999998942.5-0.8: 0.01046.7173846153844942.5-0.9: 0.01043.3932307692307942.5-0.9: 0.01040.0690769230769942.5-0.9: 0.01036.7449230769232942.5-0.9: 0.01033.420769230769942.5-0.9: 0.01030.0966153846152942.5-0.9: 0.01026.7724615384616942.5-1.0: 0.01023.4483076923077942.5-1.0: 0.01020.124153846154942.5-1.0: 0.01016.8942.5-2.0: 0.0821.2615384615385942.5-2.0: 0.0817.9373846153844942.5-2.0: 0.0814.6132307692308942.5-2.1: 0.0811.2890769230769942.5-2.1: 0.0807.964923076923942.5-2.1: 0.0804.6407692307691942.5-2.1: 0.0801.3166153846154942.5-2.1: 0.0797.9924615384614942.5-2.1: 0.0794.6683076923076942.5-2.2: 0.0791.344153846154942.5-2.2: 0.0788.2155384615385942.5-2.2: 0.0784.8913846153846942.5-2.2: 0.0781.5672307692308942.5-2.2: 0.0778.2430769230768942.5-2.2: 0.0774.9189230769231942.5-2.3: 0.0771.5947692307692942.5-2.3: 0.0768.2706153846153942.5-2.3: 0.0764.9464615384616942.5-2.3: 0.0761.6223076923076942.5-2.3: 0.0758.2981538461538942.5-2.3: 0.0754.9739999999999942.5-2.4: 0.0751.6498461538462942.5-2.4: 0.0748.3256923076923942.5-2.4: 0.0745.0015384615384942.5-2.4: 0.0741.6773846153847942.5-2.4: 0.0738.3532307692308942.5-2.4: 0.0735.0290769230769942.5-2.5: 0.0731.704923076923942.5-2.5: 0.0728.3807692307691942.5-2.5: 0.0725.0566153846154942.5-2.5: 0.0721.928942.5-2.5: 0.0718.6038461538461942.5-2.5: 0.0715.2796923076922942.5-2.6: 0.0711.9555384615384942.5-2.6: 0.0708.6313846153845942.5-2.6: 0.0705.3072307692307942.5-2.6: 0.0701.983076923077942.5-2.6: 0.0698.6589230769231942.5-2.6: 0.0695.3347692307692942.5-2.7: 0.0692.0106153846153942.5-2.7: 0.0688.6864615384616942.5-2.7: 0.0685.3623076923077942.5-2.7: 0.0682.0381538461538942.5-2.7: 0.0678.714942.5-2.7: 0.0675.3898461538462942.5-2.8: 0.0672.0656923076923942.5-2.8: 0.0668.7415384615384942.5-2.8: 0.0665.4173846153845942.5-2.8: 0.0662.0932307692307942.5-2.8: 0.0658.7690769230769942.5-2.8: 0.0655.6404615384615942.5-2.9: 0.0652.3163076923076942.5-2.9: 0.0648.9921538461539942.5-2.9: 0.0645.6679999999999942.5-2.9: 0.0642.3438461538461942.5-2.9: 0.0639.0196923076923942.5-2.9: 0.0635.6955384615385942.5-3.0: 0.0632.3713846153845942.5-3.0: 0.0629.0472307692307942.5-3.0: 0.0625.723076923077942.5-4.0: 0.0430.18461538461537942.5-4.0: 0.0423.53630769230773942.5-4.1: 0.0416.88800000000003942.5-4.1: 0.0410.2396923076923942.5-4.1: 0.0403.59138461538464942.5-4.2: 0.0397.1386153846155942.5-4.2: 0.0390.4903076923076942.5-4.2: 0.0383.842942.5-4.3: 0.0377.1936923076923942.5-4.3: 0.0370.5453846153847942.5-4.3: 0.0363.89707692307684942.5-4.4: 0.0357.2487692307692942.5-4.4: 0.0350.6004615384615942.5-4.4: 0.0343.9521538461539942.5-4.5: 0.0337.3038461538462942.5-4.5: 0.0330.8510769230769942.5-4.5: 0.0324.2027692307693942.5-4.6: 0.0317.5544615384616942.5-4.6: 0.0310.9061538461538942.5-4.6: 0.0304.2578461538461942.5-4.7: 0.0297.6095384615385942.5-4.7: 0.0290.96123076923084942.5-4.7: 0.0284.31292307692297942.5-4.8: 0.0277.66461538461533942.5-4.8: 0.0271.0163076923077942.5-4.8: 0.0264.56353846153837942.5-4.9: 0.0257.91523076923073942.5-4.9: 0.0251.2669230769231942.5-4.9: 0.0244.61861538461545942.5-5.0: 0.0237.97030769230778942.5-5.0: 0.0231.32199999999995942.5-5.1: 0.0224.6736923076923942.5-5.1: 0.0218.02538461538464942.5-5.1: 0.0211.37707692307697942.5-5.2: 0.0204.7287692307693942.5-5.2: 0.0198.27600000000004942.5-5.2: 0.0191.62769230769237942.5-5.3: 0.0184.9793846153847942.5-5.3: 0.0178.3310769230769942.5-5.3: 0.0171.68276923076925942.5-5.4: 0.0165.03446153846158942.5-5.4: 0.0158.38615384615395942.5-5.4: 0.0151.7378461538461942.5-5.5: 0.0145.08953846153847942.5-5.5: 0.0138.4412307692308942.5-5.5: 0.0131.9884615384615942.5-5.6: 0.0125.34015384615383942.5-5.6: 0.0118.69184615384619942.5-5.6: 0.0112.04353846153852942.5-5.7: 0.0105.39523076923088942.5-5.7: 0.098.74692307692305942.5-5.7: 0.092.0986153846154942.5-5.8: 0.085.45030769230773942.5-5.8: 0.078.80200000000008942.5-5.8: 0.072.15369230769225942.5-5.9: 0.065.70092307692313942.5-5.9: 0.059.05261538461548942.5-5.9: 0.052.404307692307654942.5-6.0: 0.045.75599999999999942.5-6.0: 0.039.10769230769234942.5Pole at s = -4-4.0: 0.0430.18461538461537942.5Pole at s = -2-2.0: 0.0821.2615384615385942.5Pole at s = -1-1.0: 0.01016.8942.5Pole at s = 00.0: 0.01212.3384615384614942.5Zero at s = -3-3.0: 0.0625.723076923077942.5Breakaway: s = -1.609, K = -0.66-1.6: 0.0897.717076923077942.5jω crossing: s = +1.588j, K = 9.650.0: 1.61212.3384615384614654.675jω crossing: s = -1.588j, K = 9.650.0: -1.61212.33846153846141230.325ζ/ωn Reference LinesRoot LocusReal-Axis LocusPoles (×)Zero (○)BreakawayStability Boundary→ increasing gain