- Root Locus Plotting Given Below Are Open Loop System Transfer Functions That Include An Adjustable Gain K Plot Suitable 1 (290.78 KiB) Viewed 56 times
- Root Locus Plotting Given Below Are Open Loop System Transfer Functions That Include An Adjustable Gain K Plot Suitable 2 (235.63 KiB) Viewed 56 times
- Root Locus Plotting Given Below Are Open Loop System Transfer Functions That Include An Adjustable Gain K Plot Suitable 3 (246.52 KiB) Viewed 56 times
- Root Locus Plotting Given Below Are Open Loop System Transfer Functions That Include An Adjustable Gain K Plot Suitable 4 (244.12 KiB) Viewed 56 times
Root Locus plotting Given below are open loop system transfer functions that include an adjustable gain K. Plot suitable Root Locus diagrams such that closed loop performance may be evaluated. 1) G(s) = What value of gain K would result in a system with a second order dominant response with an overshoot of 25%? At this value, what are the rise time and settling time of the system? 2) K s(s+4)(s+11) 3) G(s) = Is it possible to increase the gain sufficiently to make this system unstable? What is the fastest possible rise time that may be achieved by adjusting K? K(s² +12s+49) (s +3s+5)(s+10) G(s) = K(s+10) s(s+6) Think!
Asymptotes at ±/3 rad, intersecting axis at s--5 Breakaway point is s= -1.78 Intersect on imag axis at s=±6.6j Imaginary Axis (seconds) 20 -30 580 BRO Root Locus Real Axis (seconds) Fot 25% overshoot, 0.4, therefore, on s' plane angle o subtended at origin = 66° Using plotted information, such a line intersects the locus at s-1.33+3.05) (values for hand drawn graph will be very approximate) Plotting vector magnitudes gives K=137 From imaginary value, rise time tr = n/20 - 0.5 18 From real value, settling time ts=-3/o = 2.25s
2) Asymptotes at an angle ±, ±3à etc .......explain! Intersect at s=-1 No breakaway point No intesection of imaginary axis Imag Axis Angle of departure from complex poles = +105.1 degrees Angle of arrival at complex zeros = +60.1 degrees 10 8 6 St N -4 -6 00 -10 -15 N 11 10 THING INS M Real Axis The locus does not cross into the right hand side of the "s" plane, therfore, it does not exhibit unstable behaviour. The highest rise time may be calculated from the maximum imaginary value that may be achieved: max imaginary value = 4.Sj hence min rise time tran/20-0.35s
Imag Axis 10 5 -5 -20 E 5 13 LI 12 -15 an -10 Real Axis in LE 11 # 1.3 HE LE LI 11 ELE FE -5 5