Question

Figure 1 shows the Bode diagrams of a linear system. a.) Identify the type, N, of this system. b.) Identify the crossover frequency wa, and the gain margin a in decibels. c.) Identify the crossover frequency um, and the phase margin γ in degrees.

Y values are in the above graph are the same as the lower graph.

Answer 1

Given plots (Rough sketch for understanding gamma = 0.16 rad/sec a = 0.5 rad/sec \r\n (a) From above plot The system From law free, the magnitude plot has NO Slope charge (constant upto cross ener freq) Therefore The system is type '0' system (b) From plot, Phase Cross ener freq w_pc = 0.5 rad/sec (The phase crossing -180 degrees) Therefore Gain margin G.M = 10 dB From plot (at w_pc) i, e Therefore w_alpha = 0.5 rad/sec, alpha = 10 dB (C) gain Cross ener freq w_gc = 0.16(approx) (The magnitude crossing phi dB line) phase at w_gc, phi_gc = -210 degrees Therefore phase margin gamma = 180 + phi_gc = 180 - 210 = -30 degrees Therefore W_gamma = 0.16 rad/s gamma = -30 degrees