Esercizi di Controlli Automatici: Bode

Esercizi di Controlli Automatici 3Esercizio 6 (F = zpk([], [2], 1);)F(s) = 1s − 2 = −1 12 s(−1/2) + 10Bode Diagram1Nyquist Diagram−100.8Magnitude (dB)−20−30−40−50 90(s(−1/2)+1) −1FImaginary Axis0.60.40.20−0.2Phase (deg)0−90−0.4−0.6−0.8−18010 −1 10 0 10 1 10 2Frequency (rad/sec)−1−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0Real AxisEsercizio 7 (F = zpk([10], [0], 1);)F(s) = s − 10 = −10 s(−0.1) + 1ss60Bode Diagram20Nyquist DiagramMagnitude (dB)40200−20−40−60 360270s(−0.1)+11/sFImaginary Axis151050−5System: FReal: 1Imag: 11.1Frequency (rad/sec): 0.966Phase (deg)180900−10−15System: FReal: 1Imag: −9.75Frequency (rad/sec): −1.1−9010 −1 10 0 10 1 10 2 10 3Frequency (rad/sec)−20−1 −0.5 0 0.5 1 1.5Real AxisEsercizio 8 (F = zpk([−2], [−0.1 − 10 − 10], 1);)s + 2F(s) =(s + 0.1)(s + 10) 2 = 2 s(1/2) + 110 (s10 + 1)(s0.1 + 1) 2100Bode Diagram0.1Nyquist DiagramMagnitude (dB)500−500.080.060.04System: FReal: 0.155Imag: 0.0816Frequency (rad/sec): −0.0625Phase (deg)−100−150 900−90s/2+1(10s+1) −1(s/10+1) −2FImaginary Axis0.020−0.02−0.04−0.06−0.08System: FReal: 0.169Imag: −0.0707Frequency (rad/sec): 0.0464−18010 −3 10 −2 10 −1 10 0 10 1 10 2 10 3Frequency (rad/sec)−0.10 0.05 0.1 0.15 0.2Real Axis