Transcript m (s+1)^2 L = ------------------ m=0.4 (instabile) , 0.625 (stabile) s^3

 m (s+1)^2 L = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ s^3 1
m=0.4 (instabile) , 0.625 (stabile) Nyquist Diagram
104
0.8
L04
L065
L05
0.6
Imaginary Axis
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-700
-600
-500
-400
-300
-200
-100
0
100
Real Axis
Nyquist Diagram
Imaginary Axis
1
L04
L065
L05
0.8
System: L04
0.6 (deg): -6.21
Phase Margin
Delay Margin (sec): 6.88
0.4
At frequency (rad/s): 0.897
Closed loop
0.2 stable? No
System: L04
Gain Margin (dB): 1.94
At frequency (rad/s): 1
Closed loop stable? No
0
System: L065
-0.2 -2.28
Gain Margin (dB):
At frequency (rad/s): 1
-0.4
Closed loop stable? Yes
System: L065
Phase Margin (deg): 7.76
Delay Margin (sec): 0.118
At frequency (rad/s): 1.15
Closed loop stable? Yes
-0.6
-0.8
-1
-1.5
-1
-0.5
Real Axis
daspect([1 1 1]) 0
Bode Diagram
Magnitude (dB)
50
0
-50
-90
Phase (deg)
System: L
Gain Margin (dB): -1.94
At frequency (rad/s): 1
Closed loop stable? Yes
System: L
Gain Margin (dB): 1.94
At frequency (rad/s): 1
Closed loop stable? No
-135
System: L
Phase Margin (deg): 6.57
Delay Margin (sec): 0.102
At frequency (rad/s): 1.12
Closed loop stable? Yes
-180
-225
-270
10-2
System: L
Phase Margin (deg): -6.21
Delay Margin (sec): 6.88
At frequency (rad/s): 0.897
Closed loop
10-1stable? No
100
101
102
Frequency (rad/s)
0.4 (s+1)^2 F = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (s+0.4778) (s^2 ‐ 0.0778s + 0.8372) 0.625 (s+1)^2 F = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (s+0.5224) (s^2 + 0.1026s + 1.196) stabile con margine di guadagno < 0 -1
Imaginary Axis (seconds )
instabile con margine di guadagno > 0 0.5 (s+1)^2 F = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (s+0.5) (s^2 + 1)