2. A system has a plant transfer function G(s) and is controlled via a proportional feedback controller with gain k. G(s) = = 2 (s+ 5)(s² +0.16s + 0.64)* 1 (a) The Nyquist plot for this system is shown here. Estimate the gain/phase margins. Real Axis -0.2 -0.4 Imaginary Axis 3 2 0 -2 -3 Nyquist Diagram 8 + -4 -2 -1.5 -1 -0.5 0.4 0.2 0 0 Real Axis 0.5 1 1.5 2 Figure 2: Nyquist plot of G(s) in Problem 2. -0.971 -0.218j -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 Imaginary Axis Figure 3: Nyquist plot of G(s) showing the unit circle and real axis crossings in Problem 2. (b) What range of values of k is required for closed loop stability? Explain this from the definition of Gain Margin.
2. A system has a plant transfer function G(s) and is controlled via a proportional feedback controller with gain k. G(s) = = 2 (s+ 5)(s² +0.16s + 0.64)* 1 (a) The Nyquist plot for this system is shown here. Estimate the gain/phase margins. Real Axis -0.2 -0.4 Imaginary Axis 3 2 0 -2 -3 Nyquist Diagram 8 + -4 -2 -1.5 -1 -0.5 0.4 0.2 0 0 Real Axis 0.5 1 1.5 2 Figure 2: Nyquist plot of G(s) in Problem 2. -0.971 -0.218j -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 Imaginary Axis Figure 3: Nyquist plot of G(s) showing the unit circle and real axis crossings in Problem 2. (b) What range of values of k is required for closed loop stability? Explain this from the definition of Gain Margin.
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Hi there, I need help with this control systems question.
Transcribed Image Text:2. A system has a plant transfer function G(s) and is controlled via a proportional feedback controller
with gain k.
G(s) =
=
2
(s+ 5)(s² +0.16s + 0.64)*
1
(a) The Nyquist plot for this system is shown here. Estimate the gain/phase margins.
Real Axis
-0.2
-0.4
Imaginary Axis
3
2
0
-2
-3
Nyquist Diagram
8
+
-4
-2
-1.5
-1
-0.5
0.4
0.2
0
0
Real Axis
0.5
1
1.5
2
Figure 2: Nyquist plot of G(s) in Problem 2.
-0.971 -0.218j
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
Imaginary Axis
Figure 3: Nyquist plot of G(s) showing the unit circle and real axis crossings in Problem 2.
(b) What range of values of k is required for closed loop stability? Explain this from the definition
of Gain Margin.
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