1. The Nyquist plot of a transfer function G(s) is shown in Figure 1. (a) Suppose G has two unstable open loop poles. When G(s) is placed in a unity feedback loop, is the closed loop system stable or unstable? Explain. (b) Suppose G has one unstable open loop pole. When G(s) is placed in a unity feedback loop, is the closed loop system stable or unstable? Explain. Imaginary Axis 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 1 Nyquist Diagram -1 -2 -1.5 -0.5 0 0.5 Real Axis Figure 1: Nyquist plot for Problem 1.

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1. The Nyquist plot of a transfer function G(s) is shown in Figure 1.
(a) Suppose G has two unstable open loop poles. When G(s) is placed in a unity feedback loop,
is the closed loop system stable or unstable? Explain.
(b) Suppose G has one unstable open loop pole. When G(s) is placed in a unity feedback loop, is
the closed loop system stable or unstable? Explain.
Imaginary
Axis
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
1
Nyquist Diagram
-1
-2
-1.5
-0.5
0
0.5
Real Axis
Figure 1: Nyquist plot for Problem 1.
Transcribed Image Text:1. The Nyquist plot of a transfer function G(s) is shown in Figure 1. (a) Suppose G has two unstable open loop poles. When G(s) is placed in a unity feedback loop, is the closed loop system stable or unstable? Explain. (b) Suppose G has one unstable open loop pole. When G(s) is placed in a unity feedback loop, is the closed loop system stable or unstable? Explain. Imaginary Axis 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 1 Nyquist Diagram -1 -2 -1.5 -0.5 0 0.5 Real Axis Figure 1: Nyquist plot for Problem 1.
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