Consider the plant transfer function subject to a controller Magnitude (dB) K C(s) = s(s+2) and a negative unity feedback. The Bode diagram of C(s)G(s) for K = 2 is provided in Figure 1 Phase (deg) 0 -20 -40 -60 -80 -100 -90 -135 -180 -225 -270 G(s) = 10-1 5 8+5 10 Bode Diagram 10. Frequency (rad/s) Figure 1: Bode diagram of C(s)G(s) for K = 2. 10 (a) (10 points) Using the information provided in Figure, please show that the Nyquist plot of the system C(s)G(s) will not encircle the point -1 on the complex plane. (b) (10 points) Using the information provided in Figure calculate the gain K needed so that the Nyquist plot of the system C(s)G(s) will touch the point -1 on the complex plane. (c) (10 points) In the Nyquist plot of the system C(s)G(s), a singularity issue due to s = 0 will arise. Please sketch the Nyquist plot and fix the singularity issue so that the plot is complete when s 0. Consider the plant transfer function subject to a controller Magnitude (dB) K C(s) = s(s+2) and a negative unity feedback. The Bode diagram of C(s)G(s) for K = 2 is provided in Figure 1 Phase (deg) 0 -20 -40 -60 -80 -100 -90 -135 -180 -225 -270 G(s) = 10-1 5 8+5 10 Bode Diagram 10. Frequency (rad/s) Figure 1: Bode diagram of C(s)G(s) for K = 2. 10 (a) (10 points) Using the information provided in Figure, please show that the Nyquist plot of the system C(s)G(s) will not encircle the point -1 on the complex plane. (b) (10 points) Using the information provided in Figure calculate the gain K needed so that the Nyquist plot of the system C(s)G(s) will touch the point -1 on the complex plane. (c) (10 points) In the Nyquist plot of the system C(s)G(s), a singularity issue due to s = 0 will arise. Please sketch the Nyquist plot and fix the singularity issue so that the plot is complete when s 0.