3. Consider the following three bode diagrams in Figure 1. Answer the questions for each one....

 

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3. Consider the following three bode diagrams in Figure 1. Answer the questions for each one. Note that I have also uploaded "bodel.fig", "bode2.fig", and "bode3.fig" so that you can load the plots and get precise numbers. (a) What is the transfer function? (Your answers don't have to be exact, but they should be justified) (b) If this were the open-loop transfer function, what is the gain and phase margin? Is the system stable in closed-loop? (c) If the system is stable in closed-loop, is there a steady-state error in response to a step input? If there is a steady state error, what is it? Phase (deg) Magnitude (decibles) -50 100 50 -100 10 10 10-1 -80 -100 -120 -140 -160 -180 103 10 10-1 Phase (deg) 10 Frequency (rad/sec 10 Frequency (rad/sec (a) Bodel Magnitude (decibles) -80 -60 8 88 -40 -20 -50 -100 -150 -100 0 Magnitude (decibles) 40 30 20 10 102 103 10 10 10 10 102 Frequency (rad/sec 10 Phase (deg) 100 50 0 -50 -100 -150 101 -200 102 10 102 10-1 10 Frequency (rad/sec 101 102 103 (b) Bode2 10-1 10 101 Frequency (rad/sec 102 -200 10-1 10 10 102 Frequency (rad/sec (c) Bode3 Figure 1: Bode diagrams 3. Consider the following three bode diagrams in Figure 1. Answer the questions for each one. Note that I have also uploaded "bodel.fig", "bode2.fig", and "bode3.fig" so that you can load the plots and get precise numbers. (a) What is the transfer function? (Your answers don't have to be exact, but they should be justified) (b) If this were the open-loop transfer function, what is the gain and phase margin? Is the system stable in closed-loop? (c) If the system is stable in closed-loop, is there a steady-state error in response to a step input? If there is a steady state error, what is it? Phase (deg) Magnitude (decibles) -50 100 50 -100 10 10 10-1 -80 -100 -120 -140 -160 -180 103 10 10-1 Phase (deg) 10 Frequency (rad/sec 10 Frequency (rad/sec (a) Bodel Magnitude (decibles) -80 -60 8 88 -40 -20 -50 -100 -150 -100 0 Magnitude (decibles) 40 30 20 10 102 103 10 10 10 10 102 Frequency (rad/sec 10 Phase (deg) 100 50 0 -50 -100 -150 101 -200 102 10 102 10-1 10 Frequency (rad/sec 101 102 103 (b) Bode2 10-1 10 101 Frequency (rad/sec 102 -200 10-1 10 10 102 Frequency (rad/sec (c) Bode3 Figure 1: Bode diagrams