Table 4.1 shows the experimentally measured frequency response of an open-loop process plant G(s). It is decided that a PI controller of the form K(s) = K (1+; - ( 1₁ + 7/²/3) Ts is to be used as the controller for this plant with K=1 and T=0.5. Freq (rad/s) Gain (dB) Phase (Deg) Table 4.1 0.04 0.08 0.1 0.2 0.4 0.8 0.01 0.02 -40.2 -40.8 -42.9 -49 -52.3 -65.8 -82.4 -100 -21.4 -42.1 -79.7 -135 -154 -204 -236 -252 1 -105 -256 a) Plot the Bode Diagram of the open-loop transfer function on the graph given in the next page. b) What are the Gain Margin and Phase Margin of the system? c) Determine the stability of the closed-loop system when K= 4.

EBK ELECTRICAL WIRING RESIDENTIAL
19th Edition
ISBN:9781337516549
Author:Simmons
Publisher:Simmons
Chapter29: Service-entrance Calculations
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Table 4.1 shows the experimentally measured frequency response of an open-loop process
plant G(s). It is decided that a PI controller of the form
K(s) = K (1 +;
K(1 + 7/1²)
Ts
is to be used as the controller for this plant with K=1 and T=0.5.
Table 4.1
Freq (rad/s)
0.04
0.08
0.1
0.2
0.4
0.01 0.02
-40.2 -40.8 -42.9
Gain (dB)
-49 -52.3 -65.8 -82.4
Phase (Deg) -21.4 -42.1 -79.7 -135 -154 -204 -236
0.8
-100
-252
1
-105
-256
a) Plot the Bode Diagram of the open-loop transfer function on the graph given in the next
page.
b) What are the Gain Margin and Phase Margin of the system?
c) Determine the stability of the closed-loop system when K= 4.
Transcribed Image Text:Table 4.1 shows the experimentally measured frequency response of an open-loop process plant G(s). It is decided that a PI controller of the form K(s) = K (1 +; K(1 + 7/1²) Ts is to be used as the controller for this plant with K=1 and T=0.5. Table 4.1 Freq (rad/s) 0.04 0.08 0.1 0.2 0.4 0.01 0.02 -40.2 -40.8 -42.9 Gain (dB) -49 -52.3 -65.8 -82.4 Phase (Deg) -21.4 -42.1 -79.7 -135 -154 -204 -236 0.8 -100 -252 1 -105 -256 a) Plot the Bode Diagram of the open-loop transfer function on the graph given in the next page. b) What are the Gain Margin and Phase Margin of the system? c) Determine the stability of the closed-loop system when K= 4.
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