Control systems Control systems page #21 Control systems page #22 Control systems page #23 Control...

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Control systems Control systems page #21 Control systems page #22 Control systems page #23 Control systems page #24

Robert · Accepted Answer

Solution: It is used for gain
Solution: Pi is used for improvent in transient response. 
Derivative is used for steady state improvement.
Solution: 
P= 10^1= 10 
D= 10^1=10 
Assuming gain at w=0.01 is 50 dB. 
I= 316.22/100=3.2
A) Error ratio: It is defined as the ratio of closed loop error magnitude to open loop error magnitude. 
   
 
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b) Deviation ratio: It is defined as the ratio of magnitude of closed loop error to magnitude setpoint. 
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c) It is point where error first crosses the 0 dB line.  
In this case it is approx 22 rad. 
d) Gain margin = 6 dB ( Negative of gain at phase -180 degree.) 
e) Phase Margin= 40 degree( phase angle  where gain is 0 dB+ 180) 
f)  From the Nyquist plot we can say that both phase and gain margin of the system is positive and 
hence it is satble. 
g)  gain Margin is the line drawn on -180 degree line.= 1/0.5=2 = 6 dB 
Phase margin is line which crosses origin and crossing of plot on unit circle.
Solution:  
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b) 
for K=35 
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c) Damping Ratio=  1 as poles is at real axis. 
d) It is critically damped.
Solution:
Solution:

Control systems Control systems page #21 Control systems page #22 Control systems page #23 Control systems page #24

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