Prévia do material em texto

Problem 6.39PP
The steering dynamics of a ship are represented by the transfer function
V js ) ^ ^ n - ( j / 0 . 1 4 2 ) + l ]
S f(s ) f ( j /0 .3 2 5 + l)(5 /0 .0 3 6 2 + l ) ’
where V is the ship’s iaterai veiocity in meters per second, and 5r is the rudder angle in radians, 
(a) Use the Matlab command bode to plot the log magnitude and phase of G( jo)) for K = 0.2.
(b) On your plot, indicate the crossover frequency. PM, and GM.
(c) Is the ship-steering system stable with K = 0.2?
(c) Is the ship-steering system stable with K = 0.2?
(d) What value of K would yield a PM of 30*. and what would the crossover frequency be?
Step-by-step solution
step 1 of 4
G (s)=-
K - f —^ l + l l
. U .1 4 2 J J
UO.325 A o.0362 )
Step 2 of 4
b. |g M = -5 .a jg 1 at m = 0 .0 5 7 6 ra i/ sec 
\PM = -2 3 . r \ at » = 0.087 n jrf/sw
Step 3 of 4
c. No , ship steeling system is not stable
Step 4 of 4
A At PAf = 30* ® = 0.0318raA/s»c 
|Aad K = 0.042|