# THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN - PowerPoint PPT Presentation

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THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN. 指導教授 : 曾 慶 耀 學 生 : 潘 維 剛. Outline. MATHEMATICAL MODEL MANUAL STEERING CRITERIA MANUAL STEERING MAP CONCLUSION. MATHEMATICAL MODEL.

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THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN

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## THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN

### Outline

• MATHEMATICAL MODEL

• MANUAL STEERING CRITERIA

• MANUAL STEERING MAP

• CONCLUSION

### MATHEMATICAL MODEL

• These are concerned with the phase of total forward path transfer function when its magnitude is unity , which for a stable close loop system must be algebraically greater than

-180 deg , so that if the phase is say -120 deg , then the

close loop system will be stable . Alternatively , if the phase

is less than -180 deg , say -210 deg , then the system is un- stable .

The magnitude of the ship plus steering engine transfer function (4) may be express in logarithmic

from as

and for an unstable system the phase can be written as

, so that

It can be seen that as long as L/U>10 , then from the

last equation , will be much small than and will not have a great effect on system .However when the reverse is true and L/U<10 , then the steering engine cause an increasing time lag which can greatly detract from the manual handlng ability of the ship.

• The steady state solution of the yaw rate equation (3) is simply found by ignoring the time derivatives of r ,

so that r=

Large yaw rates and rudder angles in reality the steady

state behavior is non-linear . This may be represented

here by the inclusion of a cubic term , so that

The loop width can be found by differentiating equation

(7) respect to r and setting the right hand side to zero ,

Then the loop width can be shown to be

Now for all the family of ships examined by Nomoto,

, so that in this case we can eliminate

From the last expression yield

### CONCLUSION

• This paper suggests lower limiting values of spiral loop width , which are considered to be satisfactory. The designer should be aware of this solution , until IMO amend their criterion value.