The manual steering criterion based upon phase margin
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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

THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN

指導教授:曾 慶 耀學 生:潘 維 剛


Outline

Outline

  • MATHEMATICAL MODEL

  • MANUAL STEERING CRITERIA

  • MANUAL STEERING MAP

  • CONCLUSION


Mathematical model

MATHEMATICAL MODEL


The manual steering criterion based upon phase margin

  • 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 manual steering criterion based upon phase margin

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


The manual steering criterion based upon phase margin

, 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 manual steering criterion based upon phase margin

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

    so that r=


The manual steering criterion based upon phase margin

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 manual steering criterion based upon phase margin

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


The manual steering criterion based upon phase margin

Now for all the family of ships examined by Nomoto,

, so that in this case we can eliminate

From the last expression yield


Manual steering criteria

MANUAL STEERING CRITERIA


Manual steering map

MANUAL STEERING MAP


Conclusion

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.


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