THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN

1. THE MANUAL STEERING CRITERION BASED UPON PHASE MARGIN 指導教授:曾 慶 耀學 生:潘 維 剛

2. Outline • MATHEMATICAL MODEL • MANUAL STEERING CRITERIA • MANUAL STEERING MAP • CONCLUSION

3. MATHEMATICAL MODEL

4. 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 .

5. 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

6. , 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.

7. The steady state solution of the yaw rate equation (3) is simply found by ignoring the time derivatives of r , so that r=

8. 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

9. 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

10. Now for all the family of ships examined by Nomoto, , so that in this case we can eliminate From the last expression yield

11. MANUAL STEERING CRITERIA

13. MANUAL STEERING MAP

16. 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.