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# A Squaring Method for Nonlinear Shaping

IP.com Disclosure Number: IPCOM000093570D
Original Publication Date: 1967-Nov-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 2 page(s) / 36K

IBM

## Related People

Wilford, CR: AUTHOR

## Abstract

The circuitry digitally squares the velocity feedback signal in a bang-bang servosystem. Squaring the velocity and comparing to the position error provides the near optimum switchover time from acceleration to deceleration to bring the system to rest at the desired position in the shortest time.

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A Squaring Method for Nonlinear Shaping

The circuitry digitally squares the velocity feedback signal in a bang-bang servosystem. Squaring the velocity and comparing to the position error provides the near optimum switchover time from acceleration to deceleration to bring the system to rest at the desired position in the shortest time.

A transducer, not shown, is to be positioned at a desired track. The address of the desired track is inserted in desired position register 10. Periodically, the present position of the transducer is sampled and its address is inserted in present position register 11. The difference between the two is obtained by subtraction circuit 12. If the difference is nonzero, the output of circuit 12 causes the servosystem to drive the transducer in the direction to reduce the position error. The magnitude of the difference comprises the position error.

The square of the velocity is to be compared to the position error to drive the servo. The digital square of the velocity is added to the sampled present position in register 10, thus effectually being subtracted from the position error by subtractor 12.

The digital squaring is also accomplished on a sampled basis. A tachometer continuously supplies at input 13 a voltage proportional to the instantaneous velocity of the transducer. A sampling pulse at input 14 operates pulse generator
15. The latter provides an output pulse 16 having a duration d proportional to the velocity voltage from input...