33970 datasheet(24/36 Pages) FREESCALE

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Analog Integrated Circuit Device Data

Freescale Semiconductor

33970

FUNCTIONAL DEVICE OPERATION

LOGIC COMMANDS AND REGISTERS

The motor is stepped by providing index commands at

intervals. The time between steps defines the motor velocity,

and the changing time defines the motor acceleration.

The state machine uses a table to define the allowed time

and also the maximum velocity. A useful side effect of the

table is that it also allows the direct determination of the

position at which the velocity should reduce to allow the

motor to stop at the desired position.

The motor equations of motion are generated as follows.

(The units of position are steps, and velocity and acceleration

are in steps/second and steps/second².)

From an initial position of 0 with an initial velocity (u), the

motor position (s) at a time (t) is:

For unit steps, the time between steps is:

This defines the time increment between steps when the

motor is initially travelling at a velocity u. In the ROM, this time

is quantized to multiples of the system clock by rounding

upwards, ensuring acceleration never exceeds the allowed

value. The actual velocity and acceleration is calculated from

the time step actually used.

Using

v2 = u2 + 2as

and

v = u + at

and solving for v in terms of u, s, and t gives:

v =

t - u

The correct value of t to use in this equation is the

quantized value obtained above.

From these equations a set of recursive equations can be

generated to give the allowed time step between motor

indexes when the motor is accelerating from a stop to its

maximum velocity.

Starting from a position p of 0 and a velocity v of 0, these

equations define the time interval between steps at each

position. To drive the motor at maximum performance, index

commands are given to the motor at these intervals. A table

is generated giving the time step

∆t at an index position n.

where

indicates rounding up.

Pn = n

Note Pn = n. This means on the nth step the motor has

indexed by n positions and has been accelerating steadily at

the maximum allowed rate. This is critical because it also

indicates the minimum distance the motor must travel while

decelerating to a stop. For example, the stopping distance is

also equal to the current value of n.

The algorithm of pointer movement can be summarized in

two steps:

1. The pointer is at the previously commanded position

and is not moving.

2. A command to move to a pointer position (other than

the current position) has been received. Timed index

pulses are sent to the motor driver at an ever-

increasing rate, according to the time steps in

Table 21, until:

a. The maximum velocity (default or selected) is

reached after which the step time intervals will no

longer decrease; or,

b. The distance in steps that remain to travel are less

than the current step time index value. The motor

then decelerates by increasing the step times

according to Table 21 until the commanded position

is reached. The state machine controls the

deceleration so that the pointer reaches the

commanded position efficiently.

An example of the velocity table for a particular motor is

provided in Table 21. This motor’s maximum speed is

4800 microsteps/s (at 12 microsteps/degrees), and its

maximum acceleration is 54000 microsteps/s2. The table is

quantized to a 1.0 MHz clock.

* Denotes normalized values.

Table 20. Coil Step Value

1 at

−

⇒

⎥

⎤

⎢

⎡

−

∆

−

⎡⎤

−

∆

Table 21. Velocity Table

Velocity

Position

Time Between

Steps (

µs)

Velocity

(

µSteps/s)

Velocity

Position

Time Between

Steps (

µs)

Velocity

(

µSteps/s)

Velocity

Position

Time Between

Steps (

µs)

Velocity

(

µSteps/s)

0.00

380

2631.6

152

257

3891.1

27217

36.7

377

2652.5

153

256

3906.3

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