LM628, LM629

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SNVS781C – JUNE 1999 – REVISED MARCH 2013

and

P = 2000 * desired number of revolutions

P = 2000 * 100 revs = 200,000 counts (value to load)

P (coding) = 00030D40 (hex code written to LM628)

let

V = velocity (units = counts/sample)

let

T = sample time (seconds) = 341

μs (with 6 MHz clock)

let

C = conversion factor = 1 minute/60 seconds

then V = R * T * C * desired rpm

and

V = 2000 * 341E

−6 * 1/60 * 600 rpm

V = 6.82 counts/sample

V (scaled) = 6.82 * 65,536 = 446,955.52

V (rounded) = 446,956 (value to load)

V (coding) = 0006D1EC (hex code written to LM628)

let

A = acceleration (units = counts/sample/sample)

A = R * T * T * desired acceleration (rev/sec/sec)

then A = 2000 * 341E

−6 * 341E-6 * 1 rev/sec/sec

and

A = 2.33E

−4 counts/sample/sample

A (scaled) = 2.33E

−4 * 65,536 = 15.24

A (rounded) = 15 (value to load)

A (coding) = 0000000F (hex code written to LM628)

The above position, velocity, and acceleration values must be converted to binary codes to be loaded into the

LM628. The values shown for velocity and acceleration must be multiplied by 65,536 (as shown) to adjust for the

required integer/fraction format of the input data. Note that after scaling the velocity and acceleration values,

literal fractional data cannot be loaded; the data must be rounded and converted to binary. The factor of four

increase in system resolution is due to the method used to decode the quadrature encoder signals, see

Figure 10.

PID COMPENSATION FILTER

The LM628 uses a digital Proportional Integral Derivative (PID) filter to compensate the control loop. The motor is

held at the desired position by applying a restoring force to the motor that is proportional to the position error,

plus the integral of the error, plus the derivative of the error. The following discrete-time equation illustrates the

control performed by the LM628:

where

•

u(n) is the motor control signal output at sample time n, e(n) is the position error at sample time n, n

′ indicates

sampling at the derivative sampling rate, and kp, ki, and kd are the discrete-time filter parameters loaded by

the users.

(1)

The first term, the proportional term, provides a restoring force porportional to the position error, just as does a

spring obeying Hooke's law. The second term, the integration term, provides a restoring force that grows with

time, and thus ensures that the static position error is zero. If there is a constant torque loading, the motor will

still be able to achieve zero position error.

The third term, the derivative term, provides a force proportional to the rate of change of position error. It acts

just like viscous damping in a damped spring and mass system (like a shock absorber in an automobile). The

sampling interval associated with the derivative term is user-selectable; this capability enables the LM628 to

control a wider range of inertial loads (system mechanical time constants) by providing a better approximation of

the continuous derivative. In general, longer sampling intervals are useful for low-velocity operations.

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