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LM628 Datasheet(PDF) 10 Page  National Semiconductor (TI) 


LM628 Datasheet(HTML) 10 Page  National Semiconductor (TI) 
10 / 24 page Theory of Operation (Continued) tion goes undetected, and the impeding force on the motor is subsequently released, the motor could reach a very high velocity in order to catch up to the desired position (which is still advancing as specified). This condition is easily de tected; see commands LPEI and LPES. All trajectory parameters are 32bit values. Position is a signed quantity. Acceleration and velocity are specified as 16bit, positiveonly integers having 16bit fractions. The in teger portion of velocity specifies how many counts per sam pling interval the motor will traverse. The fractional portion designates an additional fractional count per sampling inter val. Although the position resolution of the LM628 is limited to integer counts, the fractional counts provide increased av erage velocity resolution. Acceleration is treated in the same manner. Each sampling interval the commanded accelera tion value is added to the current desired velocity to generate a new desired velocity (unless the command velocity has been reached). One determines the trajectory parameters for a desired move as follows. If, for example, one has a 500line shaft en coder, desires that the motor accelerate at one revolution per second per second until it is moving at 600 rpm, and then de celerate to a stop at a position exactly 100 revolutions from the start, one would calculate the trajectory parameters as follows: let P = target position (units = encoder counts) let R = encoder lines * 4 (system resolution) then R = 500 * 4 = 2000 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 * 341E6 * 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 mul tiplied by 65,536 (as shown) to adjust for the required integer/fraction format of the input data. Note that after scal ing 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 9. 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 inte gral of the error, plus the derivative of the error. The following discretetime equation illustrates the control performed by the LM628: (1) where u(n) is the motor control signal output at sample time n, e(n) is the position error at sample time n, n' indi cates sampling at the derivative sampling rate, and kp, ki, and kd are the discretetime filter parameters loaded by the users. 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 en sures that the static position error is zero. If there is a con stant torque loading, the motor will still be able to achieve zero position error. The third term, the derivative term, provides a force propor tional 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 userselectable; this capability enables the LM628 to control a wider range of in ertial loads (system mechanical time constants) by providing a better approximation of the continuous derivative. In gen eral, longer sampling intervals are useful for lowvelocity op erations. In operation, the filter algorithm receives a 16bit error signal from the loop summingjunction. The error signal is saturated at 16 bits to ensure predictable behavior. In addition to being multiplied by filter coefficient kp, the error signal is added to an accumulation of previous errors (to form the integral sig nal) and, at a rate determined by the chosen derivative sam pling interval, the previous error is subtracted from it (to form the derivative signal). All filter multiplications are 16bit op erations; only the bottom 16 bits of the product are used. The integral signal is maintained to 24 bits, but only the top 16 bits are used. This scaling technique results in a more us able (less sensitive) range of coefficient ki values. The 16 bits are rightshifted eight positions and multiplied by filter coefficient ki to form the term which contributes to the motor control output. The absolute magnitude of this product is compared to coefficient il, and the lesser, appropriately signed magnitude then contributes to the motor control sig nal. The derivative signal is multiplied by coefficient kd each de rivative sampling interval. This product contributes to the mo tor control output every sample interval, independent of the userchosen derivative sampling interval. The kp, limited ki, and kd product terms are summed to form a 16bit quantity. Depending on the output mode (wordsize), either the top 8 or top 12 bits become the motor control out put signal. www.national.com 10 
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