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Techno Linear Motion Catalog 38 Technical Information at all velocity changes.  Parabolic changes in velocity take advantage of the torque versus speed characteristics of stepper motors.  Acceleration during a velocity increase is highest at the beginning of the change, when the torque output of the motor is at its peak (see Figure 2).  Since acceleration is proportional to torque, this situation is optimal. Trapezoidal profiles require high accelerations at all points, even when the torque output of the stepper motor is at a minimum (see Figure 3), and thus should be avoided.  Parabolic changes provide a smooth transition from one point to the next, holding dynamic shock or change of acceleration, to a minimum.  Trapezoidal profiles, in contrast, introduce large changes in acceleration, i.e. shock, two times at points in the velocity profile where torque is relatively low, making the motor susceptible to stalling (see Figure 3).  Parabolic velocity control is especially effective when producing arc sections because arcs require constantly changing acceleration.  Techno stepper motor controllers have been designed to minimize the possibility of dynamic shock during program execution by incorporating parabolic ramping functions into the control electronics. Servo Control (closed loop):  The presence of a feedback mechanism is what provides the signal checking, creating a closed control loop.  Feedback is most often found in the form or position feedback, supplied from a rotary optical encoder.  Even with the presence of a comparison routine, several methods must be employed to overcome system errors. Proportional gain is a technique that supplies a correction force proportional to the magnitude of the detected position error.  This adjustment puts the system back to close to the desired state, but is incapable by itself of fully correcting deviations.  Integral gain is used to measure and cumulate position errors (steady state errors) so that a restoring force proportional to the cumulative position error can be applied to the system.  A larger cumulative error results in a larger restoring force, and the system becomes more accurately corrected.  Differential gain is a method that utilizes the time rate of change of the position feedback information and compares it to the desired velocity.  A restoring force proportional to the difference of velocities will act to minimize deviations from actual and desired velocity rates.  These concepts are designed into a PID (Proportional, Integral, Differential) chip on the controller card.  The Techno Servo Controller Card utilizes all three types of system correcting techniques, providing PID control. A  second  factor  to  be  aware  of  when choosing a servo controller is the degree to which the system is damped.  There are three different scenarios to consider with  respect  to  damping,  as  shown below. An     underdamped     system     will overshoot its destination, then oscillate back and forth about its desired state. This  causes  large  inaccuracies  and vibrations, which should be avoided. A critically damped system is provided with   enough   motion   damping   to overshoot  the  target  one  time,  then asymptotically  approach  the  steady state.  This is preferred in theory, but it is a difficult state to maintain in reality. An overdamped system will take a very long time to reach the desired position, asymptotically  reaching  the  desired state  without  position  overshoot.  This will tend to put a higher burden on the driving motors. Underdamped Critically Damped Overdamped