These two figures are both examples of velocity profiles that can be implemented using the FlexMotion hardware and software. In the first example, the motor simply accelerates to a target velocity at a specified acceleration, runs at the target velocity, and then decelerates after a certain amount of time. In the second example, the motor accelerates to a certain velocity, runs at that target velocity for a period of time, accelerates to a higher velocity, then travels at that velocity for a period of time, and then decelerates to zero.

National Instruments - Fundamentals of Motion Control

http://zone.ni.com/devzone/cda/tut/p/id/3367

In this paper an approach is proposed for velocity profile control of an AC motor. The dynamic control algorithms for calculation and estimation of the S-curve profile adapt in real time to variations in system behavior to improve their performance.

The S-curve velocity profile is similar to trapezoidal, and in this case, trapezium sides are replaced by S-curves, which enables smoother velocity transitions in acceleration and deceleration periods [1, 9].

The first order trapezoidal velocity profile is a typical point-to-point move. An

axis accelerates from rest to a given velocity at a constant rate. Then traverses, or slews, to a certain point where it decelerates at a constant rate until finally, the end position is reached and the axis will come to a rest. Sometimes the slew velocity and the end position can be changed on the fly. The S-curve velocity profile can be represented as a second-order polynomial in velocity. We have an extra term here – jerk (jerk is a derivative of acceleration and a measure of impact). The second order S-curve provides complete flexibility in the control of profiles for smoothing motion and eliminating jerk from mechanical systems. The degree of S-curve on a motion

profile is controlled by separate acceleration and deceleration smoothing (jerk-limit) factors.

National Instruments - Fundamentals of Motion Control

http://zone.ni.com/devzone/cda/tut/p/id/3367

**Creation of velocity profile using s-curves**In this paper an approach is proposed for velocity profile control of an AC motor. The dynamic control algorithms for calculation and estimation of the S-curve profile adapt in real time to variations in system behavior to improve their performance.

The S-curve velocity profile is similar to trapezoidal, and in this case, trapezium sides are replaced by S-curves, which enables smoother velocity transitions in acceleration and deceleration periods [1, 9].

The first order trapezoidal velocity profile is a typical point-to-point move. An

axis accelerates from rest to a given velocity at a constant rate. Then traverses, or slews, to a certain point where it decelerates at a constant rate until finally, the end position is reached and the axis will come to a rest. Sometimes the slew velocity and the end position can be changed on the fly. The S-curve velocity profile can be represented as a second-order polynomial in velocity. We have an extra term here – jerk (jerk is a derivative of acceleration and a measure of impact). The second order S-curve provides complete flexibility in the control of profiles for smoothing motion and eliminating jerk from mechanical systems. The degree of S-curve on a motion

profile is controlled by separate acceleration and deceleration smoothing (jerk-limit) factors.