September 1997, Issue 86

PC/104 Quarter:
Motion Control with PC/104

S CURVES AND TRAPEZOIDALS

Trapezoidal and S-curve profiles are the two main types considered when developing a motion-control requirement.

In the motion-control industry, "profile" describes a complete and controlled motion event. That is, the move accelerating from a base velocity to a slew or run velocity, continuing at the slew velocity to a designated deceleration point, and then decelerating back to the base velocity.

Base velocity doesn't have to start at zero. A profile can begin from any previously established velocity V1 and be considered complete at any other velocity.

In a trapezoidal profile, the acceleration and deceleration rates of a motion are constant, as you see in Figure 2a. The velocity accelerates linearly until the profile reaches the required slew velocity. During deceleration, velocity decreases linearly until motion reaches its target velocity (Vx).

By contrast, an S-curve profile is a controlled velocity (or ramped acceleration) profile. As Figure 2b shows, the S curve is more complex than a trapezoid since it's based on two linear incrementing or decrementing variables over time.

A trapezoidal profile applies only half as much torque loading as the S profile does at halfway up the velocity profile in the same time frame. However, the S curve generates a softer move at the profile's leading and trailing ends, thus lowering impulse torque loading (i.e., jerk).

To gain these advantages, carefully match the update timing for the S acceleration profile to system dynamics.

Medium-to-high friction systems, noncounterbalanced vertical systems, or other similarly imbalanced systems may defeat S curve's ability to perform. Gain structures can be implemented to overcome this deficiency.

Using only a PID gain structure without any other form of gain assistance, the S curve may not perform any better than the trapezoidal when placed in a high-friction environment (above a 0.15 coefficient). The same holds true when operating in a medium-friction environment (0.075-0.15) and applying a current motor operation without tachometer feedback.

Interestingly, to achieve the same acceleration time versus distance, the peak acceleration achieved at the S's crossover is twice that of a trapezoid. Wherever the product is not secured to the conveying surface, the G-force exerted on the product may cause it to slip.