A common task for a positioning system is to start from a stationary position, move to a new location, and then stop. Of course, one way to do this is to apply an appropriate size step to the reference input of the position control system. However, depending on the system bandwidth, a sufficiently large step may require torques (current) and/or velocities (voltages) that exceed the motor/driver capabilities. In addition, the dynamic characteristics (e.g., rise time and overshoot) may be inconsistent with the application requirements. One remedy is to use a form of truncated ramp instead of the step reference input.
Suppose that we wish to reposition a mass-dominated load by \(X_\mathrm{max}\) as rapidly as possible, subject to limitations on the maximum acceleration \(A_\mathrm{max}\) and velocity \(V_\mathrm{max}\), while avoiding discontinuities in the position slope. One such command is constructed as shown in …
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