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Velocity profiling in linear and rotational systems

Profiling scan velocity in linear and rotational machines (cameras and gimbal sets in particular) is common practice. Typically, these are given as trapezoidal profiles that ramp up from zero to a desired velocity, then ramp down to zero velocity at some later time. These profiles tend to be unidirectional, making implementation at the trapezoidal approach straightforward. The task is somewhat more complicated if one desires bidirectional operation. Consider the case where the displacements are identical for either direction, and scan velocities are dependent on scan direction. If cycle rate, the time required to perform a scan and return to the starting position, is a concern, the interaction between the scan profile and system dynamics needs to be considered. Tradeoffs, such as peak accelerations and settling times, and the type of controller need to be among the considerations. This paper presents some interesting results from these considerations, including a set of equations that may be implemented for either trapezoidal or sinusoidal profiles. It examines these in light of cycle rate requirements, and presents analytical results generated from Advanced Continuous Simulation Language (ACSL).