Ray position in slope-controlled waveguides is studied. A linear combination of three consecutive position measurements is used to calculate the slope error of the middle lens. This is the error input to the middle lens positioning system. Independent lens correction results and thus a decoupling of space and time response is achieved. The system is shown to be stable. Overshoot in the transient response due to cross coupling between controllers is eliminated. Performance is compared to that of the position-controlled waveguide. Computer simulations indicate that the system is stable in the presence of statistical parameter variations.

Beam position control in beam waveguides subject to statistical variations is studied. Variations in alignment and component values cause the beam to be displaced from the guide axis. A control system to correct this displacement is described. Both the expected and the rms values of the beam position are discussed. An approximate expression for the stability conditions is determined.