Laser beam tracking by repetitive and variable-order adaptive control

This paper addresses laser beam tracking control problem for tracing dynamic trajectories subject to random disturbances. A variable-order adaptive control scheme based on a recursive least-squares lattice filter is applied for suppressing random jitter. For tracking a reference trajectory generated by a deterministic dynamic model, an internal model principle based feedback loop is introduced as an outer loop to the adaptive feedback loop to achieve asymptotic tracking performance. Particularly a repetitive control is applied to track periodic trajectories. A feature of the control system proposed in this paper is that the design of the adaptive and repetitive control are independent because each design is based only on the plant model. Experiment conducted on a two-axis fast steering mirror for tracking diamond-shaped beam path demonstrates the ability of the integrated control to achieve asymptotic tracking of periodic trajectories by the repetitive control while optimally rejecting random disturbances by the adaptive control.