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. 2016 Jul 11;6:29231. doi: 10.1038/srep29231

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Copyright © 2016, Macmillan Publishers Limited

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Overview of the PI control system. Initially, the PI controller uses the previous errors to calculate the push [n] for the next goniometer motion to correct the previous positional error. Goniometer motion incurs additional environmental error [n], which yields the shift [n] through imaging and cross-correlation. The accumulated shift [n] is calculated by incorporating the historical motion [n − 1] and the current shift [n]. This [n] is used as historical data for the next tilt loop. The difference of [n] from the target [n] is the residual error [n]. Within the proportional integral (PI) controller, the accumulated residual error [n] is calculated by incorporating the historical error [n − 1] and current residual error [n].

Inline graphic — Overview of the PI control system. Initially, the PI controller uses the previous errors to calculate the push [n] for the next goniometer motion to correct the previous positional error. Goniometer motion incurs additional environmental error [n], which yields the shift [n] through imaging and cross-correlation. The accumulated shift [n] is calculated by incorporating the historical motion [n − 1] and the current shift [n]. This [n] is used as historical data for the next tilt loop. The difference of [n] from the target [n] is the residual error [n]. Within the proportional integral (PI) controller, the accumulated residual error [n] is calculated by incorporating the historical error [n − 1] and current residual error [n].