In view of the special requirements of the secondary mirror control system on large aperture telescopes, an improved 6-DOF parallel manipulator is designed and used to replace the traditional hexapod used in telescope secondary mirror position dynamic compensation. A highly robust active disturbance rejection controller (ADRC) is designed, which consists of a nonlinear tracking differentiator (NTD), an extended state observer (ESO), a nonlinear state error feedback law (NLSEF), and disturbance compensation. The ESO can track the all-order state variables, as well as estimate and compensate for unmodeled dynamics and total external disturbance of the system. The results of simulation indicate that the ADRC can improve tracking precision and control performance when it is compared with the proportion integration differentiation (PID) controller. The test results show that the absolute accuracy of the three dimensional parallel motions is about ±4 µm, and the two dimensional tilts' is about 10 µrad. The control precision meets the system design for a telescope secondary mirror.

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Inverse square root has played an important role in Cholesky decomposition, which devoted to hardware efficient compressed sensing. However, the performance is usually limited by the trade-off between throughput and precision. This paper presents hardware implementation of fixed-point single iterated multiplicative inverse square root. Multiple piecewise linear approximation in softly nonlinear range is used to compute the initial value. Single iterated Newton-Raphson method is employed to obtain high precision. Multiple constants multiplication technique is proposed to achieve high throughput. The combination of these techniques yields high performance in terms of throughput and precision. It obtains more than 70 % of throughput improvement and almost 100 × higher precision over the inverse square root Intellectual Property (IP) from Altera. In addition, Cholesky decomposition has been presented to validate the proposed architecture, which shows that 42 % of throughput improvement is achieved compared with the IP.