Abstract
Vibration rejection is a key technology of practical engineering, especially in optical telescopes with a stable accuracy of urad level. The closed-loop performance of optical telescopes is largely determined by the control bandwidth, while it is severely limited by the low sampling rate and large time delay of the image sensor, so it is difficult to mitigate structural vibrations in optical telescopes, especially wideband vibrations, because they exist universally and greatly influence the stability of the system. This paper develops an improved error-based disturbance observer (EDOB) based on the Youla parameterization approach to mitigate wideband vibrations in optical telescopes. This novel method can greatly improve the vibration rejection ability of the system by designing a proper Q-filter to accommodate wideband vibrations when their frequencies can be acquired. Because wideband vibrations in optical telescopes can be considered as multiple narrow-band vibrations with similar central frequencies, a novel Q-filter instead of a single wideband notch filter is proposed to mitigate wideband vibrations when considering the stability and closed-loop performance of the system. Moreover, this method only relies on a low frequency model, leading to a reduction in model dependence. Both the simulations and experimental results show that the error-based disturbance observer based on Youla parameterization can greatly improve the closed-loop performance of the system compared with the traditional feedback control loop.
Highlights
The invention and improvement of optical telescopes have greatly facilitated to observe farther and darker objects
Many improved control structures and some optimized controllers, such as the Linear Quadratic Gaussian (LQG), H∞/H2 controller or the Disturbance Observer (DOB), have been proposed on the basis of disturbance feedforward control [11]–[22], and the existing research results show that these vibration rejection methods can improve the closedloop performance of a system by 20% ∼ 30% [16], [23] compared with the conventional proportional-integral controller, while it is difficult to acquire accurate disturbance characteristics and precise dynamic models for minimizing the closed-loop residuals in terms of these techniques, especially large model errors could seriously degrade the performance of the tip-tilt mirror control system performance
The wideband vibrations in optical telescopes can be considered as the vibration caused by the interaction of multiple narrow-band vibrations with similar central frequencies, so multiple notch filters can be designed for specific narrowband vibrations
Summary
The invention and improvement of optical telescopes have greatly facilitated to observe farther and darker objects. Considering the stability and closed-loop performance of the system, this paper proposes a novel Q-filter design method to mitigate wideband vibrations, which is wideband vibrations in optical telescopes that can be considered multiple narrowband vibrations with similar central frequencies, so multiple notch filters can be designed to act simultaneously to mitigate wideband vibrations In this control mode, there is no extra sensor except the image sensor to implement the EDOB. At low and medium frequencies, it is relatively easy to obtain an accurate system model G(s), but at high frequencies, it becomes difficult, so Q(s) has to feature a low-pass filter to suppress the high-frequency dynamics and noise to make e−T0sG(s)G−m1(s) − e−T1s Q(s) close to zero In this case, the closed-loop stability of the control system in FIGURE 3(b) can be satisfied. It is obvious that (10) is easy to reach if Q(s) is designed to a low bandwidth that is less than the frequency at which G(s) can be modeled accurately, which is the reason we cannot just insert a band-stop filter corresponding to the wideband vibrations to mitigate them
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