Hysteresis compensation of piezoelectric deformable mirror based on Prandtl-Ishlinskii model

LCoS display phase self-calibration method based on diffractive lens schemes

In this paper, to enhance the tracking ability of a charge-coupled device (CCD) and micro-electro-mechanical-system (MEMS) accelerometer based low-cost tracking control system, an acceleration feed-forward control method based on fusion of model output and sensor data is proposed. To achieve the acceleration feed-forward control, the target acceleration is fed into the traditional acceleration-position dual closed-loop. Considering the CCD can only detect the line-of-sight (LOS) error of the target, the double integration of accelerometer measurement is regarded as the platform's position and is combined with the LOS error to build the target trajectory. The target acceleration is predicted by a Kalman filter, in which the combined target trajectory is used as the observed value. However, the basic acceleration feed-forward control method fails to improve the tracking ability at low frequencies due to inaccuracy of the accelerometer measurement caused by drift and noise. To solve this problem, we further propose to calculate an acceleration using the system acceleration model, and then use this calculated acceleration to fuse with the measured acceleration to obtain a new acceleration. The new acceleration, which is more accurate than the original measured acceleration in low frequency, is utilized to rebuild the target trajectory and predict the target acceleration again. Experimental results confirm the effectiveness of the proposed method.

An acceleration feed-forward control method based on fusion of model output and sensor data

A novel design of a two-axis fast steering mirror (FSM) with piezoelectric actuators is proposed for incoherent laser beam combination. The mechanical performance of the FSM is tested. The results show that the tilting range of the mirror is about 4 mrad, and the 1st-order resonance frequency is about 250 Hz. A self-designed grating encoder is taken as the sensor, which ensures the optimal precision of 10 μrad. The novel mechanical design can meet the requirement of engineering in incoherent laser beam combination.

Design and performance test of a two-axis fast steering mirror driven by piezoelectric actuators

The charge couple device (CCD) tracking loop of a fast steering mirror (FSM) is usually used to stabilize line of sight (LOS). High closed-loop bandwidth facilitates good performance. However, low-rate sample and time delay of the CCD greatly limit the high control bandwidth. This paper proposes an error-based observer (EBO) to improve the low-frequency performance of the CCD tracking system. The basic idea is by combining LOS error from the CCD and the controller output to produce the high-gain observer, forwarding into the originally closed-loop control system. This proposed EBO can improve the system both in target tracking and disturbance suppression due to LOS error from the CCD's sensing of the two signals. From a practical engineering view, the closed-loop stability and robustness of the EBO system are investigated on the condition of gain margin and phase margin of the open-loop transfer function. Two simulations of CCD experiments are provided to verify the benefits of the proposed algorithm.

Error-Based Observer of a Charge Couple Device Tracking Loop for Fast Steering Mirror.

The time delay engendered by wavefront sampling and data processing inevitability exists in almost all the wavefront sensor (WFS) based adaptive optics (AO) systems. Also, when WFS is used for tip-tilt aberration detection, the time delay significantly reduces the tip-tilt correction performance of the AO system. In this paper, we focus on researching time delay in a tip-tilt (TT) control system and introduce a predicted signal compensation method (PSCM) to compensate the time delay by modifying the WFS detected signals. Based on a precise model of a TT dynamic control system, the detection delay of TT corrections included in a WFS detected signal can be compensated. Experiments are conducted in the lab: the pure integrator (I), proportional and integral (PI) wavefront TT controllers, and these controllers with PSCM are compared to test the efficiency of the PSCM for TT corrections. For the PI controller, the rejection bandwidth increases from 52 to 62 Hz by using PCSM; meanwhile, the open-loop phase margin increases from 45 to 60 deg. In addition, astronomical observation results are also given based on the PI wavefront TT controller. The PSCM improves the Strehl ratio by a factor of 1.3. The new method is proven to improve the AO system closed-loop performance not only for increasing the closed-loop rejection bandwidth but also in favor of the error attenuation at low frequency. Furthermore, the method does not introduce more noise to the system.

Time delay compensation method for tip–tilt control in adaptive optics system

In adaptive optics system (AOS) for optical telescopes, the reported wavefront sensing strategy consists of two parts: a specific sensor for tip-tilt (TT) detection and another wavefront sensor for other distortions detection. Thus, a part of incident light has to be used for TT detection, which decreases the light energy used by wavefront sensor and eventually reduces the precision of wavefront correction. In this paper, a single Shack-Hartmann wavefront sensor based wavefront measurement method is presented for both large amplitude TT and other distortions’ measurement. Experiments were performed for testing the presented wavefront method and validating the wavefront detection and correction ability of the single-sensor based AOS. With adaptive correction, the root-mean-square of residual TT was less than 0.2 λ, and a clear image was obtained in the lab. Equipped on a 1.23-meter optical telescope, the binary stars with angle distance of 0.6″ were clearly resolved using the AOS. This wavefront measurement method removes the separate TT sensor, which not only simplifies the AOS but also saves light energy for subsequent wavefront sensing and imaging, and eventually improves the detection and imaging capability of the AOS.

Wavefront detection method of a single-sensor based adaptive optics system.

The invention belongs to the technical field of atmosphere adaptive optics, and aims at a problem that the deflection of a tilting mirror is added to a detection signal in the continuous detection and adaptive correction closed loop control of wavefront inclination. A control process is shown in figure 1: t1 is an exposure link of a wavefront detector, t2 is a reading link of the detection signal, t3 is a signal processing link, t4 is a deflection operation link of the tilting mirror and tx is pure waiting time. The exposure time of the detector is enabled to comprise a complete superposed deflection operation link of the tilting mirror, thereby achieving the design of a method for measuring the deflection superposing amount of the tilting mirror. A measured deflection response function of the tilting mirror is employed. The deflection superposing amount of the tilting mirror is removed from the detection signal, and the deflection amounts, generating in parallel in a former period, of the tilting mirror are also removed from the detection signal reading and processing delay links. The wavefront inclination residual error is accurately calculated before the driving of the tilting mirror. Meanwhile, a PI controller is employed, thereby remarkably improving the closed loop correction precision of the wavefront inclination.

Continuous detection and correction closed loop control method for wavefront inclination

The intrinsic hysteresis nonlinearity of the piezo-actuators can severely degrade the positioning accuracy of a tip-tilt mirror (TTM) in an adaptive optics system. This paper focuses on compensating this hysteresis nonlinearity by feed-forward linearization with an inverse hysteresis model. This inverse hysteresis model is based on the classical Presiach model, and the neural network (NN) is used to describe the hysteresis loop. In order to apply it in the real-time adaptive correction, an analytical nonlinear function derived from the NN is introduced to compute the inverse hysteresis model output instead of the time-consuming NN simulation process. Experimental results show that the proposed method effectively linearized the TTM behavior with the static hysteresis nonlinearity of TTM reducing from 15.6% to 1.4%. In addition, the tip-tilt tracking experiments using the integrator with and without hysteresis compensation are conducted. The wavefront tip-tilt aberration rejection ability of the TTM control system is significantly improved with the −3  dB error rejection bandwidth increasing from 46 to 62 Hz.

Chongchong Wang

Papers

Time delay compensation method for tip–tilt control in adaptive optics system

Wavefront detection method of a single-sensor based adaptive optics system.

Continuous detection and correction closed loop control method for wavefront inclination

Hysteresis compensation of the piezoelectric ceramic actuators–based tip/tilt mirror with a neural network method in adaptive optics