The pointing and imaging performance of precision optical systems is degraded by disturbances on the system that create optical jitter. These disturbances can be caused by structural motion of optical components due to vibration sources that (1) originate within the optical system, (2) originate external to the system and are transmitted through the structural path in the environment, and (3) are air-induced vibrations from acoustic noise. Beam control systems can suppress optical jitter, and active control techniques can be used to extend performance by incorporating information from accelerometers, microphones, and other auxiliary sensors. In some applications, offline fixed gain controllers can be used to minimize jitter. However there are many applications in which a real-time adaptive control approach would yield improved optical performance. Often we would like the capability to adapt in real-time to a system which is time-varying or whose disturbances are non-stationary and hard to predict. In the presence of these harsh, ever-changing environments we would like to use every available tool to optimize performance. Improvements in control algorithms are important, but another potentially useful tool is a real-time adaptive control method employing optimal sensing strategies. In this approach,
real-time updating of reference sensors is provided to minimize optical jitter. The technique selects an optimal subset of sensors to use as references from an array of possible sensor locations. The optimal, weighted reference sensor set is well correlated with the disturbance and when used with an adaptive control algorithm, results in improved line-of-sight jitter performance with less computational burden compared to a controller which uses multiple reference sensors. The proposed technique is applied to an experimental test bed in which multiple proof-mass actuators generate structural vibrations on a flexible plate. These vibrations are transmitted to an optical mirror mounted on the plate, resulting in optical jitter as measured by a position sensing detector. Accelerometers mounted on the plate are used to form the set of possible optimal reference sensors. Reduction of the structural vibration of optical components is attained using a fast steering mirror which results in a reduction of the corresponding jitter.
Optical jitter degrades the pointing and imaging performance of precision optical systems. When a correlated measurement of the disturbance is available, improved control performance can be attained. In this research, an adaptive optimal sensing strategy for optical systems is proposed. An array of reference sensors makes it possible to estimate the disturbance and model the disturbance-to-reference paths. The least-square algorithm is applied for the disturbance model estimation. A sensor scoring algorithm is then used to select an optimal disturbance reference from the available reference signals. The optimal disturbance reference is comprised of sensors which are well correlated with the disturbance. This disturbance reference is then fed forward and used in an adaptive generalized predictive control design. This adaptive control approach is advantageous in the presence of time-varying or uncertain disturbances. The proposed technique is applied to an experimental test bed in which an array of accelerometer sensors measures the structural vibration of optical elements. Reduction of the structural vibration of optical components is attained using a fast steering mirror which results in a reduction of the corresponding jitter. Performance using optimally selected disturbance reference is shown to be better than for system in which a disturbance reference signal is chosen to be the sensor with the lowest score.
Proc. SPIE. 5383, Smart Structures and Materials 2004: Modeling, Signal Processing, and Control
KEYWORDS: Data modeling, Digital filtering, Control systems, Linear filtering, System identification, Algorithm development, Adaptive control, Acoustics, Systems modeling, Filtering (signal processing)
The generalized predictive control (GPC) concept is extended to an adaptive control algorithm by combining with a least-squares lattice filter. A least-squares lattice (LSL) filter, another class of exact least-squares filters, has a modular structure that is advantageous in the application of on-line system identification. The modular structure passes system information from lower order to higher order in a wave motion. The adaptive GPC algorithm combined with a LSL filter is implemented for a real-time computer algorithm and its performance is experimentally demonstrated to a structural system and an acoustic enclosure. In addition, the adaptive GPC algorithm with a LSL filter is compared with the adaptive GPC algorithm combined with a classical recursive least-squares (RLS) filter in terms of complexity, computational cost and other on-line application concerns. The average task execution time (TET) --- the measured processing time to run the algorithm during each sample interval --- is reduced by over 35 \% by using the adaptive GPC algorithm with a LSL filter.
The recursive generalized predictive control (RGPC), which combines the process of system identification using recursive least-squares (RLS) algorithm and the process of generalized predictive feedback control design, has been presented and successfully implemented on testbeds. In this research, the RGPC algorithm is extended when the disturbance measurement signal is available for feedforward control. First, the feedback and feedforward RGPC design algorithm is presented when the disturbance is stochastic or random, and is applied to an optical jitter suppression testbed. Second, the feedback and feedforward algorithm is further extended when the disturbance is deterministic or periodic. The deterministic disturbance measurement is used to estimate the future disturbance values that are then used in the control design to enhance the performance. The RGPC with future disturbance estimation algorithm is applied to a structural system and an acoustic system.
The concept of generalized predictive control (GPC) design is extended by combining it with the recursive least squares (RLS) system identification algorithm. In this paper, GPC is combined with the classical RLS system identification algorithm, and with the fast transversal filter (FTF), a modified version of the classical RLS algorithm. The classical RLS algorithm is a straightforward approach for identifying a model from input and output data, and one of the advantages of the classical RLS algorithm is that a model is obtained without time-consuming processes like matrix inversion. The FTF is also an RLS algorithm, but it exploits the shifting property of serialized data and thereby results in a substantial reduction in computational complexity. The advantages of both combined algorithms are no prior system model is required, since the process of system identification is performed recursively from real-time system input and output data, and the controller is updated adaptively in the presence of a changing operating environment.
Proc. SPIE. 4697, Smart Structures and Materials 2002: Damping and Isolation
KEYWORDS: Actuators, Ferroelectric materials, Weapons of mass destruction, Control systems, Process control, System identification, Information technology, Picosecond phenomena, Acoustics, Smart materials
The recursive generalized predictive control algorithm, conjugating the process of system identification and the process of the controller design, is presented and applied to real time. In the control design process, there are three parameters to be chosen: the prediction horizon, the control horizon, and the input weighting factor. The prediction horizon and the control horizon are the finite horizons of the system output and control input predictions. Two practical parameters are defined to express effects of the prediction horizon and the control horizon. A time varying algorithm for the input weighting factor and a dual-sampling-rate algorithm are presented. A time varying input weighting factor algorithm allows the recursive generalized predictive controller to be designed aggressively. A dual-sampling-rate algorithm between data acquisition and control design allows higher-order controllers to be designed. The recursive generalized predictive control algorithm is applied to two different systems: a sound enclosure and an optical jitter suppression testbed. For each experiment, the estimation of the frequency response magnitude corresponding to the open loop identified system and the closed loop identified system is shown and compared. The advantages of the proposed recursive generalized predictive control algorithm are: no prior system information is required since the process of the system identification is performed recursively from real time system input and output data, and the controller is updated adaptively in the presence of a changing operating environment.
The objective of the research is to investigate an effective method of using servo control through the use of a fast steering mirror and/or acoustic actuators and sensors for optical jitter suppression. The experimental testbed is built in an anechoic chamber at Duke University. Two optical benches are used to isolate metrology components from vibrating optical elements. A Helium-Neon laser and a position sensor are mounted on one optical bench and a turning flat mirror and a 3-axis fast steering mirror are on the other optical bench. External acoustic disturbances from the speaker are used to generate vibration in the optical components. A speaker housed within an enclosure and a fast steering mirror are the two allowable control actuators and external microphones are used for reference measurement, microphones/accelerometers mounted on or nearby the optical elements and the optical sensor are the three allowable control sensors in the experiment. The generalized predictive controller is used to conjugate the process of the system identification algorithm and the process of the controller design, and can be updated adaptively in the changes of the operating environment. The generalized predictive controllers are designed for each actuator and each sensor: Case 1) Fast steering mirror and position detector, Case 2) Control speaker and position detector, Case 3) Fast steering mirror and external microphones. The generalized predictive controller for all control actuators and sensors is also designed.