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This paper presents identification and control of a 10-m antenna via accelerometers and angle encoder data. Artificial neural networks can be used effectively for the identification and control of nonlinear dynamical system such as a large flexible antenna with a friction drive system. Some identification results are shown and compared with the results of conventional prediction error method. And we use a neural network inverse model to control the large flexible antenna. In the neural network inverse model, a neural network is trained, using supervised learning, to develop an inverse model of the antenna. The network input is the process output, and the network output is the corresponding process input. The control results show the validation of the ANN approach for identification and control of the 10-m flexible antenna.

This paper presents identification and control of a 10-m antenna dynamics using accelerometers and angle encoders data.

ALMA—the Atacama large millimeter array—will be a single instrument composed of 64 high-precision antennas located on the Chajnantor plain of the Chilean Andes in the District of San Pedro de Atacama, 16,500 feet (5,000 meters) above sea level (shown in Figure

Rending of ALMA.

The ALMA is an international collaboration between Europe and the North America to build a synthesis radio telescope that will operate at millimeter and submillimeter wavelengths. Japan also becomes a partner, making this a truly global collaboration.

Its main targets include planetary system formation and galaxy formation/evolution. The technical challenges to key instruments for such arrays are now performed, that is, developments of high precision antenna, low-noise submillimeter mixers, high-power submillimeter LO sources, and very high-speed samplers and wideband spectrocorrelators. The specifications imposed for recent submillimeter antennas of a 10/12-m size in the open air are demanding and challenging. For example, 12-m antennas for Atacama large millimeter/submillimeter Array (ALMA) have a surface accuracy of better than 25

Loads on antenna structure due to wind cause elastic deformations, which deteriorate antenna's pointing and surfaces accuracies. The structural behavior of the telescope is typically measured at the encoders of azimuth and elevation axes, while the critical performance is the actual pointing on the sky. We need to make direct measurements of vibration motion of the main-dish and subreflector with a resolution of typically 3–5

With all advanced control schemes, mathematical knowledge of the dynamics of the process of interest is necessary. System identification refers to the process of developing a mathematical process model from experimental data. System identification in control engineering is a key element for understanding and controlling unknown dynamical systems. Traditional system identification techniques such as least square estimation, quasilinearization and stochastic modeling have been successfully used in nonlinear dynamical systems. In traditional system, model structure must be defined a priori to estimate all required system parameters. In case of antenna dynamics, defining a priori model is difficult to get. Given input and output data, artificial neural networks (ANNs) is capable of identifying underlying relationship between the input and output data. Some identification results are shown and compared with the results of conventional prediction error method. The results show the validation of the ANN approach for identification of the 10-m antenna dynamics.

We use a neural network inverse model for control the large flexible antenna. In the neural network inverse model, a neural network is trained, using supervised learning, to develop an inverse model of the antenna. The network input is the process output, and the network output is the corresponding process input. The control results show the validation of the ANN approach for identification and control of the 10-m flexible antenna.

10-m antenna structure is shown in Figure ^{−1} and 0.1–0.001 deg s^{−1}, respectively. The telescope was located at a highland of 1350 m elevation. There are three piezoelectric seismic sensors (PCB Model 393B12) at a subreflector mount chassis, four beneath a panel support board of the backup structure (BUS), normal to the surface, one at a reference point near the center of the BUS, and four capacitive accelerometers (PCB Model 3701G3) at yoke arm ends (horizontal directions, perpendicular and parallel to the elevation axis). These data sampled simultaneously are combined to figure out the oscillations of antenna global structure. For example, differences between pairs of sensors in the BUS tell us a tilt motion of the dish in the reflector axis. The system had a noise floor of 3^{−8} × 10^{−4} [m s^{−2}/root Hz] in the 0.1 to 1 Hz band and 2 × 10^{−4} [m s^{−2}/root Hz] in the frequency range from 1 to 20 Hz under a condition of no wind. Our 16-bit ADC has 16 single-ended input channels with a bipolar input range of ±5 Volt, and makes negligible contribution to the noise floor. Comparisons between Fourier spectra of the sensor outputs under windy and no-wind conditions suggest that the components below 0.7 Hz seem to be due to noise (poor stability) of the sensors and/or measurement system. Sensor outputs and angle encoder readouts were simultaneously recorded at a rate of 100 Hz, while the antenna was driven at a rotational speed of 10^{−5} deg s^{−1} and was pointed at various wind attack angles under a windy condition of typically 10 m s^{−2 }(Figure

Antenna structure.

Sensors and encoders position.

Control requirements can narrow the regions of time frequency over which an adequate model fit is necessary.

Therefore, if the control requirements are incorporated in the parameter estimation problem, it becomes possible to obtain improved models over the frequency band which is of importance to the control problem.

This is the objective of the control-relevant parameter estimation problem.

In a more generalized mathematical sense, the control- relevant parameter estimation problem is interpreted an optimization problem which requires minimizing a functional of the weighted error between the true and estimated plant models.

Parametric identification methods are techniques used to estimate parameters in given model structures.

It is basically a matter of finding those numerical values of parameters that give the best fit between the model output and the measured one.

System identification is concerned with the building of dynamic models which describe the relationships between measured signals. The system identification problem is to estimate the model of a system based on observed input-output data. Here, the parametric identification methods are used. Parametric identification methods are techniques used to estimate parameters in given model structures. It is basically a matter of finding those numerical values of parameters that give the best fit between the model output and measured one. The applied parametric model is the ARMAX (auto-regressive moving average eXogeneous) model which corresponds to the description [

The most popular control system application of neural networks is also the most straightforward conceptually. The supervised learning capabilities of neural networks can be used for identifying process models from input/output data. The process data are the training set for the network, the weights of which are adjusted until the network model output accurately predicts the actual process output. Once the training process is successfully concluded, the neural network constitutes a black-box, nonparametric process model [

Figure

Identification system.

Multiple layers neural networks.

Identification results are shown in Figures

NN identification results.

Sensor 1

Sensor 5

Identification using PEM.

Sensor 1

Sensor 5

The inverse model of a dynamical system yields input for given output. The model is a crucial role in a range of control structures. Conceptually, the simplest approach is direct inverse modeling. A synthetic training signal is introduced to the system. The system output is then used as input to the network. The network output is compared with the system input and this error is used to train the network. This structure will clearly tend to force the network to represent the inverse of the plant [

Control system.

Figures

Simulation result using error learning.

Desired acceleration of sensor1

Input trajectory

Sensor1

Sensor5

Simulation result using Jacobian learning.

Desired acceleration of sensor1

Input trajectory

Sensor1

Sensor5

Simulation results using vector and acceleration value.

Input trajectory

Sensor1

Sensor2

Identification and control of a 10-m antenna dynamics for the Atacama large millimeter array project using accelerometers and angle encoders data were presented. Compared with prediction error method and NN identification method, one cycle squared estimation error of the NN method was smaller than that of the prediction error method.

A neural network inverse model was used for control of the large flexible antenna. In the neural network inverse model, a neural network was trained, using supervised learning, to develop an inverse model of the antenna. The network input was the process output, and the network output was the corresponding process input. The control results showed the validation of the ANN approach for identification and control of the 10-m flexible antenna, especially the system Jacobian learning.

This work was supported in part by the ALMA cooperative research project.