Two-step Structural Design of Mesh Antennas for High Beam Pointing Accuracy

A well-designed reflector surface with high beam pointing accuracy in electromagnetic performance is of practical significance to the space application of cable mesh reflector antennas. As for space requirements, cir- cular polarizations are widely used in spaceborne antennas, which usually lead to a beam shift for offset reflectors and influence the beam pointing accuracy. A two-step structural design procedure is proposed to overcome the beam squint phenomenon for high beam pointing accuracy design of circularly polarized offset cable mesh reflectors. A simple structural optimal design and an integrated structural electromagnetic optimization are combined to alleviate the beam squint effect of circular polarizations. It is imple- mented by cable pretension design and adjustment to shape the offset cable mesh surface. Besides, in order to increase the efficiency of integrated optimization, an update Broy- den-Fletcher-Goldfarb-Shanno （BFGS） Hessian matrix is employed in the optimization iteration with sequential quadratic programming. A circularly polarized offset cable mesh reflector is utilized to show the feasibility and effectiveness of the proposed procedure. A high beam pointing accuracy in order of 0.0001~ of electromagnetic performance is achieved.

Special Issue on Electromechanical Coupling Design for Electronic Equipment

With the development of electronic equipment to high accuracy, high density, high frequency, and atrocious ser- vice environment, the functional surface in this type of equipment has increasingly serious problems,

Refiector Deformation Measurement and Correction Methodology of Large Antenna Based on Phased Array Feed

To solve the problem of time-consuming measurement and correction of large antennas’reflector deformation,a new microwave holography methodology based on a Phased Array Feed(PAF)is proposed.Starting from the known expression of receiving signals in microwave holography,the theory of PAF holography is derived through Geometrical Optics.Reflector deformation,as well as pointing deviation and subreflector offset,can be calculated out by applying the derived equations.A measurement and correction system based on PAF holography is depicted,and two kinds of measurement methods are illustrated.The proposed measurement methodology is verified by numerical simulation,and its measurement error is analyzed.The results indicate that our proposed methodology is feasible,especially for Cassegrain antennas.

Coupling Modeling for Functional Surface of Electronic Equipment

High performance electromechanical equipment is widely used in various fields, such as national defense, industry and so on [ 1]. In addition, the technical level of high performance electromechanical equipment is the embodiment of the national level of science and technology.

A Reverse-Design Strategy for the Track Error of the Qi Tai Telescope Based on Pointing Accuracy

The Qi Tai Telescope(QTT),which has a 110 m aperture,is planned to be the largest scale steerable tele-scope in the world.Ideally,the telescope’s repeated pointing accuracy error should be less than 2.5 arc seconds(arcsec);thus,the telescope structure must satisfy ultra-high precision requirements.In this pur-suit,the present research envisages a reverse-design method for the track surface to reduce the difficulty of the telescope’s design and manufacture.First,the distribution characteristics of the test data for the track error were verified using the skewness coefficient and kurtosis coefficient methods.According to the distribution characteristics,the azimuth track error was simulated by a two-scale model.The error of the long period and short amplitude was characterized as large-scale and described by a trigonometric function,while the short period and high amplitude error was characterized as small-scale and simulated by a fractal function.Based on the two-scale model,effect of the error on the pointing accuracy was deduced.Subsequently,the relationship between the root mean square(RMS)of the track error and the RMS of the pointing accuracy error of the telescope was deduced.Finally,the allowable RMS value of the track error was derived from the allowable pointing accuracy errors.To validate the effectiveness of the new design method,two typical radio telescopes(the Green Bank Telescope(GBT)and the Large Millimeter Telescope(LMT))were selected as experimental examples.Through comparison,the theoretical calculated values of the pointing accuracy of the telescope were consistent with the measured values,with a maximum error of less than 10%.

Kernel extreme learning machine‐based general solution to forward kinematics of parallel robots

The forward kinematics of parallel robots is a challenging issue due to its highly coupled non‐linear relation among branch chains.This paper presents a novel approach to for-ward kinematics of parallel robots based on kernel extreme learning machine(KELM).To tackle with the forward kinematics solution of fully parallel robots,the forward ki-nematics solution of parallel robots is equivalently transformed into a machine learning model first.On this basis,a computational model combining sparrow search algorithm and KELM is then established,which can serve as both regression and classification.Based on SSA‐optimised KELM(SSA‐KELM)established in this study,a binary discriminator for judging the existence of the forward kinematics solution and a multi‐label regression model for predicting the forward kinematics solution are built to obtain the forward kinematics general solution of parallel robots with different structural configurations and parameters.To evaluate the proposed model,a numerical case on this dataset collected by the inverse kinematics model of a typical 6‐DOF parallel robot is conducted,followed by the results manifesting that the binary discriminator with the discriminant accuracy of 88.50%is superior over ELM,KELM,support vector machine and logistic regression.The multi‐label regression model,with the root mean squared error of 0.06 mm for the position and 0.15°for the orientation,outperforms the double‐hidden‐layer back propagation(2‐BP),ELM,KELM and genetic algorithm‐optimised KELM.Furthermore,numerical cases of parallel robots with different structural con-figurations and parameters are compared with state‐of‐the‐art models.Moreover,these results of numerical simulation and experiment on the host computer demonstrate that the proposed model displays its high precision,high robustness and rapid convergence,which provides a candidate for the forward kinematics of parallel robots.

Multimodality-based Wind Speed Forecasting Method for the Wind Resistance Control of Large Radio Telescope

A large,fully steerable radio telescope is susceptible to the wind load,leading to structure deformation andpointing deviation of the telescope.To effectively suppress the influence of dynamic wind load,the wind resistancecontrol of the telescope is carried out based on wind speed forecasting.This study developed a wind speedforecasting model to efficiently forecast the wind speed at the telescope position.The proposed model successfullyeliminates the random noise of the original wind speed,effectively extracts the wind speed features and solves theautomatic optimization of the hyperparameters of the forecasting network.This model significantly improves theaccuracy and reliability of wind speed forecasting.To verify the forecasting performance of the proposed model,the wind data from the Qitai Radio Telescope site is examined as a case study.The wind speed forecasting model’sMAE,RMSE and MAPE are 0.0361,0.0703 and 3.87%,respectively.The performance of the proposed modelmeets the requirements of wind resistance control and can provide data support for the radio telescope.

Optimal subreflector position determination of shaped dual-reflector antennas based on the parameters iteration approach

A new method based on the parameters iteration technique has been developed to determine the optimal subreflector position for shaped Cassegrain antennas, that are distorted by gravity, to improve their electromagnetic(EM) performance. Both the features of shaped surface and the relationship between optical path difference(OPD) and far field beam pattern are employed. By describing the shaped dualreflector surface as a standard discrete parabola set, we can utilize the optical features of the standard Cassegrain system in the classical OPD relationship. Then, the actual far field beam pattern is expressed as the synthesis of ideal beam and error beam by decomposing subreflector adjustment parameters using a mechanical-electromagnetic-field-coupling-model(MEFCM). Furthermore, a numerical method for determining optimal subreflector position is presented. The proposed method is based on the iteration technique of subreflector adjustment parameters, and the optimal far field pattern is used for the iteration. The numerical solution of optimal adjustment parameters can be obtained rapidly. Results for a 25 m shaped Cassegrain antenna demonstrate that the adjustment of the subreflector to the optimal position as determined by the proposed method can improve the EM performance effectively.

Effect of Facet Displacement on Radiation Field and Its Application for Panel Adjustment of Large Reflector Antenna

Large reflector antennas are widely used in radars, satellite communication, radio astronomy, and so on. The rapid developments in these fields have created demands for development of better performance and higher surface accuracy. However, low accuracy and low effi- ciency are the common disadvantages for traditional panel alignment and adjustment. In order to improve the surface accuracy of large reflector antenna, a new method is pre- sented to determinate panel adjustment values from far field pattern. Based on the method of Physical Optics （PO）, the effect of panel facet displacement on radiation field value is derived. Then the linear system is constructed between panel adjustment vector and far field pattern. Using the method of Singular Value Decomposition （SVD）, the adjustment value for all panel adjustors are obtained by solving the linear equations. An experiment is conducted on a 3.7 m reflector antenna with 12 segmented panels. The results of simulation and test are similar, which shows that the presented method is feasible. Moreover, thediscussion about validation shows that the method can be used for many cases of reflector shape. The proposed research provides the instruction to adjust surface panels efficiently and accurately.

B-spline surface fitting and simplified GO/PO analysis of subreflector correction for large Cassegrain antenna distortion compensation

The main surface of a large Cassegrain antenna consists of a large number of panels. There are inevitably random and systematic errors which will degrade the antenna pattern and limit its applicability when working at high frequencies. Correcting the subreflector surface is difficult to describe by a global expansion effectively with a small amount of data. This paper presents a simple and clear way for correcting the subreflector surface of a large Cassegrain antenna for achieving such compensation. The advantage of the method is that the geometrical optics （GO） analysis is extremely simplified by the concept of equivalent prime-focus paraboloid, and corrected deformations of the subreflector surface are determined by simple formulas which represent the relationship between distortions of the subreflector surface and phase of the main surface current. The final shape of the subreflector surface is represented by a B-spline surface. To obtain a satisfactory antenna pattern with the simplest subreflector surface, the optimal number of B-spline patches are searched by particle swarm optimization （PSO）. The shaping process is verified by compensating a 22-m Cassegrain antenna whose main reflector has 96 panels. The results are satisfactory and demonstrate the simplicity and effectiveness of the approach.

An adjustment method for active reflector of large high-frequency antennas considering gain and boresight

The design of the Qitai 110 m Radio Telescope（QTT） with large aperture and very high working frequency（115 GHz） was investigated in Xinjiang, China. The results lead to a main reflector with high surface precision and high pointing precision. In this paper, the properties of active surface adjustment in a deformed parabolic reflector antenna are analyzed. To assure the performance of large reflector antennas such as gain and boresight, which can be obtained by utilizing an electromechanical coupling model, and satisfy them simultaneously, research on active surface adjustment applied to a new parabolic reflector as target surface has been done. Based on the initial position of actuators and the relationship between adjustment points and target points, a novel mathematical model and a program thatdirectly calculates the movements of actuators have been developed for guiding the active surface adjustment of large reflector antennas. This adjustment method is applied to an 8 m reflector antenna,in which we only consider gravity deformation. The results show that this method is more efficient in adjusting the surface and improving the working performance.

Multivariate Rational Response Surface Approximation of Nodal Displacements of Truss Structures

Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis(MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.

Phase Compensation of Composite Material Radomes Based on the Radiation Pattern

Some compensation methods have been pro- posed to mitigate the degradation of radiation characteris- tics caused by composite material radomes, however most of them are complex and not applicable for large radomes, for example, the modification of geometric shape by grinding process. A novel and simple compensation strat- egy based on phase modification is proposed for large reflector antenna-radome systems. Through moving the feed or sub-reflector along axial direction opportunely, the modification of phase distribution in the original aperture of an enclosed reflector antenna can be used to reduce the phase shift caused by composite material radomes. The distortion of far-field pattern can be minimized. The modification formulas are proposed, and the limitation of their application is also discussed. Numerical simulations for a one-piece composite materials sandwich radome and a 40 m multipartite composite materials sandwich radome verify that the novel compensation strategy achieves sat- isfactory compensated results, and improves the distortion of the far-field pattern for the composite material radomes. For one-piece dielectric radome, more than 60% phasedifference caused by radome is reduced. For multipartite radome, the sidelobe level improves about 1.2 dB, the nulling depth improves about 3 dB. The improvement of far-field pattern could be obtained effectively and simply by moving the feed or sub-reflector according to phase shift of the radome.

Analysis and compensation of the reflector antenna pointing error under wind disturbance

A large reflector antenna has been widely used in satellite communications,gravitational wave detection,galaxy origin observation and other fields due to its narrow beam and high gain.With the increase of the antenna aperture and the improvement of the working frequency,the requirements for the pointing accuracy of an antenna are also rising.However,the effect of environmental load on the deformation of the antenna structure,which in turn affects its beam pointing,has become a key problem to be solved urgently in the antenna engineering applications.The key issue to solving this problem involves accurately estimating the pointing error caused by the structural deformation and designing an effective controller that is based on the structural deformation.In this paper,we first establish a dynamic model for antenna structure based on the modal superposition method.The model is then modified by using modal characteristics and the dynamic displacement information of the sampling points to achieve the purpose of accurately estimating the structural deformation.Secondly,by considering the influence of the deformation of the rotating shaft and the reflector surface on the pointing accuracy,a control-oriented pointing error analysis model is established for estimating the pointing error caused by the environmental load in real time.Thirdly,based on considering the influence of the shaft deformation on the error compensation,the feedback error amount is decoupled and corrected to improve the accuracy of the compensation error.Finally,this paper analyzes and verifies the 65 m S/X-band dual reflector antenna with a numerical example.We consider a fluctuating wind with an average wind speed of 10 m s^(-1) as an example,which results in a maximum pointing error of 55.82″as calculated by the antenna theoretical model,whereas the maximum pointing error as predicted by our model is 68.27″.The pointing error after compensating for the cause of the environmental load with the modified controller is reduced to 10.57″,which effectively improves the antenna pointing performance.

Edge sensor based real-time calculation method for active panel position of QTT

QiTai Telescope(QTT),the world’s biggest full-steerable telescope,will be constructed in Xinjiang,China.Its extra high operating frequency(115 GHz)imposes strict requirements on the accuracy of the reflector,while its large aperture(110 m)increases the impact of antenna weight and environment on surface accuracy.However,the panels of reflector will deform under the influence of gravity and the environment.Therefore,to compensate for the performance degradation caused by this deformation,a technique called active surface adjustment has been proposed.The existing adjustment methods cannot detect the deformation caused by environment of the reflector surface in real time,which can result in a delay in the compensation.Consequently,it is difficult to achieve an optimal compensating result.To solve this problem,a real-time method to estimate the large-aperture reflector antenna surface by calculating the antenna panel position based on edge sensors is proposed in this paper.In the proposed method,a panel coordinate transfer matrix has been formulated and the data measured from these edge sensors can then be treated as input for the proposed transfer matrix to calculate the actual position of the antenna panel in real time.A numerical simulation has been carried out in the QTT model and the results obtained show that the proposed real-time method is a promising tool to estimate the large reflector surface position in real time.It is believed that this active surface adjustment method has laid the foundation for new methods that will be developed to compensate for the reflector electrical performance.

Accurate Data Match and Call Method for the Thermal Compensation Database of the Reflector Antenna

The influence of thermal deformation on the performance of reflector antennas has become increasingly significant with the increasing aperture and working frequency.The use of a thermal compensation database is an efficient method to compensate for the deformation caused by the non-uniform temperature distribution.However,how to efficiently and accurately match and call the database remains as one of the tough challenges for the antenna thermal compensation system to achieve real time compensation.Therefore,this study proposes a data match and call method for the thermal compensation database of the reflector antenna,matching the database from three aspects:the overall rms match of temperature data,the similarity area match of each data sample,and the key area match of key structural positions.The validation of this method is demonstrated in an example.The difference between the pointing adjustment amount calculated by the matched data and the collected data was found to be less than 1",which satisfied the requirements of practical engineering,thus achieving real-time thermal compensation of the antenna.

Thermal Distortion Compensation for Improving Electrical Performance of Reflector Antennas

Aiming at the problem of the surface accuracy and electrical performance of the antenna in space environment are reduced due to thermal deformation caused by temperature load. This paper presents a method to compensate the thermally induced shape distortion of antenna reflector by actively adjusting actuators in order to improve the electrical performance. The adjustment of each actuator is related to the local deformation of the panel. Then, taking a space deployable antenna with a diameter of 5 meters as an example, the finite element model is established. According to the range of the temperature variation in space (−180°C - 200°C), different temperature loads are applied to the antenna. The variation of electrical properties and surface accuracy is analyzed and the worst working condition is determined, and the antenna is compensated based on this condition. Then, four different electrical performance parameters are used as the optimization objectives, and the electromechanical coupling optimization model is established, and the PSO algorithm is used to optimize the actuators adjustments. The results show that the method can effectively improve the electrical performance of the deformed reflector antenna.

Effect of Surface Roughness in Micro-nano Scale on Slotted Waveguide Arrays in Ku-band

Modeling of the roughness in micro-nano scale and its influence have not been fully investigated, however the roughness will cause amplitude and phase errors of the radiating slot, and decrease the precision and efficiency of the SWA in Ku-band. Firstly, the roughness is simulated using the electromechanical coupled（EC） model. The relationship between roughness and the antenna＇s radiation properties is obtained. For verification, an antenna proto- type is manufactured and tested, and the simulation method is introduced. According to the prototype, a contrasting experiment dealing with the flatness of the radiating plane is conducted to test the simulation method. The advantage of the EC model is validated by comparisons of the EC model and two classical roughness models （sine wave and fractal function）, which shows that the EC model gives a more accurate description model for roughness, the maxi- mum error is 13%. The existence of roughness strongly broadens the beamwidth and raises the side-lobe level of SWA, which is 1.2 times greater than the ideal antenna. In addition, effect of the EC model＇s evaluation indices is investigated, the most affected scale of the roughness is found, which is 1/10 of the working wavelength. The proposed research provides the instruction for antenna designing and manufacturing.

Electromagnetic performance analysis of reflectorantennas with non-uniform errors along radius

Based on the works of Greve and Rahmat-Samii, theelectromagnetic （EM） performance of the reflector antenna withnon-uniform surface errors along radius is further addressed. Amathematical model is developed to describe the weighting functionfor the non-uniform surface errors along radius. Then, somediscussions on the peak gain loss （PGL） and the first sidelobelevel increase （SLLI） caused by the non-uniform surface errors arepresented and several significant radiation characteristics of thereflector with non-uniform errors are pointed out. Last, based onthe proposed model, the weighted root mean square （RMS） valueof the surface errors is produced to evaluate the EM performanceand several representative cases with different non-uniform errorsare presented with good results. Results show that the weightedRMS value should be taken into account for a better quality evaluationof the reflector surface.

Synchronization Control of Planar 2-DOF Robot with Redundant Actuation

Considering the special characteristics of the redundant parallel manipulator, with emphasis on the variable of structure, the relatively small workspace and the strong coupling relationship among arms, a synchronization control strategy is presented in this paper. Since in the feedforward, the inertial and the coriolis matrix are designed constant according to the relatively small workspace, position measurement of the endeffector in plane is ignored. Synchronization error and coupling error are introduced to reject the model errors of inertial and coriolis matrix as stated above. Using the method, the errors of driving arms can be reduced, and the synchronization performance among axes can be improved. The stability of the controllers was proved by Lyapunov method. Finally, experimental results show the feasibility of the method.