| In recent years,earth observation satellites,mobile communication satellites,and deep space exploration satellites have posed higher and higher design requirements for antenna gain,and large-aperture and high-precision have become the main development direction of spaceborne antennas.When the antenna diameter is determined,the shape precision of a reflector(root mean square(RMS)error of discrete points on the reflector surface)is the main factor affecting the antenna gain.A reflector could be affected by many factors to cause shape errors from design,manufacture to on-orbit operation,which in turn leads to a decrease in shape precision.The piezoelectric actuators are used to actively control the deformation of a reflector structure,which can effectively compensate for shape errors and improve on-orbit shape precision.At present,domestic and abroad researchers on the active shape control of reflectors mostly use open-loop control methods,which have a simple structure,but poor control precision,anti-interference ability,and robustness.Besides,the spacecraft needs to strictly restrict the number of power supplies of the control system to reduce weight and cost.This active shape control that needs to consider the constraint of the number of power supplies poses new challenges for the controller design and specific applications.In this dissertation,the researches focusing on how to realize the high-precision shape control for a grid reflector driven by the lead zirconate titanate(PZT)are carried out.The researches mainly include mechanical modeling of base structure/piezoelectric actuator and thermal deformation analysis for the reflector,active shape control of the high-precision reflector,active shape control using limited control system power supplies,and design and verification of the experimental system.The main works of this paper are as follows:(1)The integrated model of base structure/piezoelectric actuator for the grid reflector is established and its on-orbit thermal deformation is analyzed.The base structure model of the reflector is established by using the finite element method,and the equivalent model of the PZT actuator voltage is given by using the thermoelastic analogy method.The accuracy of the model is verified by the static deformation experiment for a plane hexagonal grid reflector model.The combination of the base temperature and the linear gradient is used to approximate the on-orbit temperature field of the reflector,and the thermal deformations under three typical temperature fields are analyzed.The analysis results show that the established finite element model of the grid reflector can accurately predict the deformation trend of the reflector surface.The three typical temperature loads cause large deformations,which results in a decrease in the shape precision.It is necessary to use an active shape control method to improve on-orbit shape precision.(2)The active closed-loop shape control of the high-precision reflector under model uncertainty is studied.A closed-loop control method based on least-squares(LS)is first proposed to solve the problem of ineffectively dealing with the model uncertainty using the traditional control method.This method is based on the influence coefficient matrix and finds the optimal control laws step by step through the feedback of the shape error.And then,an adaptive control method based on feedback error learning(FEL)for the on-line update model is proposed to solve the problem that the LS closed-loop control method does not converge due to the large model error existing in the influence coefficient matrix.This method is based on the generalized inverse model of the influence coefficient matrix,and the inverse model of the reflector system is online identified by using shape error and learning rate.An adjustment strategy of the learning rate according to the change of the shape error is proposed to ensure rapid convergence.The control laws are updated adaptively based on this inverse model,which effectively avoids the influence of reflector system model errors on the control accuracy.Finally,the effectiveness of the LS and FEL methods is verified through numerical simulations and experiments.The results show that the FEL method is less sensitive to model errors than the LS method.Even if a large model error exists in the influence coefficient matrix,the FEL method can not only control the reflector to achieve a high-precision shape but also identify an accurate reflector system model.(3)The active shape control of the reflector using limited control system power supplies is studied.Due to practical engineering restrictions on the weight and cost,the number of power supplies of the control system is constrained,and the controller is designed by optimizing the actuators grouping and the power supply voltage.The number of the power supply is predetermined,and the grouping design without connecting power supplies is proposed,which greatly improves the shape control effect.An optimization model for active shape control using the minimum RMS error as the objective function is established to study the control precision under the different quantities of power supplies.A hybrid optimization method is proposed to greatly reduce the difficulty and complexity of solving the large-dimensional solution space optimization problem caused by vast actuator groups and a wide range of the power supply voltage.A genetic algorithm is used to optimize the grouping of actuators,and then the LS method is used to optimize the power supply voltage.The simulation results show that the shape precision can still be improved by more than 90%,even if only two power supplies are used.Furthermore,a control method using the minimum energy consumption as the objective function and the shape precision as the constraint is proposed to reduce the power consumption of actuators,and the effectiveness is verified by numerical simulations.The results show that the proposed method can not only meet the shape precision requirement but also effectively reduce control energy consumption.(4)An experimental system applied to rapid verification of high-precision shape control algorithms is designed and built.A digital image correlation(DIC)binocular vision measuring instrument is used to measure the deformation of the reflector.Because of the high-frequency sampling characteristics of the DIC measuring instrument and the quasi-static characteristics of the active shape control process,a method of averaging multiple measurements is used to improve the measurement accuracy,which solves the problem of insufficient measurement precision for high-precision shape control in the actual work of this paper.The optimal control laws are calculated based on the measured data,the 30 PZT actuators are used for driving the 0.65m grid reflector to realize high-precision deformation.The experiment system realizes high-precision shape control by using the low-precision and low-cost measuring equipment.The experiment system is used to verify the effectiveness of the proposed FEL method.The experiment results show that the designed experiment system combined with the FEL method can achieve adaptive shape control of the high-precision reflector,which can provide an experiment platform for the development and verification of the high-precision control algorithm.The research of this paper provides theoretical methods for solving the mechanical modeling of the space-borne antenna reflectors,the high-precision active shape control,and the active shape control using limited power supplies,and it also provides a reference scheme for the design,integration,and application of the active shape control experiment system. |
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