Research On Dynamics And Passivity-based Control For Flexible Space Structures

Due to the complexity of space missions,structures of spacecraft have been gradually becoming more flexible and larger.At first,flexible appendages were a type of flexible components outfitted on central rigid bodies,such as large-scale antennas,solar panels,etc.Then entire structures of spacecraft become large flexible structures while the central rigid bodies get smaller.Hence,a significant problem has emerged that to find methodologies to attenuate vibration of flexible structures and further to stabilize entire systems.The first step is to model dynamics of flexible structures,which can yield truncated dynamic equations.Control schemes can be designed based on these truncated dynamic equations to stabilize attitude of flexible space structures and to attenuate their vibration as well.To stabilize high-order modes and to avoid them spillover are worth to be paid more attention in the process of controller design.Moreover,given the usage of different shapes for some flexible space structures like disk solar sails,active shape control merits to be implemented to make the structure realize more functions.This thesis investigates the dynamic features of flexible space structures and devises a set of passivity-based control schemes for attitude stabilization and vibration suppression.An approach of active shape control for flexible structures are also presented.Hopefully,some research could be motivated by this thesis in the future.The outline of this thesis is given as follows.A gain-scheduled strictly positive real control scheme is presented for attitude stabilization and vibration attenuation of flexible space structures.This control scheme is proposed using the passivity theory which can stabilize closed-loop systems by regulating their energy.Firstly,a pair of collocated sensor and actuator are mounted at the central site of a rectangular flexible structure,which yields a passive dynamic system.Two distinctive gain scheduling signals are provided for two different types of actuators,thrusts and fly wheels,in the control system in which saturation of the fly wheel is considered.The stability of the closed-loop system is proved via Lyapunov approach.Numerical simulation results illustrate effectiveness of the proposed control scheme.Secondly,an output-based gain-scheduled controller is proposed for attitude stabilization and vibration suppression in repurposing a large annular flexible structure.All sensors’ outputs are selected as the gain-scheduled signals to maintain passivity of the structure equipped with multiple collocated actuators.Applying these special gain-scheduled signals permits the use of a strictly passive controller which degenerates to a scalar transfer function.The computational cost of the controller decreases dramatically.System stability can be guaranteed using the passivity theorem along with the Kalman-Yakubovich-Popov(KYP)Lemma.Numerical simulation results are given to make a comparison between the proposed gain-scheduled controller and a non-scheduled controller.In addition,optimal scheduling signals are found by minimizing vertical displacements on the rim of the structure,attitude errors,and control efforts so as to obtain good control performance.The gain-scheduled control scheme is then extended be applied on spacecraft attitude control with input quantization.A passivity-based controller with quantization for spacecraft attitude control is developed.This passive control scheme includes two parts which are a proportional controller for quaternion feedback and a strictly positive real controller for angular velocities.To alleviate the errors caused by quantization,a special modification for the nonlinear quantized input is employed in the strictly positive real controller.An asymptotic stability can be guaranteed with the presented controller.Numerical simulation results demonstrate the effectiveness of the proposed controller.In practice,collocation of sensors and actuators are almost impossible to be implemented due to the sizes of sensors and actuators.It is called non-collocation configuration and it can prompt passivity violation.A flexible structure system could maintain passivity at low frequency ranges and have a finite gain at high frequency ranges when sensors and actuators are put closely,which can be demonstrated through frequency domain analysis.A hybrid finite frequency controller is proposed for vibration suppression of a large flexible structure mounted with collocated sensors and actuators.The controller has passive characteristics at low frequencies and small gain characteristics at high frequencies.Compared with a strictly positive real controller based on the standard Kalman-Yakubovich-Popov(KYP)lemma,the hybrid finite frequency controller has less energy consumption but can obtain approximately identical performance.Furthermore,when the plant passivity is violated at high frequencies by non-collocation of sensors and actuators,the strictly positive real controller based on the KYP lemma is no longer able to attenuate the vibration of large flexible structures,while the hybrid finite frequency controller is effective in suppressing the vibration and avoiding spillover instability.Simulation results are presented to validate the effectiveness of the hybrid finite frequency controller.Besides,an analytical solution of Euler’s equation is exhibited using the Volterra series theory in the frequency domain.It provides motivation to implement the finite-frequency controller for Euler’s equation to accommodate its energy-transfer phenomenon.Simulation results are demonstrated to validate the effectiveness of the proposed hybrid finite-frequency control schemes.An interesting idea is attempting to control the shape of flexible structures actively to facilitate multi functional platforms.A flexible space structure could endow gyroelastic properties when a large number of spin rotors are implanted in it.This property can be used to change shape of flexible space structures from plain shapes to parabolic ones.The optimal control theory for dynamics governed by partial differential equations are introduced to generate optimal radial gyricity distribution.Furthermore,a flexible structure’s dynamic equations with three-dimensional gyricity terms are established using the Finite Element Method.In-plane stress is considered as well.Numerical simulation demonstrates the shape of flexible space structures can be changed successfully.