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It is well known that the traditional modeling theories adopt the Cartesian coordinates to establish the dynamic equation of solar array system. The order of this equation is often very high, which is inconvenient for controller design. The Cartesian coordinates are difficult to be measured in practice. In this paper, the joint coordinates are used...
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This article proposes a dynamic feedforward control method for a four-degree-of-freedom parallel robot in decoupling space to improve the control accuracy and robust stability. The mass matrix and the gravity component are obtained from the rigid-body dynamic model that is formulated by means of the link Jacobian matrices and the principle of virtu...
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... 7 Moreover, the motion forms of the space structure are also complex and diverse when they are in large scales, such as large maneuvering, [8][9][10] space movement of large manipulator, [11][12][13] rendezvous and docking, [14][15][16] and large-scale appendage deployment and locking. [17][18][19] For example, the flexible vibration of the solar panels poses a strong coupling effect on the attitude of the spacecraft body and the joint motion of the robotic arm for large or substantially large spacecraft platforms with enormous flexible solar panels, such as GEO communication satellites. 20 Therefore, these problems cannot ignore the influence of structural deformation or vibration characteristics. ...
A spacecraft composed of a central body and flexible appendages is a typical rigid-flexible coupling system. Current modeling methods generally regard the central body as rigid. As the central body becomes larger and more flexible, the elastic deformation of the central body may not be ignored. In this study, considering the flexibility effect of the central body and based on the recursive kinematics, a complete coupled dynamic model of the orbit, attitude, and elastic deformation of a fully flexible spacecraft is established. Compared with traditional methods, the model has smaller generalized coordinate dimension and can more clearly reveal the kinematic relationship between the appendages and the central body. By comparing the simulation results of typical working conditions with the ADAMS software, the correctness of the built model is verified. The PD controller for the attitude of the spacecraft is used, and three models of different rigid/flexible settings are compared in detail. The dynamic response of the system in uncontrolled and controlled states are discussed. Numerical simulation results show that the flexibility of the central body poses a certain influence on the attitude response of the spacecraft, the flexible vibration of the appendages, and the attitude control accuracy.
... Therefore, the considered two-dimensional approach will be incorrect. In a real situation, many characteristic sizes of the solar panels of various small spacecrafts allow us to neglect transverse oscillations compared with longitudinal ones [18,23]. Therefore, this hypothesis has a basis. ...
... Taking into account the expression for temperature (20) and derivative (22), Equation (23) can be rewritten as follows: ...
The paper investigates the stress–strain state of a homogeneous rectangular plate after a temperature shock. It is believed that the plate is the first approximation of the solar panel model of a small spacecraft. To study the stress–strain state of the plate, a two-dimensional thermoelasticity problem is posed. The problem has a static formulation, since it does not take into account the dynamics of the plate’s natural oscillations. These oscillations affect the stress–strain state through the initial deflection of the plate at the time of the temperature shock. This deflection changes the parameters of the temperature shock and does not allow the use of a one-dimensional formulation of the thermoelasticity problem. As a result of solving the static two-dimensional thermoelasticity problem, approximate solutions are obtained for the components of the plate point’s displacement vector after the temperature shock. An approximation of the temperature field is presented. A numerical simulation is carried out. The correspondence of the obtained approximate analytical dependencies of the components of the plate point’s displacement vector to the numerical simulation data is analyzed. The proposed method can be used to assess the significance of the influence of the small spacecraft’s solar panels temperature shock on the dynamics of its rotational motion.
... Multiple flexible components jointed by hinges appear in variety engineering field, such as the aircraft wing [1], flexible planar manipulators [2], deployable solar arrays [3] and so on. The solar array that consists of multiple plates is deployed when the spacecraft is on orbit. ...
The dynamical modelling method and nonlinear characteristics of the multi-plate structure are investigated in this paper. The structure presents as a chain, which consists of multiple plates and adjacent plates are connected by a long hinge. The length of the hinge should be considered therefore the boundary conditions of each plate are discontinuous. A novel constraining method based on the power series polynomial is proposed to establish the mathematical model of the connection and constraint for the plate with the local restrained boundary. The characteristic equation of the multi-plate structure is derived by using the Rayleigh–Ritz method and then natural frequencies are obtained. The discrete nonlinear dynamical equation is established by using the obtained linear modal shapes. By comparing natural characteristics with the result of the finite element model, the correctness of the present model and the validation of the proposed method are verified. The modal analysis shows that the complex frequency phenomena are due to the different influence of the long hinge on symmetric and antisymmetric modes of each plate. The parameter analysis reveals nonlinear characteristics of the whole multi-plate structure. Numerical results demonstrate that the proposed constraining method can impose constraints on interval discontinuous boundaries of the plate, which goes beyond the traditional Lagrange multiplier method.
... Friction phenomenon is very complex, which have been discussed and reviewed by many scholars, including Stribeck effect [15] , friction hysteresis [16] , pre-sliding characteristics [17] , and critical friction [18] . In the process of dynamics modeling of mechanism with clearance, the influence of friction force on mechanism dynamics has attracted the attention of scholars [19][20][21] . ...
The contact force of the clearance joints in the mechanical system is strongly nonlinear, which is influenced by the amount of clearance, the material property of the parts and the contact state during movement. In some fields which need to control the dynamic response of mechanical system accurately, it is very important to predict the contact process of clearance joints and the time-frequency characteristics of contact force. In this paper, a dynamic modelling method combining neural network model and co-simulation technology is proposed, which can effectively model and simulate the mechanical system with clearance. The contact friction data set is generated based on the friction experiment of sliding bearing, and the contact collision force data set is generated based on the theoretical model of impact force. The nonlinear contact force neural network model of clearance joints is constructed by deep learning method, and transplanted to Simulink. According to the 3D model of transmission test bench, the dynamic simulation model of mechanical system is established by using ADAMS, and the fusion of neural network model and traditional dynamics model is finally realized based on Simulink/ADAMS co-simulation technology. The creativity of this method lies in the use of neural network model to describe the clearance joints and the use of ideal constraints to describe other kinematic pairs. The combination of force and constraint can not only improve the accuracy of solution, but also ensure the fast calculation speed, which provides a feasible idea for the application of deep learning method in the direction of nonlinear system dynamics modelling.
... With an emerging range of high technology science missions, dynamicists have been concerned with the effect of flexible structures on spacecraft attitude control systems and payloads. The equations that govern flexible bodies undergo large angular motions which are coupled and nonlinear [1], although the exact modeling of structural flexibility and interaction of rigid-flexible body behavior will also be challenging [2][3][4][5][6][7][8]. All these issues contribute to wider control bandwidth and a lower structural frequency, resulting in the possibility of structural-control system interactions. ...
This paper is aimed at developing several control scenarios for vibration suppression of a flexible microsatellite as a multibody system with nonlinear fully coupled dynamics in different but interconnected in-orbit mission phases. The design approach is to exploit different actuators in a single and hybrid configuration with an optimal switching mechanism to achieve a desirable maneuvering performance by means of agility and accuracy. In this regard, a genetic algorithm (GA)-particle swarm optimization (PSO) based nonsingular terminal sliding mode control (GP-NSTSMC) and extended Lyapunov-based controller design (LD) are developed to cope with the limitations of bounded uncertainty and external disturbances. Great features of the GP-NSTSMC are its gains which are selected based on two major criteria, system energy and maneuver time, and for LD we consider the piezoelectric (PZT) and reaction wheel (RW) performance in the form of mechanical and electrical energies in the structure of the control algorithm. Despite the capabilities of these algorithms, they still excite high-frequency flexible modes. Accordingly, by applying feedback voltages to the PZTs, the extra vibration is actively damped, where the strain rate feedback (SRF) method is set to determine the control voltages. Furthermore, to satisfy one of the mission’s requirements, which is solar panels deployment, a classical Levenberg–Marquardt (CLM) technique for online mass property identification along with an effective fault detection scenario is employed. A comparative assessment of the proposed hybrid actuator/controllers is presented to clarify the technical aspects of this multimode scenario for further investigations and practical real-time space missions.
... Najafizadeh et al. [52] designed a novel fuzzy PID controller for geostationary satellite attitude control, which achieved faster convergence rates and higher accuracy. Li et al. [4,53] designed a fuzzy PD controller to compensate for the attitude change of the spacecraft caused by the deployment of solar arrays. Although the above mentioned studies have investigated the adaptive fuzzy PID/PD control scheme for attitude control of the spacecraft, there are very few researches on eliminating the attitude and position drift caused by the deployment of solar arrays. ...
... Once the deployment angle θ k reaches the collision point ( φ 3 ∼ φ 4 ), the BISTOP function begins to produce torques to push pin F toward the expected angle. ese lock torques can be expressed as [15,53] where _ θ k is the relative rotation velocity of the k-th solar panel. K s and c are the equivalent stiffness and damping coefficients of the latch mechanism, respectively, d denotes the distance depth, and e is an exponent. ...
... Fuzzification maps the input state errors (e and ec) into two fuzzy variables (E and EC) that are defined with three fuzzy sets where the associated linguistic terms are negative (N), zero (Z), and positive (P) by using membership functions. e fuzzy IF-THEN rules are adopted to relate these fuzzy sets to output fuzzy gains with the Mamdani-type fuzzy inference [53]. Defuzzification converts the output linguistic variables into precise numerical values. ...
Modern spacecraft are often equipped with large-scale, complex, and lightweight solar arrays whose deployment involves a highly dynamic movement. This paper proposed a novel adaptive proportional-derivative typed fuzzy logic control scheme for the attitude stabilization of a flexible spacecraft during the deployment of a composite laminated solar array. First, a constrained rigid-flexible coupling spacecraft model consisting of a rigid main body and a flexible solar array was proposed. The solar array, which is composed of composite laminated shells, was described by the absolute nodal coordinate formulation. Then, the detailed derivation of the adaptive fuzzy PD controller for attitude stabilization of the spacecraft was discussed. In addition, the spacecraft dynamic model which integrated the adaptive fuzzy PD controller was derived as a set of differential-algebraic equations. Several simulations were developed to investigate the solar array deployment dynamics and to verify the effectiveness of the proposed adaptive fuzzy PD controller. The results suggested that the proposed dynamic model is able to exactly describe the deployment dynamics of the composite laminated solar array. The solar array deployment causes obvious translational and rotational motions of the spacecraft. The proposed adaptive fuzzy PD control scheme has better performance in terms of the control precision and time response in stabilizing spacecraft during the deployment of the composite laminated solar array, comparing with that of the conventional PD controller.
... The existence of friction in kinematic pairs not only has a negative influence on spacecraft lifetime and reliability but also complicates the design procedure. Reducing the impact of frictional torque on a reaction wheel's attitude-adjustment function to obtain better control accuracy requires complex algorithms to compensate for the effect of friction [101][102][103]. There are also cases in which antennas fail to deploy because of friction [104]. ...
Superlubricity has been developing very rapidly in recent years as a new and important area in tribology. Many new phenomena and materials, as well as some new mechanisms in both liquid and solid superlubricity have been obtained. In liquid superlubricity, tens of new kinds of liquids with superlubricity have been found (e.g., water-based liquids, oil-based lubricants, and liquids combined with additives of two-dimensional (2D) materials that exhibit very good superlubricity properties under high pressure). In the field of solid superlubricity, more materials with superlubricity have been observed, including graphene-to-graphene surfaces, highly oriented pyrolytic graphite to graphene surfaces, and heterostructure surfaces where a friction coefficient as low as 0.00004 has been obtained. However, superlubricity is still under laboratory research. What is the future of superlubricity? What is the barrier restricting superlubricity from industrial applications? How do we transfer superlubricity from scientific research to industrial application? These questions and application fields of superlubricity in near future have been analyzed, and the concept of “superlubricitive engineering” has been proposed in the present work.
... Li et al. [22] investigated the coupling effects of joint clearance and panel flexibility on the overall dynamic characteristics of a deployable solar array system. Li et al [23,24] established the dynamic equation of the solar array system by using single direction recursive construction method and the Jourdain's velocity variation principle to study the deployment and control of flexible solar array system considering joint friction. Furthermore, Li et al. [25] established the rigid-flexible coupling dynamics model of deployable solar array system with multiple clearance joints based on nodal coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) to analyze and control satellite attitude under deployment disturbance, and presented significant guidance for the key parameters design of torsional spring, closed cable loops (CCL) configuration, and latch mechanism [26]. ...
... A BISTOP function is introduced to present the equivalent moment T lock in the latch mechanism [23][24][25][26]. BISTOP function allows free motion between x 1 and x 2 at which point the contact function begins to push the joint back toward the expect center angle. ...
This paper establishes a thermal-structural coupling model of planar spacecraft system with large flexible composite solar array under nodal coordinate formulation and absolute nodal coordinate formulation framework. Perfect revolute joint is adopted as connection type to give the different influences from fixed constraint used in previous researches, and consequently, torsional spring, latch mechanism, and attitude controller are involved into the spacecraft system. Imperfect revolute joint is further introduced to investigate the coupling effects of thermal load, adjustment motion, and joint clearance on dynamics of the system, including spacecraft attitude, solar panel responses, and wear prediction. Results of six comparison models (with or without clearance joint, considering thermal environment, or adjustment motion, and considering both these two conditions) show that the coupling effect of thermal environment and overall motion brings dramatic and unmanageable shock to the system with clearance joint, that is no longer can be seen as a simple superposition of each single condition effect like the system with ideal joint, although the suspension damper property of clearance joint can weaken thermal-induced vibration or motion induced vibration separately. For a period after attitude adjustment, wear depth of the system subjected to solar radiation is two orders of magnitude lager than that of the system without considering thermal environment. Joint clearance and thermal environment should be considered both; for on-orbit spacecraft system, the coupling effects of them are significant and non-ignorable for relevant mechanism design and performance analysis.
... A novel computational approach for modeling and analysis of a spacecraft with symmetric flexible solar arrays within the framework of global analytical modes was proposed [16][17][18][19] . Li et al. [20][21][22][23] investigated the deployment dynamics of a spacecraft solar array system with joint friction and developed a fuzzy proportional derivative (PD) controller to eliminate the drift of the base spacecraft. ...
... The trajectory state regulation problem is stated as an optimal control problem, i.e., find the required control inputs δu(t) and corresponding state variables δx(t) which satisfy Eq. (22) and minimize the following performance index: ...
... The traditional numerical method, such as the tool function LQR in MATLAB, is used to solve the strong backward integration problem of the matrix Riccati differential equation (29), which not only consumes a large amount of calculation time, but also may lead to numerical instability. Thus, the indirect pseudospectral method is used in this paper to obtain the optimal feedback control of the linear control system (22). ...
A control strategy combining feedforward control and feedback control is presented for the optimal deployment of a spacecraft solar array system with the initial state uncertainty. A dynamic equation of the spacecraft solar array system is established under the assumption that the initial linear momentum and angular momentum of the system are zero. In the design of feedforward control, the dissipation energy of each revolute joint is selected as the performance index of the system. A Legendre pseudospectral method (LPM) is used to transform the optimal control problem into a nonlinear programming problem. Then, a sequential quadratic programming algorithm is used to solve the nonlinear programming problem and offline generate the optimal reference trajectory of the system. In the design of feedback control, the dynamic equation is linearized along the reference trajectory in the presence of initial state errors. A trajectory tracking problem is converted to a two-point boundary value problem based on Pontryagin’s minimum principle. The LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations which can be easily calculated. Then, the closed-loop state feedback control law is designed based on the resulting optimal feedback control and achieves good performance in real time. Numerical simulations demonstrate the feasibility and effectiveness of the proposed control strategy.
... Considering panel flexibility and multiple clearance joints, Li et al. [49,50] further studied dynamics of deployable solar array system with multiple clearance joints and given some design suggestions of the whole system by using commercial software ADAMS. Hai-Quan Li et al. [51] study the deployment and control of flexible solar array system considering joint friction without normal contact force. However, to study the effects of joint clearance on attitude of solar array system with flexible panels, considering both contact force and friction force, is still insufficient. ...
... The BISTOP function allows free motion between x 3 and x 4 at which point the contact function begins to push the joint back towards the expect center angle. The specific details are set referencing literature [5,51,52]. ...
Based on Nodal Coordinate Formulation (NCF) and Absolute Nodal Coordinate Formulation (ANCF), this paper establishes rigid-flexible coupling dynamic model of the spacecraft with large deployable solar arrays and multiple clearance joints to analyze and control the satellite attitude under deployment disturbance. Considering torque spring, close cable loop (CCL) configuration and latch mechanisms, a typical spacecraft composed of a rigid main-body described by NCF and two flexible panels described by ANCF is used as a demonstration case. Nonlinear contact force model and modified Coulomb friction model are selected to establish normal contact force and tangential friction model, respectively. Generalized elastic force are derived and all generalized forces are defined in the NCF-ANCF frame. The Newmark-β method is used to solve system equations of motion. The availability and superiority of the proposed model is verified through comparing with numerical co-simulations of Patran and ADAMS software. The numerical results reveal the effects of panel flexibility, joint clearance and their coupling on satellite attitude. The effects of clearance number, clearance size and clearance stiffness on satellite attitude are investigated. Furthermore, a proportional-differential (PD) attitude controller of spacecraft is designed to discuss the effect of attitude control on the dynamic responses of the whole system.
