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A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

• A time-averaged method is proposed for efficient analysis of slender rods moving in tubes. • Two time-averaged contact models are developed based on the time-averaged sample set between the time-averaged gaps and time-averaged forces. • The inclined and rolling experiments are conducted to validate the accuracy of the time-averaged method. • The high computational efficiency of the time-averaged method is confirmed compared with six continuous contact models. The motion of slender rods in narrow tubes involves the coupling of axial movements and transverse vibrations, in which the transverse vibration exhibits high frequency and chaotic characteristics. These characteristics render the computational cost of the time integration to the motions of rods and tubes expensive. To solve this problem, this paper proposes a novel time-averaged method, which contains two innovations: 1) By time averaging the traditional dynamic equations, the time-averaged dynamic equations describing the rod-tube system are established based on the time-averaged concept used in turbulence problems; 2) Two time-averaged contact models are developed, by fitting the time-averaged sample set using the polishing function and the machine learning, respectively, to construct the relationship between the time-averaged contact gaps and the time-averaged contact forces. The time-averaged method can use a large time step, which is far larger than that required for the time integration of traditional methods, thus reducing the computational cost. Inclined and rolling experiments of the rod-tube system, as well as numerical experiments of the control rod drop in a nuclear reactor, are conducted to validate the accuracy of the time-averaged method. Comparative analyses are carried out between the time-averaged method and six continuous contact models, demonstrating the high computational efficiency of the proposed method. Moreover, the experimental results can provide benchmark data for algorithm verification for scholars studying dynamic contact algorithms. [Display omitted] [ABSTRACT FROM AUTHOR]

• The mechanical friction force during the control rod drop is treated as a time-variant uncertainty for uncertainty analysis; • The interval process model is used to describe the time-variant uncertain mechanical friction during the CR drop; • The uncertainty analysis of CR drop considering various uncertain parameters is conducted; • A novel and general computational framework for uncertainty analysis of CR drop, UA-CRD, is proposed. Due to the influence of multiple factors, the control rod drop involves some uncertain parameters. The mechanical friction on the control rod is a time-variant uncertain parameter and is related to the position of the control rod. For the first time, this paper adopts the interval process model, which accurately describes the uncertainty parameters by using small-scale samples, to describe the uncertain mechanical friction on the control rod. The numerical experimental results demonstrate that the interval process model can describe the mechanical friction with high accuracy, even when employing small-scale samples. Furthermore, it is found that the uncertainty analysis can be considered as solving the extremal problem of a black-box model. Based on it, we propose a novel and general calculation framework for uncertainty analysis of control rod drop, UA-CRD. Through the analysis of numerical examples, it is verified that UA-CRD can accurately and efficiently conduct the uncertainty analysis of control rod drop. [ABSTRACT FROM AUTHOR]

• A deterministic simplified model of the control rod drop and fluid flow is established. • A fifth-order adaptive collocation stochastic perturbation (ACSP) method is established to approximate the random responses. • The uncertainty analysis of the CR drop based on the ACSP method is carried out in both large and small reactor. • The research results can provide guidance for the analysis and design optimization of the control rod scram process. There are many uncertain factors to affect the control rod drop from its design and manufacture to the chain reaction in the reactor. They have to be considered in the simulation to realistically predict the dynamic behavior of control rod drop. Different from the previous method by using the nominal and extreme values of the uncertain factors, a statistical method is applied in this paper to analyze them in the process of the control rod drop. The uncertain factors obey uniform distribution, based on which a fifth-order adaptive collocation stochastic perturbation (ACSP) method is established in this paper, which is featured with simple format, high precision, and high calculation efficiency. The mean and standard deviation of the responses (such as the final time of the control rod drop) in two different types of reactors are calculated by using the ACSP method. On this basis, the response intervals and corresponding probabilities of the control rod drop are obtained. Besides, influences of each random variable on the responses are analyzed by the sensitivity analysis. In addition, the linear correlation degree and correlation between the two are discussed through the correlation coefficient of random variables and the responses. The uncertainty analysis of control rod drop in this paper not only provides a relatively strong theoretical support for scientifically dealing with uncertain factors, but also offers specific help for the optimal design of control rod assembly. [ABSTRACT FROM AUTHOR]

This paper addresses the dynamic analysis of the clustered tensegrity structures via the framework of the positional formulation finite element method (FEM). The nodal coordinates are chosen as the generalized coordinates. The rod element and multi-nodes clustered cable element are first formulated. A comprehensive dynamic model for investigating the dynamic properties of the clustered tensegrity is then developed. The dynamic model is subsequently modified for the structural vibration analysis and modal analysis. The results of the modal analysis show that each order of natural frequency of a clustered tensegrity is lower than that of its corresponding classical tensegrity, indicating that the structure tends to be more flexible if a classical tensegrity is transformed into a clustered tensegrity. The results of the nonlinear deployment analysis show that the motion characteristics differ from those of the quasi-static analysis as the actuation speed increases. To pursuit a fast actuation speed to actuate the structure, mere quasi-static analysis in the existing literature is inadequate, and dynamic effects must be taken into account. The proposed method provides an effective tool to capture the dynamic properties, such as the determination of an appropriate actuation speed, and to actuate the clustered tensegrity. [ABSTRACT FROM AUTHOR]

This paper presents a sliding cable element for multibody system analysis. Unlike the existing literature on sliding cables developed using the finite element approach, the novelty of this approach is the use of the configuration of the attached rigid bodies as the generalized coordinates, rather than the traditional nodal displacements. The generalized force vector, and its related tangent stiffness and damping matrix, of the sliding cable and that of the classical cable element are analytically derived. It can also be found that the proposed sliding cable element can degenerate to the existing element formulated using the finite element approach. This allows us to use less generalized coordinates to address a system that contains few rigid or flexible body but with many pulleys. Then, this sliding cable element is employed to investigate the deployment of clustered tensegrity. Both quasi-static and dynamic analyses are carried out. Two representative examples show the effectiveness of the proposed element. The dynamic results also show that the motion characteristics of the system differ from the quasi-static solutions as the actuation speed increases. To achieve a fast actuation speed for deploying such systems, quasi-static analysis seems inadequate, and the dynamic effect must be taken into account. Under this background, the proposed element, coupled with the multibody dynamic methodology used in this work, does provide a powerful tool for analyzing the mechanical properties of such systems. [ABSTRACT FROM AUTHOR]

Control rod drop is the key part of ensuring the safety of nuclear reactor shutdown. Aiming at the control rod drop problem, we established a physical model of the control rod drive line. The proposed model considers the influence of the absorbing rod's position and hence evaluates the resultant force accurately on the control rod during the whole dropping process. Based on the physical model, a unified coupling state equation on the control rod drop and fluid flow is developed by integrating the motion variables of the control rod and the fluid into a state vector. A time step adaptive symplectic (TSAS) algorithm is proposed to solve the proposed state equation. The TSAS algorithm efficiently and stably predicts the motion states of the control rod and the fluid synchronously and accurately captures the sudden change of flow state. Numerical examples confirm the correctness of the proposed model and the TSAS algorithm. Sensitivity analysis is also conducted to discuss the effects of different parameters on the control rod drop, which provides reference and help for the design and manufacturing of the control rod drive line. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the design and computation of a guidance law for a transfer mission from an orbit near the Earth to a halo orbit around the libration point L 2 in the Sun–Earth system. The guidance law, which is designed based on receding horizon control and compensates for launch velocity errors that are introduced by inaccuracies of the launch vehicle, is solved using the generating function method. During the design of the closed-loop guidance law, the entire transfer mission, which is considered a nonlinear optimal control problem, is evaluated to obtain a nominal reference trajectory. Using the launch velocity errors and the uncertainty of the model, a spacecraft controlled by the proposed guidance law tracks the reference trajectory. Furthermore, the original Riccati differential equation in the receding horizon control algorithm is replaced by an equivalent convenient form of the Riccati differential equation that is based on the generating function. The high-efficiency solution of the equivalent equation avoids the online direct integration of the original Riccati differential equation, which significantly increases the computational efficiency for the receding horizon control problem. Numerical simulations using a nonlinear bicircular four-body model demonstrate the capabilities of the proposed receding horizon guidance law for the transfer mission. In addition, the generating function method improves the computational efficiency by at least one order of magnitude over the backward sweep method in solving the receding horizon control problem. [Copyright &y& Elsevier]

Abstract: An optimal periodic controller based on continuous low-thrust is proposed for the stabilization missions of spacecraft station-keeping and formation-keeping along periodic Libration point orbits of the Sun–Earth system. Additionally, a new numerical algorithm is proposed for solving the periodic Riccati differential equation in the design of the optimal periodic controller. Practical missions show that the optimal periodic controller (which is designed with the linear periodic time-varying equation of the relative dynamical model) overcomes the problems and limitations of the time-variant LQR controller. Furthermore, nonlinear numerical simulations are presented for the missions of a leader spacecraft station-keeping and three follower spacecraft formation-keeping. Numerical simulations show that the velocity increments for spacecraft control and relative position errors vary little with changes in the altitude of periodic orbits. In addition, the actual trajectories of the leader and the follower spacecraft track the periodic reference orbit with high accuracy under the perturbation of the eccentric nature of the Earth''s orbit and the initial injection errors. In particular, the relative position errors obtained by the optimal periodic controller for spacecraft formation-keeping are all in the range of millimeters. [Copyright &y& Elsevier]