Tension Control Law Research Articles

Tension Control Law for Three-Dimensional Deployment of a Geostationary Space Solar Power Station

Tension Control Law for Three-Dimensional Deployment of a Geostationary Space Solar Power Station

Dynamic Behavior Analysis and Stability Control of Tethered Satellite Formation Deployment.

In recent years, Tethered Space Systems (TSSs) have received significant attention in aerospace research as a result of their significant advantages: dexterousness, long life cycles and fuel-less engines. However, configurational conversion processes of tethered satellite formation systems in a complex space environment are essentially unstable. Due to their structural peculiarities and the special environment in outer space, TSS vibrations are easily produced. These types of vibrations are extremely harmful to spacecraft. Hence, the nonlinear dynamic behavior of systems based on a simplified rigid-rod tether model is analyzed in this paper. Two stability control laws for tether release rate and tether tension are proposed in order to control tether length variation. In addition, periodic stability of time-varying control systems after deployment is analyzed by using Floquet theory, and small parameter domains of systems in asymptotically stable states are obtained. Numerical simulations show that proposed tether tension controls can suppress in-plane and out-of-plane librations of rigid tethered satellites, while spacecraft and tether stability control goals can be achieved. Most importantly, this paper provides tether release rate and tether tension control laws for suppressing wide-ranging TSS vibrations that are valuable for improving TSS attitude control accuracy and performance, specifically for TSSs that are operating in low-eccentricity orbits.

Simulation and tension control of a tether-actuated closing mechanism for net-based capture of space debris

The growth of space debris in Earth's orbit is recognized as a serious threat to future space missions. To contain the growth of space debris in the long term, active removal of large defunct spacecraft is needed. A promising solution to this problem is the use of tether-nets. In the envisaged mission, a net is released from a chaser spacecraft toward a target debris; the net entangles the debris and the tether provides a flexible link between chaser and debris to tug the debris to a disposal orbit. The present work is focused on the simulation and control of a tether-actuated closing mechanism. In this concept, proposed only recently, the tether is looped through the center of the net and around the perimeter, and spooling the tether in draws the net perimeter closed. In this paper, a dynamic model of a tether-actuated closing mechanism for net-based capture of space debris is developed. The model of the winch, which is key to the control of the closing mechanism, is established based on literature on the design of reeling mechanisms for tether-nets. Two control laws for the winch velocity during deployment and closure of the net, respectively, are formulated and tested in simulation. Simulations of the capture of a Zenit-2 rocket upper stage are performed using a proportional-derivative tension control law with gain scheduling based on tether length. Results support feasibility of the tether-actuated closing mechanism.

Fixed-time terminal sliding mode control of spinning tether system for artificial gravity environment in high eccentricity orbit

In this paper a new strategy is introduced to produce an artificial gravity environment by spinning tether system (STS) in high eccentricity transfer orbit. Compared with other common artificial gravity environment methods, spinning tether system has simple structure, light weight and suitable spin velocity, which is more favorable for the spacecraft to generate the artificial gravity in the weightless space. The mathematical model of the spinning tether system is established by the second type of Lagrangian equation firstly. Then, the tension control law and the tangential thrust control law of tether system are designed. Through the mutual coordination of both control law, a method of Variable Moment-of-Inertia and Angular Momentum is realized which makes the tether system spin along the expected spinning velocity in most of the processes of uniform velocity development by constant tangential thrust. With the end of development, the artificial gravity environment level on the spacecraft also met the expected requirements, and the nominal trajectory curve of STS under the high-eccentricity transfer orbit was obtained. Finally, considering the rapidity of convergence time, a fixed time terminal sliding mode controller is designed to control the closed-loop trajectory curve of the tether system.

Dynamics and control of tethered multi-satellites in elliptic orbits

This paper studies the dynamics and libration suppression of tethered multi-satellites in elliptic orbits, where the tethered system is subject to periodic excitation resulting from the change of gravity gradient. The tethered system is modeled as a multiple dumbbell model and the relationship between periodical libration and tether length rate is studied. The outcome of study leads to a new tension control law to suppress the libration of tethered multi-satellites in a desired periodic motion by regulating tether length without thrust. The simulation results show that the libration motion of tethered multi-satellites is successfully stabilized to the desired periodic motion with the proposed tension control law. When the orbital eccentricity is small, the analytical solution of time-dependent tether lengths is derived to minimize the magnitudes of tether length rate. Furthermore, the tension control law is modified by including a sliding mode control to suppress initial external perturbations to increase the robustness of control law.

Nutation damping and spin orientation control of tethered space debris

As a preliminary of an active debris removal process, the attitude motion control of the debris need to be carried out to ensure security of following operations. The tethered space system is one of the most attractive methods for active debris removal missions. However, the tether tension becomes the only input to manipulate the attitude motion of the debris, causing a highly underactuated problem. Fortunately, the fully attitude stabilization of the debris is not a prerequisite for a secure deorbit operation. As long as the nutation of the debris is not so violent that makes the tether winds, the towing process can be applied continually, which is a significant advantage of the tether method. In this paper, a switched tension control law is presented to damp the nutation of the debris. Only two constant tension values are needed in the control method. Under the assumption that the tether direction is fixed in the inertia frame, the bounded stability of the control algorithm is proved based on the Barbalat's Lemma, and an asymptotic stability can be achieved for an asymmetrical debris symmetrically captured. Numerical simulations with tether libration considered are carried out to show the capability of the control method.

Deployment control of tethered space systems with explicit velocity constraint and invariance principle

This paper develops control laws for the deployment of tethered spacecraft systems with an explicit non-negative velocity constraint using invariance principle of control systems. It addresses a class of space tether deployment control problems where the tether is deployed out only. This implies the tether deployment velocity must be always positive and approaches to zero at the end of deployment. This non-negative velocity constraint is explicitly satisfied in the proposed tension control laws by transforming it into an invariance property of control system. Two control laws with nonlinear feedback are derived with two complementary manifolds. The Lyapunov stability of the control laws is proved and the controllability of the tethered spacecraft system with tension input is analyzed. Finally, the effectiveness of control laws is demonstrated by numerical simulation.

Stable orbital transfer of partial space elevator by tether deployment and retrieval

This paper investigates the stable orbital transfer of a climber in a partial space elevator system in circular orbits. The elevator includes a main satellite, an end body, and a climber, which are connected by two straight, inextensible, massless and variable length tethers. Derived from system dynamics, two closed-loop velocity control strategies are proposed to regulate the tethers' deploying and retrieving speeds directly to control the Coriolis forces acting on the climber and the end body directly. The stable region of the control strategies is analyzed, and the effectiveness of the proposed strategies is demonstrated by numerical simulation. Simulation results show that the newly proposed strategies effectively minimize the libration of a partial space elevator system during the orbital transfer of the climber and the system states successfully approach to the desired equilibrium by the end of the orbital transfer. Furthermore, the proposed deployment/retrieval control strategies can be converted to tension control laws easily.

Space tether deployment with explicit maximum libration angle constraint and tension disturbance

This paper investigates the deployment control problem of tethered space systems subject to an explicit constraint of maximum libration angle and disturbance of tether tension. A two-stage control procedure is developed to design a simple and effective tension control law that is capable of limiting the magnitude of libration angle and suppressing the tension disturbance in the tether deployment process. First, the deployment reference trajectory is designed by a modified barrier Lyapunov function with an explicit constraint on the maximum libration angle. Then, a disturbance observer-based tension control law is developed to track the reference trajectory with the consideration of tension disturbance. Stability analysis of the controller shows that the estimate and tracking errors are bounded to desired ranges. Simulation results demonstrate the proposed simple tension control law is effective and robust in restricting the maximum amplitude of libration angle and suppressing tension disturbance, while guaranteeing a stable deployment without tether slack.

Tether tension control law design during orbital transfer via small-gain theorem

Issues of controller design via small gain theorem for tethered satellite system (TSS) during orbit maneuvering under transversal thrust are considered. First, dynamic equations of tethered satellite system in orbital maneuvering are established based on a dumbbell model. It is proved that the in-plane system is weak minimum phase by selecting a proper Lyapunov candidate function, and there are some difficulties for controller designing based on nonlinear model directly. Next, a controller is designed by utilizing Small-gain Theorem based on a control oriented model. An input-to-state stable (ISS) based tether rate control law is derived as the reference signal for the tether length system. A tether tension control law is proposed such that the uncertainties caused by linearization will be suppressed by properly selected control parameters and the closed loop system will be forced to a small neighborhood of origin as time approaches infinity. Finally, numerical simulation results demonstrate the validity of the proposed algorithm.

Constrained tension control of a tethered space-tug system with only length measurement

The paper presents a tension control law to stabilize the motions of a Tethered Space-Tug system during its deorbiting process by regulating the tension in the tether. The tension control law is designed on a basis of two straightforward ideas, i.e., the potential energy shaping and the damping injection. The law is expressed in an analytical feedback form in terms of only the tether length without the need of the feedback of full state information. Meanwhile, the requirements of measuring velocities are removed with the aid of a dynamic extension technique based on the feedback interconnection of Euler-Lagrange systems. The positive and bounded tension constraint is taken into consideration explicitly by including a pair of special saturation terms in the feedback control law. The relative motions of the space-tug and the debris are described with respect to a local non-inertial orbital frame of reference, whereas the orbital motion equations of the system are formulated in terms of the modified equinoctial elements of the orbit. Finally, the effectiveness of the proposed scheme is demonstrated via numerical case studies.

Dynamic control of space tether deployment

This paper investigates the dynamic control of space tether deployment by: 1) optimal tuning of control gains of a simple tension law; 2) a passivity based tension law. The tethered spacecraft system is modelled with a nonlinear 'dumbbell' model. The tuned simple tension control law has the advantage of achieving fast tether deployment while keeping the simplicity of control law design. The passivity based control law has no overshoot of tether length and can reduce maximum in-plane pitch angle significantly. The simulation results demonstrate the efficiency and robustness of the proposed control methods.

Fractional order tension control for stable and fast tethered satellite retrieval

The retrieval of a tethered satellite system is intrinsically unstable. This paper develops a new control strategy to retrieve the tethered satellite system stably and quickly using the fractional order control theory. The governing equation of the tethered satellite system and classic linear feedback tension control law were first reviewed and examined as a benchmark. Then, a new fractional order tension control law has been to avoid the tethered satellite winds around the main satellite near the end of retrieval by existing integer order tension control laws. The newly proposed control law has been discretized and implemented by the Laplace transform and Tustin operator. Unlike the existing integer order control laws, which are based on the feedback of current state and memoryless, the fractional order control law has the memory of previous states and thus controls the tether retrieval more smoothly while maintaining the retrieving speed. The effectiveness and advantage of the new fractional order tension control law is demonstrated numerically by comparing with its integer order counterpart. The results show that the new control law not only retrieves the subsatellite without winding around the main satellite, but also provides a better control performance with smaller in-plane libration angles.

Deployment/retrieval optimization for flexible tethered satellite systems

A methodology for deployment/retrieval optimization of tethered satellite systems is presented. Previous research has focused on the case where the tether is modeled as an inelastic, straight rod for the determination of optimal system trajectories. However, the tether shape and string vibrations can often be very important, particularly when the deployment/retrieval speed changes rapidly, or when external forces such as aerodynamic drag or electrodynamic forces are present. An efficient mathematical model for flexible tethered systems is first derived, which treats the tether as composed of a system of lumped masses connected via inelastic links. A tension control law is presented based on a discretization of the tether length dynamics via Chebyshev polynomials. A scheme that minimizes the second derivative of length over the trajectory based on physically meaningful coefficients is presented. This is utilized in conjunction with evolutionary optimization methods to minimize the rigid body and flexible modes of the system during deployment/retrieval. It is shown that only a very small number of parameters are required to generate accurate trajectories. The results are compared to the case where the tether is modeled as a straight rod.

Extension of tethered satellites in the atmosphere

An important application of tethered satellites is atmospheric studies by extension of a subsatellite into the atmosphere through tether while the parent spacecraft flies at an altitude high enough so that the deleterious effects of the atmosphere on it are inconsequential. The key issue in the operation is the swift extension of the tether. Inordinate librations of the tether during extension are undesirable. Tension control, in conjunction with a thruster to control the out-of-pane motion, is a popular technique of control during extension. Many nonlinear feedback tension control laws based on Liapunov's direct method have been proposed. In this paper, an alternate technique, a linear state variable feedback control law is used. The control gains are determined from theorems in analytical mechanics. Simulation of the nonlinear equations using this controller affirms that the tether extends to the desired length in a reasonable amount of time.

Strategies for three dimensional deployment of tethered satellites

Tethered satellites deployed from the Space Shuttle have been proposed for diverse applications. A funda- mental issue in the utilization of tethers is quick deployment and retrieval of the attached payload. Inordinate librations of the tether during deployment and retrieval is undesirable. The structural damping present in the system is too low to contain the librations. Rupp [1] proposed to control the tether reel located in the parent spacecraft to alter the tension in the tether, which in turn changes the stiffness and the damping of the system. Baker[2] applied the tension control law to a model which included out of plane motion. Modi et al.[3] proposed a control law that included nonlinear feedback of the out-of plane tether angular rate. More recently, nonlinear feedback control laws based on Liapunov functions have been proposed. Two control laws are derived in [4]. The first is based on partial decomposition of the equations of motion and utilization of a two dimensional control law developed in [5]. The other is based on a Liapunov function that takes into consideration out-of-plane motion. It is shown[4] that the control laws are effective when used in conjunction with out-of-plane thrusting. Fujii et al.,[6] used the mission function control approach to study the control law including aerodynamic drag effect explicitly into the control algorithm.

A new tension control law for deployment of tethered satellites

Tethered satellites have been proposed for a variety of uses such as creation of artificial gravity, gravity gradient stabilization, minimization of impact loads during spacecraft docking, electrodynamic drives for spacecraft, power generators for spacecraft, exploration of the upper atmosphere, orbital transfer, aerodynamic deceleration of satellites to prepare for reentry, and as part of space escalators. The issue of deployment and retrieval of tethers from orbiting spacecraft (the Space Shuttle is the currently used the parent spacecraft) is critical to the success of the tethered satellite mission. The problem of deployment and retrieval of tethers from the Space Shuttle is extremely complicated because it leads to nonlinear time varying differential equations. One of the methods proposed for deployment and retrieval of tethered satellites is the tension control law [1]. In this method, the tension in the tether is varied in accordance with s predetermined control law to extend or retrieve the tether to the required length, while minimizing the oscillations of the tether. The governing equations being nonlinear, Liapunov's second method may be used to determine the tension control law. This approach has two drawbacks: firstly, Liapunov functions can be found only by trial and error, and consequently, the experience of the analyst plays a major role in the selection of the control law. The relaxation of any one of the assumptions made in the derivation of the equations would lead to a new set of governing equations, which in turn implies a new problem as far as the determination of the Liapunov function is concerned. Secondly, the procedure leads to a nonlinear control law. Despite these limitations, Vadali [2] and Fujii and Ishijima [3] have successfully employed this technique.

Real-time optimal state feedback control for tethered subsatellite system

Introduction A LTHOUGH many are devoted to the study of control problems of the tethered subsatellite systems, only a few papers treat the control problems as optimization problems. Bainum and Kumar introduced an optimal-control law based on an application of the linear quadratic regulator (LQR) to the tethered satellite system. They apply the tension control law, employing feedback of tether length, in-plane angle, their rates, and the commanded length for the deployment and retrieval and stationkeeping of the subsatellite; the performance index for the optimization problems is set to correct deviations from the instantaneous equilibrium state at each time. No and Cochran show that the LQR can be applied to control stationkeeping and maneuvering of the tethered subsatellite by utilizing the atmospheric aerodynamics, and the performance index for the optimization problem is set to correct deviations from the reference trajectory and to converge into the desired state at the final time. Netzer and Kane obtain an optimal-length law of the tethered subsatellite system with the performance index involving penalties on the terminal values of the states as well as on the states and controllers throughout the maneuver, and the optimal solution is used as a nominal path to follow. They show that the LQR can be applied to derive tracking-type feedback control law to decrease the deviation of the subsatellite from the nominal path by using the thrusters. On the assumption that the control force is only the tether tension and that no control force or energy dissipation exists for motion perpendicular to the tether line, Fujii and Anazawa obtain an optimal path in the sense that the time integral of squared tension plus squared in-plane angle is the performance index with inequality constraints on the control force. The Lyapunov approach is applied to derive the tracking-type feedback control law to follow the optimal path in Ref. 4. It is generally difficult to obtain the optimal path by solving the two-point boundary-value problem. To overcome this difficulty, Ohtsuka and Fujii adopted the stabilized continuation method, which converts the two-point boundary-value problem into the initial-value problem. Combining this method with the receding horizon control method, they have succeeded in developing the real-time optimal state feedback controller. This Note applies this real-time optimal state feedback control to the deployment and retrieval control problem of the tethered subsatellite and to determine the effective application of the control.

Nonlinear feedback deployment and retrieval of tethered satellite systems

The Lyapunov approach for controller design is applied to the tethered subsatellite deployment and retrieval problem. The tether dynamic model includes tether mass as well as in-plane and out-of-plane librations. The nonlinear feedback tension control law developed guarantees stability of the closed-loop system and is used in combination with out-of-plane thrusting during retrieval. Simulation results show the tension and the combined tension and thruster control laws perform well for deployment and retrieval, respectively, even when aerodynamic drag is considered.

Ground-based implementation and verification of control laws for tethered satellites

Davis and Banerjee (1990) have developed a tethered-spacecraft system model in which out-of-plane librations are damped, using a length-rate control after the tether has been deployed. Attention is presently given to the implementation of such control schemes to prototype hardware designed for space flight. A prototype reel mechanism has been constructed for use in the Getaway Tether Experiment; both the Davis and Banerjee control scheme and a converted tension-control law have been implemented with tether length and length rate available as feedback.