Spacecraft Control Laboratory Experiment Research Articles

Passive vibration control of the SCOLE beam system

We investigate the optimization of multiple tuned mass dampers (TMDs) to reduce vibrations of flexible structures described by partial differential equations, using the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) beam system with multiple dominant modes as an illustrative application. We use multiple groups of TMDs with each group being placed at the antinode of the mode shape of a dominant mode of the SCOLE beam. We consider both the harmonic and random excitations, for which we employ frequency-limited H ∞ and H 2 optimizations respectively to determine the parameters of the TMDs. Our optimization scheme takes into account the trade-off between effectiveness and robustness of the multiple TMDs to suppress the multiple dominant modes of the SCOLE beam. Simulation studies show that our scheme achieves substantial improvements over the traditional methods in terms of both effectiveness and robustness and that with equal total mass, TMD systems with each group having multiple TMDs are more effective and more robust than the ones with each group having a single TMD.

Stability Properties of Coupled Impedance Passive LTI Systems

We study the stability of the feedback interconnection of two impedance passive linear time-invariant systems, of which one is finite dimensional. The closed-loop system is well known to be impedance passive, but no stability properties follow from this alone. We are interested in two main issues: 1) the strong stability of the operator semigroup associated with the closed-loop system, 2) the input–output stability (meaning transfer function in $H^\infty$ ) of the closed-loop system. Our results are illustrated with the system obtained from the nonuniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, connected with a trolley mounted on top of the rigid body, via a spring and a damper. Such an arrangement, called a tuned mass damper (TMD), is used to stabilize tall buildings. We show that the SCOLE-TMD system is strongly stable on the energy state space and that the system is input–output stable from the horizontal force input to the horizontal velocity output.

Load reduction of a monopile wind turbine tower using optimal tuned mass dampers

ABSTRACTWe investigate to apply tuned mass dampers (TMDs) (one in the fore–aft direction, one in the side–side direction) to suppress the vibration of a monopile wind turbine tower. Using the spectral element method, we derive a finite-dimensional state-space model Σd from an infinite-dimensional model Σ of a monopile wind turbine tower stabilised by a TMD located in the nacelle. Σ and Σd can be used to represent the dynamics of the tower and TMD in either the fore–aft direction or the side–side direction. The wind turbine tower subsystem of Σ is modelled as a non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) system consisting of an Euler–Bernoulli beam equation describing the dynamics of the flexible tower and the Newton–Euler rigid body equations describing the dynamics of the heavy rotor-nacelle assembly (RNA) by neglecting any coupling with blade motions. Σd can be used for fast and accurate simulation for the dynamics of the wind turbine tower as well as for optimal TMD designs. We show that Σd agrees very well with the FAST (fatigue, aerodynamics, structures and turbulence) simulation of the NREL 5-MW wind turbine model. We optimise the parameters of the TMD by minimising the frequency-limited -norm of the transfer function matrix of Σd which has input of force and torque acting on the RNA, and output of tower-top displacement. The performances of the optimal TMDs in the fore–aft and side–side directions are tested through FAST simulations, which achieve substantial fatigue load reductions. This research also demonstrates how to optimally tune TMDs to reduce vibrations of flexible structures described by partial differential equations.

Strong stabilisation of a wind turbine tower model in the plane of the turbine blades

We investigate the strong stabilisation of a wind turbine tower model in the plane of the turbine blades, which comprises a nonuniform NASA Spacecraft Control Laboratory Experiment (SCOLE) system and a two-mass drive-train model (with gearbox). The control input is the torque created by the electrical generator. Using a strong stabilisation theorem for a class of impedance passive linear systems with bounded control and observation operators, we show that the wind turbine tower model can be strongly stabilised. The control is by static output feedback from the angular velocities of the nacelle and the generator rotor.

Suppression of the vibrations of wind turbine towers

We investigate the suppression of the vibrations of a wind turbine tower using colocated feedback to achieve strong stability. We decompose the system into one model describing the vibrations in the plane of the turbine axis and another model in the plane of the turbine blades. In the plane of the turbine axis, we obtain a non-uniform Spacecraft Control Laboratory Experiment (SCOLE) model with either force control or torque control. We show that this system is strongly stabilizable by static output feedback from either the velocity or the angular velocity of the nacelle. In the plane of the turbine blades, we model the wind turbine tower as a non-uniform SCOLE system coupled with a two-mass drive-train model, the control being the torque created by the electrical generator. We prove that generically, this system can be strongly stabilized by feedback from the angular velocity of the nacelle and the angular velocity of the generator rotor.

L-shaped structure mass and stiffness matrices by substructure synthesis

The L-shaped structure is a basic and important engineering structure. Its dynamic characteristics have drawn attention since the sixties, being Hurty [1] one of the first to study the vibrations of this two-member open frame, not surprisingly, by using his componentmode synthesis method. Nonetheless, not much work was reported until some structures in engineering practice seemed to be well modeled by the L-shaped beam system, for example, the NASA Spacecraft Control Laboratory Experiment structure [2]; in general, some space structures, as antenna reflectors, and mechanical systems, as robots and earth movers, can definitely be analyzed using this model [3, 4]. Thus, there has been recently quiet an interest in the dynamics of this structure, being a discussion which solution, the analytical or the FEM, is more convenient in the case of this simple system [3, 5, 6]. For simple structures, it can be concluded that the analytical solution is more diffi-

Strong Stabilization of a Non-uniform SCOLE Model

The SCOLE (NASA Spacecraft Control Laboratory Experiment) model is considered the best model for the coupled system consisting of a flexible beam with one end clamped and the other end linked to a rigid body. This model has been studied extensively, with most papers assuming that the flexible beam is uniform. In our study we allow the coefficients of the beam equation to vary with position, like in Guo [2002] which has considered the non-homogeneous structure of the beam. It has been proved that the exponential stabilization of the uniform SCOLE model is impossible to achieve by boundary feedback from the natural output signals (the speed and the angular velocity of the rigid body) (see Rao [1995]). Thus the non-uniform SCOLE model is not exponentially stabilizable in general, by using these signals. Although the exponential stabilization of the SCOLE model can be obtained by high order output feedback (see Guo [2002] and Rao [1995]), the corresponding closed-loop system is not well-posed. In addition, such a feedback is difficult to realize in practice. Thus we have to compromise for strong stabilization. Following a recent strong stabilization theorem for passive systems in Curtain and Weiss [2007], we have shown that the non-uniform SCOLE model is strongly stabilizable by static output feedback from either the speed or the angular velocity of the rigid body.

On the Boundary Control of a Hybrid System with Variable Coefficients

A model of the spacecraft control laboratory experiment with variable coefficients is considered. It is shown that the closed-loop system under boundary feedback damping has a sequence of generalized eigenfunctions, which form a Riesz basis for the state Hilbert space. The spectrum-determined growth condition, the exponential stability, and an asymptotic expression of the spectrum are obtained. Moreover, the exact controllability and exact observability of the system are also presented.

Stability and robustness analysis of boundary control of a flexible space structure

Abstract We consider the question of the robustness of boundary control for a simplified SCOLE (spacecraft control laboratory experiment) model. A continuum model consisting of a long flexible mast joining two rigid bodies, one of which represents the space shuttle orbiter, the other an antenna reflector, is developed. The dynamics of the system are represented by a coupled set of ordinary and partial differential equations, and formulated as a wave equation in a Hilbert space by using a semigroup approach. For a continuum, distributed controls have often been proposed to stabilize the perturbed system. However, distributed controls for the continuous system are not practical to implement. Hence, for easy implementation we employ the boundary controls, as a special class of localized controls, that are control forces or torques applied only at the boundary. In this paper it is shown that the flexible system subject to a certain class of perturbations remains stabilizable by the same boundary feedback cont...

Integrated modeling and control for the Large Spacecraft Control Laboratory experiment facility

A software package which integrates model reduction and controller design is applied to design controllers for the Jet Propulsion Laboratory Large Spacecraft Control Laboratory experiment facility. Modal cost analysis is used for the model reduction, and various output covariance constraints are guaranteed by the controller design. The main motivation is to find the controller with the best performance with respect to output covariances. It is shown that by iterating on the reduced-order design model, the controller designed does have better performance than that obtained with the first model reduction, demonstrating an effective strategy for integrating modeling and control design.

Nonlinear rotational maneuver and vibration damping of NASA SCOLE system

We treat the question of large rotational maneuver and vibration stabilization of NASA Spacecraft Control Laboratory Experiment (SCOLE) system. The mathematical model of SCOLE system includes the dynamical equations for rigid body slew maneuver and three-dimensional vibration of the flexible beam and the reflector with an offset mass. The design approach taken here is to decompose the rigid mode control from vibration stabilization. Feedback input (Shuttle torque)-output (attitude angles) map linearization technique is used for designing attitude control system for large-angle slewing. Linearization of the input-output (i-o) map is accomplished by nonlinear inversion theory. It is shown that attitude control system asymptotically decouples the flexible dynamics and a linear feedback law is easily designed for vibration suppression. For the synthesis of the control law an observer is designed. Simulation results are presented to show that in the closed-loop system large angle maneuvers can be accomplished using only the measured state variables.

Active damping of flexible structures via saturating actuators

Abstract The active damping aspect is treated of the spacecraft control laboratory experiment (SCOLE). A continuum model, rather than a finite element model, is used. First, a group of rather weak sufficient conditions for strong stabilizability is presented. Structural passive damping is no longer required to be positive definite and, in fact, can even be zero, while strong stabilizability can still be achieved by active damping. Then, the mode excitation problem is studied for both linear and (saturating) nonlinear active damping. The popular notions of ‘characteristic equation’ and ‘root locus’ in feedback control are extended to our distributed parameter system, which is a feature of this work. The root locus provides an insight into the nature of active damping

Dynamics and control of the Shuttle based large antenna system during slewing maneuvers

A relatively general formulation for studying dynamics of a large class of interconnected flexible and/or rigid bodies forming a chain type topology is developed. The problem is approached using the Lagrangian procedure with the generalized forces accounting for the environmental effects, damping and control. The flexible members are taken to be the Euler-Bernoulli beams with their bending and torsional deformations discretized using a series of admissible functions. As a particular case, the general formulation is applied to study complex dynamics of the SCOLE (Spacecraft COntrol Laboratory Experiment) system as proposed in the NASA's design challenge. The classical infinite time linear state feedback regulator utilizing the Shuttle's primary and vernier thrusters is designed to suppress the vibrations as well as control the Shuttle attitude motion. The results suggest that flexibility of the mast during the prescribed slewing maneuver substantially induces the line-of-sight error if the Shuttle is uncontrolled. However, the proposed control strategy can damp both the vibrational motion of the mast and librational motion of the Shuttle to the specified acceptable limit within 5 s of the completion of the maneuver.

Detumbling and reorientation maneuvers and stabilization of NASA SCOLE system

The questions of rotational maneuver and vibration stabilization of the NASA Spacecraft Control Laboratory Experiment (SCOLE) system is considered. The mathematical model of the SCOLE system includes the rigid body dynamics as well as the elastic dynamics representing transverse and torsional deformations of the elastic beam connecting the orbiter and end body (reflector). For the rotational maneuver, a new control law (orbiter control law) is derived using an orbiter input torque vector. Detumbling and reorientation maneuvers of the SCOLE system are accomplished using this control law; however, this excites the elastic modes of the beam. The orbiter control law asymptotically linearizes the flexible dynamics. Using the linearized model, a linear feedback control law is designed for vibration suppression. An observer is designed for estimating the state variables using sensor outputs which are also used for the synthesis of the control law. Simulation results are presented to show that in the closed-loop system detumbling and reorientation maneuvers can be accomplished and the effect of control and observation spillover is insignificant.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modeling of a Shape Memory Integrated Actuator for Vibration Control of Large Space Structures

Martin Marietta is developing a shape memory material actuator to pro vide active vibration and shape control for large, adaptive space structures. An important facet of this work is the development of analytical modeling capabilities for shape memory material behavior. These alloys exhibit a very interdependent force-length-temperature (FLT) response, which must be understood to best exploit their behavior for the efficient and timely conversion of heat into mechanical work. Also, the modal response of large, flexible space structures will be affected by the use of inherently non-linear, hysteretic shape memory actuators, and specialized control methodologies need to be developed spe cific to this application. In this work, Cory and McNichols' theory of non-equilibrium thermostatics (NET) was modified to account for the multiple quadrant (i.e., tension and compression) hysteretic behavior of shape memory alloys. Experimental results were used to provide the basis for spatial mapping of the austenite-to-martensite ( AM) and mar tensite-to-austenite ( MA) phase transformation boundaries, along with the relative loca tions of the 100% austenite ( ZA) and 100% aligned martensite ( ZM) saturation surfaces in the three-dimensional FLT material behavior domain. A Fortran subroutine, describing the shape memory material actuator, was incorporated into dynamic analyses of a simpli fied finite element model based on the Spacecraft Control Laboratory Experiment (SCOLE) structure. A slewing maneuver of 20 degrees in 12 seconds was used to study a number of cases for the shape memory actuator which utilized a biasing force (e.g., the biasing effect of a matrix in a strain-compliant shape memory composite) acting against 150 NiTi wires (0.5 mm dia. by 0.50 m in length). Temperature was used as the command variable to demonstrate active vibration control during and after the slew maneuver. Sig nificant passive damping was noted, in addition to effective active control when the actua tor's temperature was pulsed. This analytic "test bed" will provide critical insight into the design and analysis of smart, adaptive shape memory space truss tubes and actuators for vibration and shape control, as well as the vehicle by which future shape memory actuator control algorithms and methodologies can be assessed.

Analytic Redundancy Management for Systems with Appreciable Structural Dynamics

This paper deals with analytic redundancy management of systems that have appreciable structural dynamics and require active control. Specifically, the class of systems considered is large, light weight spacecraft that have large numbers of distributed sensors and actuators. The principal subject treated is on-line failure detection, identification, and recovery for control system component failures. An analytic redundancy management system has been proposed based on testing the residual sequence of a single Kalman filter. The NASA Langley Spacecraft Control Laboratory Experiment research facility (SCOLE) is used to evaluate the system. SCOLE is an experimental facility at the Langley Research Center which was designed for research in the control of large, flexible structures. The experimental apparatus is a functional model of the space shuttle with a large, flexible, offset-feed antenna attached.

Rapid slewing of the orbiting spacecraft control laboratory experiment (SCOLE) using LQR techniques

The rotational equations of motion, describing the dynamics of the (rigidized) proposed orbiting Spacecraft Control Laboratory Experiment during the station-keeping phase, are derived using the Eulerian formulation. When the attitude angles (roll, pitch, and yaw) are assumed small, a stability analysis is conducted for the system. It is seen that the pitch equation decouples from the roll and yaw equations when the interface between the mast on the reflector is not offset or the offset is only along the Shuttle roll axis. When a second offset is introduced along the pitch axis of the system and when the gravity-gradient torques are present in the dynamics, the system assumes a new equilibrium position. The linear regulator theory is used to derive a control law for the linear model of the rigidized SCOLE. This law is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers (20° amplitude) are simulated.

Maneuver and vibration control of SCOLE

This paper is concerned with the simultaneous maneuver and vibration control of the Spacecraft Control Laboratory Experiment (SCOLE). Summaries of the derivation of the equations of motion and of a perturbation method permitting a maneuver strategy independent of the vibration control are presented. Some of the problems encountered in dynamical modeling of a flexible spacecraft in an earth-based laboratory are high-lighted and solved. Numerical results demonstrating rotational maneuvers of the SCOLE model are included.

Experiments for Control of Large Space Structures

Recent progress in the area of control experiments for large space structures is reviewed. Topics include large angle slewing of a flexible panel and the Spacecraft Control Laboratory Experiment (SCOLE). In large angle slewing, experiments on a flexible solar panel model are discussed. Experimental results for slewing control in air and in vacuum are presented to illustrate the effect of air drag on the controller design. In SCOLE, the design of laboratory apparatus will be discussed. The status of research activities oriented primarily to the improvement of analysis capabilities through testing is presented