NASA 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.

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.

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.

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>