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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Robust Stabilizing Compensators for Flexible Structures with Collocated Controls

For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.

Balakrishman, A. V.↗
NASA NTRS1993

Modal grammian approach to actuator and sensor placement for flexible structures

The problem of selecting optimal locations of actuators and sensors for the control of flexible structures is addressed. Novel geometrical and physical interpretations are given for both controllability and observability grammians which enhances the intuitive aspects of the actuator and sensor placement problem. The explicit form of controllability and observability grammians for flexible structures is used to define modal grammian coefficients, which provides the basis for an actuator and sensor placement technique. The relationship of the proposed metric to three different existing criteria are given. The method is demonstrated on a model of an experimental large flexible structure.

Lim, K. B.↗
NASA NTRS1990

Practical model reduction for flexible structures

The most accepted methods for developing models of flexible structures for the analysis, design and simulation of control systems are finite element methods and extraction from experimental data. Using either of these methods, models are often produced with modes that do not significantly add to the fidelity of the model. This paper presents techniques for eliminating these modes. Particular attention is paid to multiple-input, multiple-output systems. First, control system models developed for flexible structures, using finite element methods and experimental data, are briefly discussed. the shortcomings of using models with unnecessary and/or residual modes are delineated. Then, two techniques for reducing the order of models are presented; the first is applicable to single-input, single-output systems and the second for multiple-input, multiple-output systems. Finally, both are illustrated using model data from the proposed NASA Shuttle-C.

Mitchell, Jerrel R.↗
NASA NTRS1983

Modeling of flexible structures for active control

If a flexible structure has a plane of symmetry, the equations of motion can be split into two uncoupled sets, one for symmetrical motions and one for anti-symmetric motions. If there are m controls, it is often convenient to assign the linear combinations of controls that enter into the m lowest frequency modes and new controls. As an example the feed-support structure of a spacecraft antenna is considered. It is modeled as a tetrahedron made up of flexible bars and connected to the spacecraft by six short flexible legs containing force actuators and displacement sensors. Due to the three-sided symmetry of this structure, both the symmetric and the anti-symmetric equations of motion can be decoupled into two subsystems. The resulting four subsystems are: (1) pitch/fore-aft motions with four degrees of freedom (DOF), two controls, and one output (the fore-aft motion of the feed); (2) vertical motions with three DOF, one control, and one output (the vertical motion of the feed); (3) roll/lateral motions with four DOF, two controls, and one output (the lateral motions of the feed); and (4) yaw motion with one DOF, one control, and no output (the feed does not move during yaw motion).

Bryson, A. E., Jr.↗
NASA NTRS1989

Experimental experience with flexible structures

The focus is on a flexible structure experiment developed at the California Institute of Technology. The main thrust of the experiment is to address the identification and robust control issues associated with large space structures by capturing their characteristics in the laboratory. The design, modeling, identification and control objectives will be discussed. Also, the subject of uncertainty in structural plant models and the frequency shaping of performance objectives will be expounded upon. Theoretical and experimental results of control laws designed using the identified model and uncertainty descriptions will be presented.

Balas, Gary J.↗
NASA NTRS1993

Balanced LQG Compensator for Flexible Structures

The analysis of open-loop balanced flexible structures has been extended for closed-loop structures. The relationships between weights/ variances and characteristic values for the system as well as between weights/variances and plant/estimator pole location are derived in this paper. Thus, the weights can be determined in advance to meet the requirements of a closed-loop system.

flexible↗
NASA NTRS1994

Vibration suppression in flexible structures via the sliding-mode control approach

Sliding mode control became very popular recently because it makes the closed loop system highly insensitive to external disturbances and parameter variations. Sliding algorithms for flexible structures have been used previously, but these were based on finite-dimensional models. An extension of this approach for differential-difference systems is obtained. That makes if possible to apply sliding-mode control algorithms to the variety of nondispersive flexible structures which can be described as differential-difference systems. The main idea of using this technique for dispersive structures is to reduce the order of the controlled part of the system by applying an integral transformation. We can say that transformation 'absorbs' the dispersive properties of the flexible structure as the controlled part becomes dispersive.

Drakunov, S.↗
NASA NTRS1989

Optimal orbit transfer suitable for large flexible structures

The problem of continuous low-thrust planar orbit transfer of large flexible structures is formulated as an optimal control problem with terminal state constraints. The dynamics of the spacecraft motion are treated as a point-mass central force field problem; the thrust-acceleration magnitude is treated as an additional state variable; and the rate of change of thrust-acceleration is treated as a control variable. To ensure smooth transfer, essential for flexible structures, an additional quadratic term is appended to the time cost functional. This term penalizes any abrupt change in acceleration. Numerical results are presented for the special case of a planar transfer.

Chatterjee, Alok K.↗
NASA NTRS1985

A robust nonlinear attitude control law for space stations with flexible structural components

In this paper, a nonlinear attitude control law for space stations with flexible structural components is derived using a rigid-body model. This control law, depending on the Cayley-Rodriguez parameters, globally stabilizes the equilibrium of the rigid-body model. The effect of elastic deformations of the flexible structural components on the resulting feedback system dynamics is analyzed. It is found that the system's stability property is highly robust with respect to structural vibrations and inertial variations. The time-domain behavior of the feedback system is studied numerically using a model of a typical space station with flexible solar panels.

Wang, P. K. C.↗
NASA NTRS1989

Model reduction for flexible structures - Test data approach

A reduced model of a system is obtained by truncating part of its state variables. Hankel singular values and component costs determine which component is deleted or retained in the reduced model. In this paper Hankel singular values and component costs of a flexible structure are obtained from the resonance test data, rather than from the system matrices. Test data, besides system dynamics, include also actuators and sensors dynamics. For this reason, the reduced model obtained from test data can be far from the optimal one. In this paper the reconstruction of the flexible structure indices from the joint actuator-sensor-flexible structure indices is discussed.

Gawronski, Wodek↗
NASA NTRS1985

A slewing control experiment for flexible structures

A hardware set-up has been developed to study slewing control for flexible structures including a steel beam and a solar panel. The linear optimal terminal control law is used to design active controllers which are implemented in an analog computer. The objective of this experiment is to demonstrate and verify the dynamics and optimal terminal control laws as applied to flexible structures for large angle maneuver. Actuation is provided by an electric motor while sensing is given by strain gages and angle potentiometer. Experimental measurements are compared with analytical predictions in terms of modal parameters of the system stability matrix and sufficient agreement is achieved to validate the theory.

Juang, J.-N.↗
NASA NTRS1989

Modeling and control system design and analysis tools for flexible structures

Described here are Boeing software tools used for the development of control laws of flexible structures. The Boeing Company has developed a software tool called Modern Control Software Package (MPAC). MPAC provides the environment necessary for linear model development, analysis, and controller design for large models of flexible structures. There are two features of MPAC which are particularly appropriate for use with large models: (1) numerical accuracy and (2) label-driven nature. With the first feature MPAC uses double precision arithmetic for all numerical operations and relies on EISPAC and LINPACK for the numerical foundation. With the second feature, all MPAC model inputs, outputs, and states are referenced by user-defined labels. This feature allows model modification while maintaining the same state, input, and output names. In addition, there is no need for the user to keep track of a model variable's matrix row and colunm locations. There is a wide range of model manipulation, analysis, and design features within the numerically robust and flexible environment provided by MPAC. Models can be built or modified using either state space or transfer function representations. Existing models can be combined via parallel, series, and feedback connections; and loops of a closed-loop model may be broken for analysis.

Anissipour, Amir A.↗
NASA NTRS1986

Modeling, estimation and identification methods for static shape determination of flexible structures

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Rodriguez, G.↗
NASA NTRS1992

Flexible structure experiments at JPL and WPAFB - H-infinity controller designs

The authors describe some control system experiments which were carried out on flexible structure facilities at the Jet Propulsion Laboratory (JPL) and the Wright Patterson Air Force Base (WPAFB). They document some recent design studies for two contrasting flexible structure facilities. The first facility was the JPL/AFAL flexible antenna in Pasadena, California. The second was the WPAFB 12-meter cantilever truss in Dayton, Ohio. Each structure possessed a number of flexible modes of vibration which were lightly damped. The purpose of the experiments was to achieve active damping of the flexible modes via a digital control system. The feedback controllers were designed using the H-infinity technique of weighted gap optimization to increase the structural damping and achieve robust control.

Buddie, Scott A.↗
NASA NTRS1990

Progress on control experiments of flexible structures

Progress at the NASA Langley Research Center in the area of control experiments for flexible structures is described. First the author presents the experimental results for a linear model which represents slewing maneuvers of a generic space station solar panel carried out to evaluate experimentally some control technologies. Then the status of the rotational/translational maneuvering experiment of a flexible steel panel carried by a translation cart is presented. Finally, experimental results of the NASA minimast testbed using velocity command stepper motors as reaction mass reactors are shown. All the test configurations are briefly described, including actuator and sensor, test setup, and test software. The status of some research activities oriented primarily to the experimental methods for control of flexible structures is presented.

Juang, Jer-Nan↗