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NASA NTRS1989

The application of TSIM software to act design and analysis on flexible aircraft

The TSIM software is described. This is a package which uses an interactive FORTRAN-like simulation language for the simulation on nonlinear dynamic systems and offers facilities which include: mixed continuous and discrete time systems, time response calculations, numerical optimization, automatic trimming of nonlinear aircraft systems, and linearization of nonlinear equations for eigenvalues, frequency responses and power spectral response evaluation. Details are given of the application of TSIM to the analysis of aeroelastic systems under the RAE Farborough extension FLEX-SIM. The aerodynamic and structural data for the equations of motion of a flexible aircraft are prepared by a preprocessor program for incorporation in TSIM simulations. Within the simulation, the flexible aircraft model may then be selected interactively for different flight conditions and modal reduction techniques applied. The use of FLEX-SIM is demonstrated by an example of the flutter prediction for a simple aeroelastic model. By utilizing the numerical optimization facility of TSIM, it is possible to undertake identification of required parameters in the TSIM model within the simulation.

Kaynes, Ian W.↗

NASA NTRS1989

Flexible missile autopilot design studies with PC-MATLAB/386

Development of a responsive, high-bandwidth missile autopilot for airframes which have structural modes of unusually low frequency presents a challenging design task. Such systems are viable candidates for modern, state-space control design methods. The PC-MATLAB interactive software package provides an environment well-suited to the development of candidate linear control laws for flexible missile autopilots. The strengths of MATLAB include: (1) exceptionally high speed (MATLAB's version for 80386-based PC's offers benchmarks approaching minicomputer and mainframe performance); (2) ability to handle large design models of several hundred degrees of freedom, if necessary; and (3) broad extensibility through user-defined functions. To characterize MATLAB capabilities, a simplified design example is presented. This involves interactive definition of an observer-based state-space compensator for a flexible missile autopilot design task. MATLAB capabilities and limitations, in the context of this design task, are then summarized.

Ruth, Michael J.↗

NASA NTRS1989

Lumped mass formulations for modeling flexible body systems

The efforts of Mechanical Dynamics, Inc. in obtaining a general formulation for flexible bodies in a multibody setting are discussed. The efforts being supported by MDI, both in house and externally are summarized. The feasibility of using lumped mass approaches to modeling flexibility in a multibody dynamics context is examined. The kinematics and kinetics for a simple system consisting of two rigid bodies connected together by an elastic beam are developed in detail. Accuracy, efficiency and ease of use using this approach are some of the issues that are then looked at. The formulation is then generalized to a superelement containing several nodes and connecting several bodies. Superelement kinematics and kinetics equations are developed. The feasibility and effectiveness of the method is illustrated by the use of some examples illustrating phenomena common in the context of spacecraft motions.

Rampalli, Rajiv↗

NASA NTRS1989

A comparison of software for the modeling and control of flexible systems

A researcher proposes a cooperative effort among specialists who use or develop software for simulating and analyzing the control of flexible aerospace systems. A comparison of existing software for modeling control systems and flexible structures, applied to several example problems would be quite valuable. The comparison would indicate computational efficiency and capabilities with respect to handling nonlinearities and graphical output. Because of the diversity of applications of such software, the researcher believes that the proposed cooperative effort can transcend projects involving specific applications. Comparisons of software capability and efficiency can be made and gaps can be identified. In this way the results of the cooperative effort can provide guidance for individual projects. Several charts which outline the objectives and approach of the proposed cooperative effort are given here.

Taylor, Lawrence W., Jr.↗

NASA NTRS1989

Enhanced element-specific modal formulations for flexible multibody dynamics

The accuracy of current flexible multibody formalisms based on assumed modes is examined in the context of standard spacecraft motions involving structural components undergoing both slow and fast overall translational and rotational motions as well as small deformations. Limitations of current techniques in treating: (1) element-specific coupling behavior of large motion and small deformation, and (2) motion-induced structural stiffness variations, are noted. The roles of nonlinear and linear elastic structural theories in accurately predicting transient large-displacement dynamic behavior of flexible multibody systems are examined in detail. Coupling effects between deformation and overall motion are carefully scrutinized in the context of assumed-mode discretization techniques. Consistently linearized beam, plate, and shell formulations involving in-plane stretch variables are proposed and shown to yield very accurate simulation results and extremely fast modal convergence for most motions involving small strains. In some particular cases, however, in which membrane stiffness dominates bending stiffness, a nonlinear strain formulation is required in order to capture proper coupling between deformation and overall motion.

Ryan, Robert R.↗

NASA NTRS1989

Optical processing for distributed sensors in control of flexible spacecraft

A recent potential of distributed image processing is discussed. Applications in the control of flexible spacecraft are emphasized. Devices are currently being developed at NASA and in universities and industries that allow the real-time processing of holographic images. Within 5 years, it is expected that, in real-time, one may add or subtract holographic images at optical accuracy. Images are stored and processed in crystal mediums. The accuracy of their storage and processing is dictated by the grating level of laser holograms. It is far greater than that achievable using current analog-to-digital, pixel oriented, image digitizing and computing techniques. Processors using image processing algebra can conceptually be designed to mechanize Fourier transforms, least square lattice filters, and other complex control system operations. Thus, actuator command inputs derived from complex control laws involving distributed holographic images can be generated by such an image processor. Plans are revealed for the development of a Conjugate Optics Processor for control of a flexible object.

Montgomery, Raymond C.↗

NASA NTRS1989

The active flexible wing aeroservoelastic wind-tunnel test program

For a specific application of aeroservoelastic technology, Rockwell International Corporation developed a concept known as the Active Flexible Wing (AFW). The concept incorporates multiple active leading-and trailing-edge control surfaces with a very flexible wing such that wing shape is varied in an optimum manner resulting in improved performance and reduced weight. As a result of a cooperative program between the AFWAL's Flight Dynamics Laboratory, Rockwell, and NASA LaRC, a scaled aeroelastic wind-tunnel model of an advanced fighter was designed, fabricated, and tested in the NASA LaRC Transonic Dynamics Tunnel (TDT) to validate the AFW concept. Besides conducting the wind-tunnel tests NASA provided a design of an Active Roll Control (ARC) System that was implemented and evaluated during the tests. The ARC system used a concept referred to as Control Law Parameterization which involves maintaining constant performance, robustness, and stability while using different combinations of multiple control surface displacements. Since the ARC system used measured control surface stability derivatives during the design, the predicted performance and stability results correlated very well with test measurements.

Noll, Thomas↗

NASA NTRS1989

Modeling and stabilization of large flexible space stations

A preliminary formulation of a large space structure is presented. The system consists of a (rigid) massive body, which may play the role of experimental modules located at the center of the space station and a flexible configuration, consisting of several beams, which is rigidly attached to the main body. The equations that govern the motion of the complete system consist of several partial differential equations with boundary conditions describing the vibration of flexible components coupled with six ordinary differential equations that describe the rotational and translational motion of the central body. The problem of (feedback) stabilization of the system is discussed. This study is expected to provide an insight into the complexity of design and stabilization of actual space stations.

Lim, S. S.↗

NASA NTRS1989

The dynamics and control of large flexible space structures - 12, supplement 11

The rapid 2-D slewing and vibrational control of the unsymmetrical flexible SCOLE (Spacecraft Control Laboratory Experiment) with multi-bounded controls is considered. Pontryagin's Maximum Principle is applied to the nonlinear equations of the system to derive the necessary conditions for the optimal control. The resulting two point boundary value problem is then solved by using the quasilinearization technique, and the near minimum time is obtained by sequentially shortening the slewing time until the controls are near the bang-bang type. The tradeoff between the minimum time and the minimum flexible amplitude requirements is discussed. The numerical results show that the responses of the nonlinear system are significantly different from those of the linearized system for rapid slewing. The SCOLE station-keeping closed loop dynamics are re-examined by employing a slightly different method for developing the equations of motion in which higher order terms in the expressions for the mast modal shape functions are now included. A preliminary study on the effect of actuator mass on the closed loop dynamics of large space systems is conducted. A numerical example based on a coupled two-mass two-spring system illustrates the effect of changes caused in the mass and stiffness matrices on the closed loop system eigenvalues. In certain cases the need for redesigning control laws previously synthesized, but not accounting for actuator masses, is indicated.

Bainum, Peter M.↗

NASA NTRS1989

Adaptive Strategies for Controls of Flexible Arms

An adaptive controller for a modern manipulator has been designed based on asymptotical stability via the Lyapunov criterion with the output error between the system and a reference model used as the actuating control signal. Computer simulations were carried out to test the design. The combination of the adaptive controller and a system vibration and mode shape estimator show that the flexible arm should move along a pre-defined trajectory with high-speed motion and fast vibration setting time. An existing computer-controlled prototype two link manipulator, RALF (Robotic Arm, Large Flexible), with a parallel mechanism driven by hydraulic actuators was used to verify the mathematical analysis. The experimental results illustrate that assumed modes found from finite element techniques can be used to derive the equations of motion with acceptable accuracy. The robust adaptive (modal) control is implemented to compensate for unmodelled modes and nonlinearities and is compared with the joint feedback control in additional experiments. Preliminary results show promise for the experimental control algorithm.

Yuan, Bau-San↗

NASA NTRS1989

Dynamics and control of flexible spacecraft during and after slewing maneuvers

The dynamics and control of slewing maneuvers of NASA Spacecraft COntrol Laboratory Experiment (SCOLE) are analyzed. The control problem of slewing maneuvers of SCOLE is formulated in terms of an arbitrary maneuver about any given axis. The control system is developed for the combined problem of rigid-body slew maneuver and vibration suppression of the flexible appendage. The control problem formulation incorporates the nonlinear dynamical equations derived previously, and is expressed in terms of a two-point boundary value problem utilizing a quadratic type of performance index. The two-point boundary value problem is solved as a hierarchical control problem with the overall system being split in terms of two subsystems, namely the slewing of the entire assembly and the vibration suppression of the flexible antenna. The coupling variables between the two dynamical subsystems are identified and these two subsystems for control purposes are treated independently in parallel at the first level. Then the state-space trajectory of the combined problem is optimized at the second level.

Kakad, Yogendra P.↗

NASA NTRS1989

Approximate minimum-time trajectories for 2-link flexible manipulators

Powell's nonlinear programming code, VF02AD, was used to generate approximate minimum-time tip trajectories for 2-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with horizontal-plane bending only. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness, EI, to transition from the semi-rigid to flexible case. Results show the level of compliance necessary to excite significant modal behavior. Quiescence of the final configuration is examined with the finite-element model.

Eisler, G. R.↗

NASA NTRS1989

Determination of joint drives for stable end-effector motion in flexible robotic systems

The prescribed tasks in high speed robotic systems are severely deteriorated because of their manipulator dynamic deflections. On the other hand conventional dynamic modeling techniques fail to reveal appropriate control forces in flexible systems. The conventional dynamic equations of motion for systems subject to kinematical constraints are modified by a new concept of control force representation. The directions of the control forces are selected such that they correspond to the joint degrees of freedom. Then the joint control forces and torques that yield unperturbed prescribed motions are solved simultaneously with the system motion. A flexible manipulator is presented to illustrate the methods proposed.

Ider, Sitki Kemal↗

NASA NTRS1989

Control of a flexible planar truss using proof mass actuators

A flexible structure was modeled and actively controlled by using a single space realizable linear proof mass actuator. The NASA/UVA/UB actuator was attached to a flexible planar truss structure at an optimal location and it was considered as both passive and active device. The placement of the actuator was specified by examining the eigenvalues of the modified model that included the actuator dynamics, and the frequency response functions of the modified system. The electronic stiffness of the actuator was specified, such that the proof mass actuator system was tuned to the fourth structural mode of the truss by using traditional vibration absorber design. The active control law was limited to velocity feedback by integrating of the signals of two accelerometers attached to the structure. The two lower modes of the closed-loop structure were placed further in the LHS of the complex plane. The theoretically predicted passive and active control law was experimentally verified.

Minas, Constantinos↗

NASA NTRS1989

Dynamic analysis of flexible mechanical systems using LATDYN

A 3-D, finite element based simulation tool for flexible multibody systems is presented. Hinge degrees-of-freedom is built into equations of motion to reduce geometric constraints. The approach avoids the difficulty in selecting deformation modes for flexible components by using assumed mode method. The tool is applied to simulate a practical space structure deployment problem. Results of examples demonstrate the capability of the code and approach.

Wu, Shih-Chin↗

NASA NTRS1989

Modeling and control of flexible space stations (slew maneuvers)

Large orbiting space structures are expected to experience mechanical vibrations arising from several disturbing forces such as those induced by shuttle takeoff or docking and crew movements. The problem is considered of modeling and control of large space structures subject to these and other disturbing forces. The system consists of a (rigid) massive body, which may play the role of experimental modules located at the center of the space station and flexible configurations, consisting of several beams, forming the space structure. A complete dynamic model of the system was developed using Hamilton's principle. This model consists of radial equations describing the translational motion of the central body, rotational equations describing the attitude motions of the body and several beam equations governing the vibration of the flexible members (platform) including appropriate boundary conditions. In summary, the dynamics of the space structure is governed by a complex system of interconnected partial and ordinary differential equations. Using Lyapunov's approach the asymptotic stability of the space structure is investigated. For asymptotic stability of the rest state (nominal trajectory), feedback controls are suggested. In the investigation, stability of the slewing maneuvers is also considered. Several numerical results are presented for illustration of the impact of coupling and the effectiveness of the stabilizing controls. Some insight is provided into the complexity of modeling, analysis and stabilization of actual space structures.

Ahmed, N. U.↗

NASA NTRS1989

Capture of free-flying payloads with flexible space manipulators

A recently developed control system for capturing free-flying payloads with flexible manipulators is discussed. Three essential points in this control system are, calculating optimal path, using a vision sensor for an external sensor, and controlling active vibration. Experimental results are shown using a planar flexible manipulator.

Komatsu, T.↗

NASA NTRS1989

Manipulators with flexible links: A simple model and experiments

A simple dynamic model proposed for flexible links is briefly reviewed and experimental control results are presented for different flexible systems. A simple dynamic model is useful for rapid prototyping of manipulators and their control systems, for possible application to manipulator design decisions, and for real time computation as might be applied in model based or feedforward control. Such a model is proposed, with the further advantage that clear physical arguments and explanations can be associated with its simplifying features and with its resulting analytical properties. The model is mathematically equivalent to Rayleigh's method. Taking the example of planar bending, the approach originates in its choice of two amplitude variables, typically chosen as the link end rotations referenced to the chord (or the tangent) motion of the link. This particular choice is key in establishing the advantageous features of the model, and it was used to support the series of experiments reported.

Shimoyama, Isao↗