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NASA NTRS1989

Frequency response modeling and control of flexible structures: Computational methods

The dynamics of vibrations in flexible structures can be conventiently modeled in terms of frequency response models. For structural control such models capture the distributed parameter dynamics of the elastic structural response as an irrational transfer function. For most flexible structures arising in aerospace applications the irrational transfer functions which arise are of a special class of pseudo-meromorphic functions which have only a finite number of right half place poles. Computational algorithms are demonstrated for design of multiloop control laws for such models based on optimal Wiener-Hopf control of the frequency responses. The algorithms employ a sampled-data representation of irrational transfer functions which is particularly attractive for numerical computation. One key algorithm for the solution of the optimal control problem is the spectral factorization of an irrational transfer function. The basis for the spectral factorization algorithm is highlighted together with associated computational issues arising in optimal regulator design. Options for implementation of wide band vibration control for flexible structures based on the sampled-data frequency response models is also highlighted. A simple flexible structure control example is considered to demonstrate the combined frequency response modeling and control algorithms.

Bennett, William H.↗

NASA NTRS1989

Modeling, design, and control of flexible manipulator arms: Status and trends

The desire for higher performance manipulators has lead to dynamic behavior in which the flexibility is an essential aspect. The mathematical representations commonly used in modeling flexible arms and arms with flexible drives are examined first. Then design considerations directly arising from the flexible nature of the arm are discussed. Finally, controls of joints for general and tip motion are discussed.

Book, Wayne J.↗

NASA NTRS1989

Dynamical modeling of serial manipulators with flexible links and joints using the method of kinematic influence

A method of formulating the dynamical equations of a flexible, serial manipulator is presented, using the Method of Kinematic Influence. The resulting equations account for rigid body motion, structural motion due to link and joint flexibilities, and the coupling between these two motions. Nonlinear inertial loads are included in the equations. A finite order mode summation method is used to model flexibilities. The structural data may be obtained from experimental, finite element, or analytical methods. Nonlinear flexibilities may be included in the model.

Graves, Philip L.↗

NASA NTRS1989

Experiments in identification and control of flexible-link manipulators

Interest in the study of flexible-link manipulators for space-based applications has risen strongly in recent years. Moreover, numerous experimental results have appeared for the various problems in the modeling, identification and control of such systems. Nevertheless, relatively little literature has appeared involving laboratory verification of tuning controllers for certain types of realistic flexible-link manipulators. Specifically flexible-link manipulators which are required to maintain endpoint accuracy while manipulating loads that are possibly unknown and varying as they undergo disturbance effects from the environment and workspace. Endpoint position control of flexible-link manipulators in these areas are discussed, with laboratory setups consisting of one and two-link manipulators.

Yurkovich, Stephen↗

NASA NTRS1989

Shaft flexibility effects on aeroelastic stability of a rotating bladed disk

A comprehensive study of Coriolis forces and shaft flexibility effects on the structural dynamics and aeroelastic stability of a rotating bladed-disk assembly attached to a cantilever, massless, flexible shaft is presented. Analyses were performed for an actual bladed-disk assembly, used as the first stage in the fan of the 'E3' engine. In the structural model, both in-plane and out-of-plane elastic deformation of the bladed-disk assembly were considered relative to their hub, in addition to rigid disk translations and rotations introduced by shaft flexibility. Besides structural coupling between blades (through the flexible disk), additional coupling is introduced through quasisteady aerodynamic loads. Rotational effects are accounted for throughout the work, and some mode shapes for the whole structure are presented at a selected rpm.

Khader, Naim↗

NASA NTRS1990

A computational procedure for multibody systems including flexible beam dynamics

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.

Downer, J. D.↗

NASA NTRS1990

Active vibration control techniques for flexible space structures

Two proposed control system design techniques for active vibration control in flexible space structures are detailed. Control issues relevant only to flexible-body dynamics are addressed, whereas no attempt was made to integrate the flexible and rigid-body spacecraft dynamics. Both of the proposed approaches revealed encouraging results; however, further investigation of the interaction of the flexible and rigid-body dynamics is warranted.

Parlos, Alexander G.↗

NASA NTRS1991

Control and dynamics of a flexible spacecraft during stationkeeping maneuvers

A case study of a spacecraft having flexible solar arrays is presented. A stationkeeping attitude control mode using both earth and rate gyro reference signals and a flexible vehicle dynamics modeling and implementation is discussed. The control system is designed to achieve both pointing accuracy and structural mode stability during stationkeeping maneuvers. Reduction of structural mode interactions over the entire mode duration is presented. The control mode using a discrete time observer structure is described to show the convergence of the spacecraft attitude transients during Delta-V thrusting maneuvers without preloading thrusting bias to the onboard control processor. The simulation performance using the three axis, body stabilized nonlinear dynamics is provided. The details of a five body dynamics model are discussed. The spacecraft is modeled as a central rigid body having cantilevered flexible antennas, a pair of flexible articulated solar arrays, and to gimballed momentum wheels. The vehicle is free to undergo unrestricted rotations and translations relative to inertial space. A direct implementation of the equations of motion is compared to an indirect implementation that uses a symbolic manipulation software to generate rigid body equations.

Liu, D.↗

NASA NTRS1991

Dynamics modeling and adaptive control of flexible manipulators

An application of Model Reference Adaptive Control (MRAC) to the position and force control of flexible manipulators and robots is presented. A single-link flexible manipulator is analyzed. The problem was to develop a mathematical model of a flexible robot that is accurate. The objective is to show that the adaptive control works better than 'conventional' systems and is suitable for flexible structure control.

Sasiadek, J. Z.↗

NASA NTRS1991

Flexible thermal apparatus for mounting of thermoelectric cooler

A flexible heat transfer apparatus used to flexibly connect and thermally couple a thermoelectric cooler to an object to be cooled is disclosed. The flexible heat transfer apparatus consists of a pair of flexible corrugated sheets made from high thermal conductivity materials such as copper, aluminum, gold, or silver. The ridges of the corrugated sheets are oriented perpendicular to one another and bonded sandwich-fashion between three plates to define an upper section and a lower section. The upper section provides X flexure, the lower section provides Y flexure, and both sections together provide Z flexure.

Jones, Jack A.↗

NASA NTRS1990

Flexibility effects on the control system performance of large scale robotic manipulators

Structural flexibility of robotic manipulators becomes significant and limits the performance of a control system when manipulators are large structures, manipulating on large payloads, and/or operating at high speeds. The question of when a manipulator can be considered rigid or must be considered flexible is studied as a function of manipulator dynamics and task characteristics. Results are interpreted in simple quantitative forms which can be used as design and analysis tools to decide whether or not the manipulator flexibility will be a significant factor for a given task condition. The limitations imposed by the manipulator flexibility on the joint variable feedback control system performance is determined using linear and nonlinear methods. The closed loop eigenstructure behavior of finite dimensional models under joint variable feedback is studied and results are compared with the previously reported results.

Cetinkunt, Sabri↗

NASA NTRS1991

Identification of dynamic characteristics of flexible rotors as dynamic inverse problem

The problem of dynamic and balancing of flexible rotors were considered, which were set and solved as the problem of the identification of flexible rotor systems, which is the same as the inverse problem of the oscillation theory dealing with the task of the identifying the outside influences and system parameters on the basis of the known laws of motion. This approach to the problem allows the disclosure the picture of disbalances throughout the rotor-under-test (which traditional methods of flexible rotor balancing, based on natural oscillations, could not provide), and identify dynamic characteristics of the system, which correspond to a selected mathematical model. Eventually, various methods of balancing were developed depending on the special features of the machines as to their design, technology, and operation specifications. Also, theoretical and practical methods are given for the flexible rotor balancing at far from critical rotation frequencies, which does not necessarily require the knowledge forms of oscillation, dissipation, and elasticity and inertia characteristics, and to use testing masses.

Roisman, W. P.↗

NASA NTRS1992

Milstar's flexible-substrate solar array: Lessons learned

The Flexible Substrate Solar Array (FSSA) is an evolutionary development of the lightweight, flexible substrate design pioneered during the seventies. Many of the features of the design are related to the Solar Array Flight Experiment (SAFE), flown on STS-41D in 1984. FSSA development has created a substantial technology base for future flexible substrate solar arrays such as the array for the Space Station Freedom. Lessons learned during the development of the FSSA can and should be applied to the Freedom array and other future flexible substrate designs.

Gibb, John↗

NASA NTRS1990

MILSTAR's flexible substrate solar array: Lessons learned, addendum

MILSTAR's Flexible Substrate Solar Array (FSSA) is an evolutionary development of the lightweight, flexible substrate design pioneered at Lockheed during the seventies. Many of the features of the design are related to the Solar Array Flight Experiment (SAFE), flown on STS-41D in 1984. FSSA development has created a substantial technology base for future flexible substrate solar arrays such as the array for the Space Station Freedom. Lessons learned during the development of the FSSA can and should be applied to the Freedom array and other future flexible substrate designs.

Gibb, John↗

NASA NTRS1993

Robust on-off pulse control of flexible space vehicles

The on-off reaction jet control system is often used for attitude and orbital maneuvering of various spacecraft. Future space vehicles such as the orbital transfer vehicles, orbital maneuvering vehicles, and space station will extensively use reaction jets for orbital maneuvering and attitude stabilization. The proposed robust fuel- and time-optimal control algorithm is used for a three-mass spacing model of flexible spacecraft. A fuel-efficient on-off control logic is developed for robust rest-to-rest maneuver of a flexible vehicle with minimum excitation of structural modes. The first part of this report is concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated and solved. The second part of this report deals with obtaining parameter insensitive fuel- and time- optimal control inputs by solving a constrained optimization problem subject to robustness constraints. It is shown that sensitivity to modeling errors can be significantly reduced by the proposed, robustified open-loop control approach. The final part of this report deals with sliding mode control design for uncertain flexible structures. The benchmark problem of a flexible structure is used as an example for the feedback sliding mode controller design with bounded control inputs and robustness to parameter variations is investigated.

Wie, Bong↗

NASA NTRS1993

Unsteady transonic potential flow over a flexible fuselage

A flexible fuselage capability has been developed and implemented within version 1.2 of the CAP-TSD code. The capability required adding time dependent terms to the fuselage surface boundary conditions and the fuselage surface pressure coefficient. The new capability will allow modeling the effect of a flexible fuselage on the aeroelastic stability of complex configurations. To assess the flexible fuselage capability several steady and unsteady calculations have been performed for slender fuselages with circular cross-sections. Steady surface pressures are compared with experiment at transonic flight conditions. Unsteady cross-sectional lift is compared with other analytical results at a low subsonic speed and a transonic case has been computed. The comparisons demonstrate the accuracy of the flexible fuselage modifications.

Gibbons, Michael D.↗

NASA NTRS1954

Structural response to discrete and continuous gusts of an airplane having wing bending flexibility and a correlation of calculated and flight results

An analysis is made of the structural response to gusts of an airplane having the degrees of freedom of vertical motion and wing bending flexibility and basic parameters are established. A convenient and accurate numerical solution of the response equations is developed for the case of discrete-gust encounter, an exact solution is made for the simpler case of continuous-sinusoidal-gust encounter, and the procedure is outlined for treating the more realistic condition of continuous random atmospheric turbulence, based on the methods of generalized harmonic analysis. Correlation studies between flight and calculated results are then given to evaluate the influence of wing bending flexibility on the structural response to gusts of two twin-engine transports and one four-engine bomber. It is shown that calculated results obtained by means of a discrete-gust approach reveal the general nature of the flexibility effects and lead to qualitative correlation with flight results. In contrast, calculations by means of the continuous-turbulence approach show good quantitative correlation with flight results and indicate a much greater degree of resolution of the flexibility effects.

Houbolt, John C↗

NASA NTRS1990

Integrated controls-structures design methodology development for a class of flexible spacecraft

Future utilization of space will require large space structures in low-Earth and geostationary orbits. Example missions include: Earth observation systems, personal communication systems, space science missions, space processing facilities, etc., requiring large antennas, platforms, and solar arrays. The dimensions of such structures will range from a few meters to possibly hundreds of meters. For reducing the cost of construction, launching, and operating (e.g., energy required for reboosting and control), it will be necessary to make the structure as light as possible. However, reducing structural mass tends to increase the flexibility which would make it more difficult to control with the specified precision in attitude and shape. Therefore, there is a need to develop a methodology for designing space structures which are optimal with respect to both structural design and control design. In the current spacecraft design practice, it is customary to first perform the structural design and then the controller design. However, the structural design and the control design problems are substantially coupled and must be considered concurrently in order to obtain a truly optimal spacecraft design. For example, let C denote the set of the 'control' design variables (e.g., controller gains), and L the set of the 'structural' design variables (e.g., member sizes). If a structural member thickness is changed, the dynamics would change which would then change the control law and the actuator mass. That would, in turn, change the structural model. Thus, the sets C and L depend on each other. Future space structures can be roughly divided into four mission classes. Class 1 missions include flexible spacecraft with no articulated appendages which require fine attitude pointing and vibration suppression (e.g., large space antennas). Class 2 missions consist of flexible spacecraft with articulated multiple payloads, where the requirement is to fine-point the spacecraft and each individual payload while suppressing the elastic motion. Class 3 missions include rapid slewing of spacecraft without appendages, while Class 4 missions include general nonlinear motion of a flexible spacecraft with articulated appendages and robot arms. Class 1 and 2 missions represent linear mathematical modeling and control system design problems (except for actuator and sensor nonlinearities), while Class 3 and 4 missions represent nonlinear problems. The development of an integrated controls/structures design approach for Class 1 missions is addressed. The performance for these missions is usually specified in terms of (1) root mean square (RMS) pointing errors at different locations on the structure, and (2) the rate of decay of the transient response. Both of these performance measures include the contributions of rigid as well as elastic motion.

Maghami, P. G.↗