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Techniques developed originally for electronic systems also useful for multibody mechanical systems. Report summarizes methods developed to solve nonlinear forward-dynamics problem for robot of multiple-link arms connected by joints. Primary objective to show equivalence between recursive methods of dynamical analysis and some filtering and smoothing techniques from state-estimation theory.
Asynchronous finite state sequential nonlinear controller synthesis with few flip-flops for dynamic space vehicle systems
The purpose of the investigation reported upon is to study the existence and characteristics of self-sustained oscillations in the dynamic behavior of the Large Space Telescope (LST) system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMGs). A continuous-data single-axis model of the LST is considered. A solid friction model is used to represent CMG gimbal friction. A rigorous mathematical model is derived for use in a continuous describing function analysis. Conditions for self-sustained oscillations are then determined.
It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.
Structural nonlinearities should be considered in the analysis and modeling of mechanical systems for accuracy in predicting dynamic behavior. Moreover, checks for nonlinearity should address the type and class of nonlinearity in the structure and identify the probable cause. A series of experimental modal survey tests were carried out to determine and characterize the structural nonlinearities of the Space Shuttle Main Engine main injector. Different excitation regimes at various amplitudes were utilized to induce vibration and strain, and acceleration measurements were taken at judiciously selected locations. The test results indicated that both stiffness and damping nonlinearities were present.
Analysis of a typical nonlinear electrohydraulic servo-model establishes the dynamic-performance capabilities of servo-actuation systems.
Nonlinear perturbation theory for optimal estimation and control of time-discrete, stochastic, dynamic systems when measurement data is noisy
A new implicit algorithm for time step integration of finite element structural dynamic equations is presented. Convergence, stability and numerical damping properties are discussed. Due to the way nonlinear structural behavior is taken into account, the algorithm is expected to compare favorably with existing ones. Some simple numerical results are presented. A related explicit algorithm is also derived and shortly discussed.
Despite the apparent regularity of planetary motions, the dynamics of the solar system is in reality extremely nonlinear and replete with chaos. The difficulty in detecting this chaos is the long time scale of this dynamics as compared with human observations.
This paper describes a technique which may be used to design the flight control system for a highly maneuverable aircraft. The control system was provided to stabilize the dynamics of the aircraft model and allow it to fly simulated, poststall 'supermaneuvers'. Although the aircraft dynamics are highly nonlinear under these conditions, the gain-scheduled, flight control system was designed using basically linear techniques. A manuever generator was implemented to pilot the mathematical model through prescribed optimal trajectories. The control system design performed well while executing maneuvers involving small angular rates where the governing dynamics could be considered linear. However, the performance deteriorated once the model was subjected to high angular rates at high angle of attack.
This short paper considers the parameter-identification problem of general discrete-time, nonlinear, multiple input-multiple output dynamic systems with Gaussian white distributed measurement errors. Knowledge of the system parameterization is assumed to be available. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems.
A nonlinear, six degree of freedom, digital computer simulation of a vehicle which has constant mass properties and whose attitudes are controlled by both aerodynamic surfaces and reaction control system thrusters was developed. A rotating, oblate Earth model was used to describe the gravitational forces which affect long duration Earth entry trajectories. The program is executed in a nonreal time mode or connected to a simulation cockpit to conduct piloted and autopilot studies. The program guidance and control software used by the space shuttle orbiter for its descent from approximately 121.9 km to touchdown on the runway.
Consider some of the control system design methods for plants with nonlinear dynamics. If the nonlinearity is weak relative to the size of the operating region, then the linear methods apply directly. Fixed-gain design may be feasible even for significant nonlinearities. It may be possible to find a single gain which provides adequate control of the linear models at several perturbation points. If the nonlinearity is restricted to a sector, that fact may be used to obtain a fixed-gain controller. Otherwise, a gain may have to be associated with each perturbation point Pi. A gain schedule K(p(v)) is obtained by connecting the perturbation points by a function, say p(v), of the scheduling parameter v (i.e., speed). When the scheduling parameter must be multidimensional, this approach is difficult; the objective is to develop an easier procedure.
Viewgraphs and charts from a briefing summarize the accomplishments, results, conclusions, and recommendations of a feasibility study using the Pinhole Occulter Facility (POF). Accomplishments for 1986 include: (1) improved IPS Gimbal Model; (2) improved Crew Motion Disturbance Model; (3) use of existing shuttle on-orbit simulation to study the effects of orbiter attitude deadband size on POF performance; (4) increased understanding of maximum performance expected from current actuator/sensor set; (5) use of TREETOPS nonlinear time domain program to obtain system dynamics describing the complex multibody flexible structures; (6) use of HONEY-X design tool to design and evaluate multivariable compensator for stability, robustness, and performance; (7) application of state-of-the-art compensator design methodology Linear Quadratic Gaussian/Loop Transfer Recovery (LQG/LTR); and (8) examination of tolerance required on knowledge of the POF boom flexible mode frequencies to insure stability, using structure uncertainty analysis.
A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformation are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.
Methods developed recently by the author to solve the problem of forward dynamics for nonlinear joint-connected multibody systems are summarized. Solution of this problem is of interest in such application areas as robotics, deploying structures, ground vehicles, and pointing of antennas and instrumented platforms. The problem is solved by the recursive filtering and smoothing techniques of state estimation theory. The filtering stage takes the applied joint moments as inputs to produce a sequence of spatial constraint forces acting at the joints of the system. The smoothing stage takes the innovations process resulting from the filter as an input and produces a set of spatial accelerations and a corresponding set of joint-angle accelerations.
There is an evident need to discover a means of establishing reliable, implementable controls for systems that are plagued by nonlinear and, or uncertain, model dynamics. The development of a generic controller design tool for tough-to-control systems is reported. The method utilizes a moving grid, time infinite element based solution of the necessary conditions that describe an optimal controller for a system. The technique produces a discrete feedback controller. Real time laboratory experiments are now being conducted to demonstrate the viability of the method. The algorithm that results is being implemented in a microprocessor environment. Critical computational tasks are accomplished using a low cost, on-board, multiprocessor (INMOS T800 Transputers) and parallel processing. Progress to date validates the methodology presented. Applications of the technique to the control of highly flexible robotic appendages are suggested.
Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.