Recursive formulas for the evaluation of certain complex integrals
Recursive formulas for stability tests and quadratic loss functions evaluation for linear discrete time dynamical systems
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Recursive formulas for stability tests and quadratic loss functions evaluation for linear discrete time dynamical systems
Interaction between structural or elastic response of spacecraft and attitude control system dynamics
Determining optimal time-invariant output feedback controllers for linear dynamic systems
Poincare hydrodynamic analogy in celestial mechanics, relating differential equations for dynamic systems with two degrees of freedom and two and three dimensional flow
Aircraft collision avoidance dynamical system, determining barriers between possible capture regions by optimal control problem solution
Optimal characteristics for single-input single- output memoryless time invariant nonlinear dynamic systems
Linear dynamic system recursive state estimation for set-membership description of uncertainty under unknown input disturbances and observation errors
Suboptimal design of closed loop least upper bound fuel control for dynamic systems, minimizing fuel consumption on basis of fixed ultimate error
Gradient search procedures application for nonlinear system unknown parameters identification from system dynamic response observations
A nonlinear analog simulation of a turbojet engine was developed. The purpose of the study was to establish simulation techniques applicable to propulsion system dynamics and controls research. A schematic model was derived from a physical description of a J85-13 turbojet engine. Basic conservation equations were applied to each component along with their individual performance characteristics to derive a mathematical representation. The simulation was mechanized on an analog computer. The simulation was verified in both steady-state and dynamic modes by comparing analytical results with experimental data obtained from tests performed at the Lewis Research Center with a J85-13 engine. In addition, comparison was also made with performance data obtained from the engine manufacturer. The comparisons established the validity of the simulation technique.
The results of research in applying statistical methods to the problem of structural dynamic system identification are presented. The study is in three parts: a review of previous approaches by other researchers, a development of various linear estimators which might find application, and the design and development of a computer program which uses a Bayesian estimator. The method is tried on two models and is successful where the predicted stiffness matrix is a proper model, e.g., a bending beam is represented by a bending model. Difficulties are encountered when the model concept varies. There is also evidence that nonlinearity must be handled properly to speed the convergence.
A test facility was designed and built for conducting complete dynamic systems tests of the OAO spacecraft. The operating principle of the facility is illustrated for a single control axis. The test facility is described which was built and used to test the stabilization and control system of the OAO B spacecraft. Fine pointing of the spacecraft was demonstrated to better than 0.5 seconds of arc. Other spacecraft functions tested were gimbaled and boresight star tracker operations, coarse and fine slew maneuvers, inertial guidance operation, settling time of the spacecraft control system, and transfers between all modes of control.
Equations of motion are established for a dynamic system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in the orbit corrections, a set of variational equations is derived. These assume a notably compact form through the introduction of a matrix operator D. The above system of differential equations is integrated numerically on a computer.
This program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form (written in FORTRAN 2 for the IBM 7094 computer). A synchronized material property concept utilizing incremental time steps and the finite element matrix displacement approach has been adopted for the current analysis. A special option enables employment of constant time steps in the logarithmic scale, thereby reducing computational efforts resulting from accumulative material memory effects. A wide variety of structures with elastic or viscoelastic material properties can be analyzed by VISCEL. The program is written in FORTRAN 5 language for the Univac 1108 computer operating under the EXEC 8 system. Dynamic storage allocation is automatically effected by the program, and the user may request up to 195K core memory in a 260K Univac 1108/EXEC 8 machine. The physical program VISCEL, consisting of about 7200 instructions, has four distinct links (segments), and the compiled program occupies a maximum of about 11700 words decimal of core storage.
Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.
This paper compares three approaches to the stability of hybrid dynamical systems, all three methods being based on the Liapunov direct method. The first method uses testing density functions, whereas the second involves defining certain integral coordinates. Both the method using testing density functions and the method of integral coordinates lead to closed-form stability criteria in terms of the system parameters. Criteria obtained using the method of integral coordinates are in general less restrictive than those derived by the method using testing density functions. On the other hand, the latter method is easier to apply and requires less work than the former. The third method is the standard modal analysis. The modal analysis generally yields more involved criteria, depending on the number of modes used to represent the elastic displacements. As an application, the attitude stability of an earth-pointing satellite with multi-elastic domains is investigated.
Discussion of 'model following,' a term used to describe a class of problems characterized by having two dynamic systems, generically known as the 'plant' and the 'model,' it being required to find a controller to attach to the plant so as to make the resultant compensated system behave, in an input/output sense, in the same way as the model. The approach presented to the problem takes a structural point of view. The result is a complex but informative definition which solves the problem as posed. The application of both the algorithm and its basis, equicontrollability, to the decoupling problem is considered.
A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.