Results for “linear dynamical systems” — Page 25

NASA NTRS1981

A real time Pegasus propulsion system model for VSTOL piloted simulation evaluation

A real time propulsion system modeling technique suitable for use in man-in-the-loop simulator studies was developd. This technique provides the system accuracy, stability, and transient response required for integrated aircraft and propulsion control system studies. A Pegasus-Harrier propulsion system was selected as a baseline for developing mathematical modeling and simulation techniques for VSTOL. Initially, static and dynamic propulsion system characteristics were modeled in detail to form a nonlinear aerothermodynamic digital computer simulation of a Pegasus engine. From this high fidelity simulation, a real time propulsion model was formulated by applying a piece-wise linear state variable methodology. A hydromechanical and water injection control system was also simulated. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model was programmed for interfacing with a Harrier aircraft simulation. Typical propulsion system simulation results are presented.

Mihaloew, J. R.↗

NASA NTRS1988

Dynamic control of robot arms in tasks space using nonlinear feedback

Differential geometric system and control theory is used to develop a new dynamic system feedback technique for robot task space commands. The nonlinear robot arm system is feedback-linearized and simultaneously is output-decoupled by an appropriate nonlinear feedback and nonlinear coordinate transformation. On the joint space level, the scheme only commands drive forces or torques or their equivalent quantities addressed to the joint drives. An important property of the technique is that the planned and commanded task space trajectory together with its time derivatives directly drive the robot arm through a linear system model. A method for task space motion planning matching the requirements of the new scheme is briefly presented. The implications of the new technique for second and third order model robot arms with and without force feedback measuremnts and for two or more dynamically cooperating robot arms are discussed.

Bejczy, A. K.↗

NASA NTRS1989

Identification of space shuttle main engine dynamics

System identification techniques are used to represent the dynamic behavior of the Space Shuttle Main Engine. The transfer function matrices of the linearized models of both the closed loop and the open loop system are obtained by using the recursive maximum likelihood method.

Duyar, Ahmet↗

NASA NTRS1989

Identification of Space Shuttle Main Engine dynamics

System identification techniques are used to represent the dynamic behavior of the Space Shuttle Main Engine. The transfer function matrices of the linearized models of both the closed loop and the open loop system are obtained by using the recursive maximum likelihood method.

Duyar, Ahmet↗

NASA NTRS1990

Optimal Regulator Algorithms For The Control Of Linear Systems (ORACLS)

Control theory design package offers engineer full range of subroutines to manipulate and solve Linear-Quadratic-Gaussian types of problems. ORACLS is rigorous tool, intended for multi-input and multi-output dynamic systems in both continuous and discrete form. Written in FORTRAN.

Frisch, Harold P.↗

NASA NTRS1976

Trends in modern system theory

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

Athans, M.↗

NASA NTRS1990

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Park, K. C.↗

NASA NTRS2003

Control Law Design in a Computational Aeroelasticity Environment

A methodology for designing active control laws in a computational aeroelasticity environment is given. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this paper solves the transonic small disturbance aerodynamic equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structure. These structural responses are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The Eigensystem Realization Algorithm is then employed to develop an explicit state-space model of the equivalent linear system. The Linear Quadratic Guassian control law design technique is employed to design a control law. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the aeroelastic system is increased through increased angle-of-attack changes.

Newsom, Jerry R.↗

NASA NTRS1984

Investigation of dynamic noise affecting geodynamics information in a tethered subsatellite

The effects of a tethered satellite system's internal dynamics on the subsatellite were calculated including both overall motions (libration and attitude oscillations) and internal tether oscillations. The SKYHOOK tether simulation program was modified to operate with atmospheric density variations and to output quantities of interest. Techniques and software for analyzing the results were developed including noise spectral analysis. A program was begun for computing a stable configuration of a tether system subject to air drag. These configurations will be of use as initial conditions for SKYHOOK and, through linearized analysis, directly for stability and dynamical studies. A case study in which the subsatellite traverses an atmospheric density enhancement confirmed some theoretical calculations, and pointed out some aspects of the interaction with the tether system dynamics.

Gullahorn, G. E.↗

NASA NTRS1986

Joint nonlinearity effects in the design of a flexible truss structure control system

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Mercadal, Mathieu↗

NASA NTRSDate not supplied

Advanced Modeling of Control-Structure Interaction in Thrust Vector Control Systems

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of 8 mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. Two actuators are used to move each engine in two planes perpendicular to one another (i.e., pitch and yaw). The TVC system design leverages hardware from the Space Shuttle program as well as new hardware designed specifically for the Core Stage. During the development of the SLS TVC system, a family of advanced dynamics models were developed to extend and compliment the simplified quasi-linear “simplex” model historically used for flight control design and stability analysis. The importance of these advanced models became increasingly evident after ambient and hot fire testing of the Core Stage, which revealed a number of findings associated with the dynamic response of the TVC integrated system. Test responses suggested that the TVC did not meet its performance specifications and its step and frequency responses exhibited unexpected departures from prior lab tests and modeled behavior. One driving factor for these results was a higher-than-expected degree of coupling between the TVC system, the engine dynamics, and the Core Stage structure. This paper is the third installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. In this paper, a new method of modeling rocket vehicle thrust vectoring servoelastic dynamics is presented. In this approach, the load dynamics are replaced by a detailed finite element model containing both the rigid body and elastic modes. A partitioning technique is used to compute the effective compliance from the modal data and obtain accurate simulation results using a reduced number of generalized coordinates. Coupled backup structure and nozzle attach compliance effects on multiple engines are captured in higher fidelity than with a spring approximation, eliciting novel effects due to the complex load paths involved in the Core Stage structure. Validation of the model is demonstrated using a variety of structural/modal, laboratory, and full-scale hot fire test data.

Launch Vehicles↗

NASA NTRSDate not supplied

Advanced Modeling of Control-Structure Interaction in Thrust Vector Control Systems

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of 8 mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. Two actuators are used to move each engine in two planes perpendicular to one another (i.e., pitch and yaw). The TVC system design leverages hardware from the Space Shuttle program as well as new hardware designed specifically for the Core Stage. During the development of the SLS TVC system, a family of advanced dynamics models were developed to extend and compliment the simplified quasi-linear “simplex” model historically used for flight control design and stability analysis. The importance of these advanced models became increasingly evident after ambient and hot fire testing of the Core Stage, which revealed a number of findings associated with the dynamic response of the TVC integrated system. Test responses suggested that the TVC did not meet its performance specifications and its step and frequency responses exhibited unexpected departures from prior lab tests and modeled behavior. One driving factor for these results was a higher-than-expected degree of coupling between the TVC system, the engine dynamics, and the Core Stage structure. This paper is the third installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. In this paper, a new method of modeling rocket vehicle thrust vectoring servoelastic dynamics is presented. In this approach, the load dynamics are replaced by a detailed finite element model containing both the rigid body and elastic modes. A partitioning technique is used to compute the effective compliance from the modal data and obtain accurate simulation results using a reduced number of generalized coordinates. Coupled backup structure and nozzle attach compliance effects on multiple engines are captured in higher fidelity than with a spring approximation, eliciting novel effects due to the complex load paths involved in the Core Stage structure. Validation of the model is demonstrated using a variety of structural/modal, laboratory, and full-scale hot fire test data.

Launch Vehicles↗

NASA NTRS1988

Studies of the dynamics of the twin-lift system

A full set of equations of motion for the twin lift system, linearized about a hover trim condition were derived and presented. It is shown that this full set of equations of motion decouples into simpler sets of equations of motion if the aerodynamic coupling derivatives of the helicopters are neglected. One of these decoupled sets of equations of motion (referred to as the planar set) was studied at length. The other decoupled set (referred to as the nonplanar set) is examined here. It is shown that when the geometric configuration of the twin-lift is symmetric that a further decoupling is possible into antisymmetric and symmetric sets of equations. One set of these reduced equations of motion referred to as the antisymmetric set is directly equivalent to the longitudinal motion of a single helicopeter with a sling load. The second set, referred to as the symmetric set corresponds to the rotation of the entire system without load motion. As in the case of the planar symmetric motion, the location of the tether attachment point influences the stability of the nonplanar symmetric mode. The trend is opposite however in the nonplanar case in that an attachment point below the helicopter center of gravity gives a favorable effect on the stability. The effect is not as strong however as the unfavorable effect on the planar symmetric mode.

Curtiss, H. C., Jr.↗

NASA NTRS1974

Analysis of the feedback system in a nonintrusive dynamic flowmeter for measuring Pogo oscillations

Equations were developed which describe the closed loop feedback system operation of a proposed ultrasonic, dynamic, nonintrusive flowmeter whose design is based on a constant phase, voltage controlled frequency feedback concept. These equations are based on linear feedback system theory. The time constant of a low pass filter is taken into account. The equations show that the larger the open loop gain, the smaller the error due to fluctuations in the speed of sound and the smaller the effective time constant.

Chapin, W. G.↗

NASA NTRS2003

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.↗

NASA NTRS1993

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Adams, Richard J.↗

NASA NTRS1982

Optimal Regulator Algorithms for the Control of Linear Systems

Control-theory design package, called Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), aids in design of controllers and optimal filters for systems modeled by linear, time invariant differential and difference equations. ORACLS is particularly attractive rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete forms.

Armstrong, E. S.↗

NASA NTRS1976

A photon counting array photometer using an intensified charge coupled device

An array photometer which uses an intensified charge coupled device was developed. This system, the University of Maryland Array Photometer (UMAP), has the ability to discriminate single photoelectron events in real time at a 4 Megahertz rate. The photosensor uses an S-20 photocathode and a Fairchild CCD202 with a 100 by 100 array of separate individual channels. The overall system has demonstrated a noise level which permits single photoelectron discrimination, a scan rate of 400 frames per second, a very linear response, and very low lag. The UMAP system has a very large dynamic range exceeding 10,000 in the photon counting mode. A special technique to extend the dynamic range to 1,000,000 was described. The performance parameters of this system, both in the laboratory and on the telescope were cited. Data from these observations were discussed to illustrate the system sensitivity, which is basically limited by the pixel size in the array, rather than the electrooptics.

Currie, D. G.↗