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At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A degree of controllability definition - Fundamental concepts and application to modal systems

Starting from basic physical considerations, this paper develops a concept of the degree of controllability of a control system, and then develops numerical methods to generate approximate values of the degree of controllability for any linear time-invariant system. In many problems, such as the control of future, very large, flexible spacecraft and certain chemical process control problems, the question of how to choose the number and locations of the control system actuators is an important one. The results obtained here offer the control system designer a tool which allows him to rank the effectiveness of alternative actuator distributions, and hence to choose the actuator locations on a rational basis. The degree of controllability is shown to take a particularly simple form when the dynamic equations of a satellite are in second-order modal form. The degree of controllability concept has still other fundamental uses - it allows one to study the system structural relations between the various inputs and outputs of a linear system, which has applications to decoupling and model reduction.

Viswanathan, C. N.↗
NASA NTRS1972

Parameter uncertainties in control system design.

Development of a design method for including the effects of parameter uncertainties in the design of linear control systems. The approach taken to this problem may be classified as a special case of the stochastic control problem. Thus the formulation is based on the minimization of the expected value of a quadratic performance index defined in terms of the system state vector. The uncertainty in the value of the performance index is the result of the statistical nature of the system parameters rather than a random input signal. It is shown that the expected value of the performance index may be written as a sum of two terms under the assumption of first-order variations of the system state. The first of these terms expresses the nominal performance of the system when the system parameters assume their mean values. The second term represents the effect of the uncertainties on the expected value of the performance index, and is interpreted as an index of system sensitivity.

Palsson, T.↗
NASA NTRS1979

Design of flight control systems via robust decoupled servomechanism theory

Decoupling theory and robust servomechanism theory are applied to the design of linear multivariable systems with large parameter variations. In addition to being approximately decoupled in the transient period, the over-all system achieves tracking and disturbance rejection robustly in the steady state. An example in flight control system is given.

Wang, S.-H.↗
NASA NTRS1987

Analyzing Feedback Control Systems

Interactive controls analysis (INCA) program developed to provide user-friendly environment for design and analysis of linear control systems, primarily feedback control. Designed for use with both small- and large-order systems. Using interactive-graphics capability, INCA user quickly plots root locus, frequency response, or time response of either continuous-time system or sampled-data system. Configuration and parameters easily changed, allowing user to design compensation networks and perform sensitivity analyses in very convenient manner. Written in Pascal and FORTRAN.

Bauer, Frank H.↗
NASA NTRS1990

Non-linear dynamic analysis of geared systems

Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. A dynamic finite element model of the linear time invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.

Singh, Rajendra↗
NASA NTRS1975

Essential uncontrollability of discrete linear, time-invariant, dynamical systems

The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

Cliff, E. M.↗
NASA NTRS1981

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

Harten, A.↗
NASA NTRS1985

The dynamics and control of large flexible space structures, 8

A development of the in plane open loop rotational equations of motion for the proposed Spacecraft Control Laboratory Experiment (SCOLE) in orbit configuration is presented based on an Eulerian formulation. The mast is considered to be a flexible beam connected to the (rigid) shuttle and the reflector. Frequencies and mode shapes are obtained for the mast vibrational appendage modes (assumed to be decoupled) for different boundary conditions based on continuum approaches and also preliminary results are obtained using a finite element representation of the mast reflector system. The linearized rotational in plane equation is characterized by periodic coefficients and open loop system stability can be examined with an application of the Floquet theorem. Numerical results are presented to illustrate the potential instability associated with actuator time delays even for delays which represent only a small fraction of the natural period of oscillation of the modes contained in the open loop model of the system. When plant and measurement noise effects are added to the previously designed deterministic model of the hoop column system, it is seen that both the system transient and steady state performance are degraded. Mission requirements can be satisfied by appropriate assignment of cost function weighting elements and changes in the ratio of plant noise to measurement noise.

Bainum, P. M.↗
DOE OSTI2022

Composing preconditioners for multiphysics PDE systems with applications to Generalized MHD

New patch smoothers or relaxation techniques are developed for solving linear matrix equations coming from systems of discretized partial differential equations (PDEs). One key linear solver challenge for many PDE systems arises when the resulting discretization matrix has a near null space that has a large dimension, which can occur in generalized magnetohydrodynamic (GMHD) systems. Patch-based relaxation is highly effective for problems when the null space can be spanned by a basis of locally supported vectors. The patch-based relaxation methods that we develop can be used either within an algebraic multigrid (AMG) hierarchy or as stand-alone preconditioners. These patch-based relaxation techniques are a form of well-known overlapping Schwarz methods where the computational domain is covered with a series of overlapping sub-domains (or patches). Patch relaxation then corresponds to solving a set of independent linear systems associated with each patch. In the context of GMHD, we also reformulate the underlying discrete representation used to generate a suitable set of matrix equations. In general, deriving a discretization that accurately approximates the curl operator and the Hall term while also producing linear systems with physically meaningful near null space properties can be challenging. Unfortunately, many natural discretization choices lead to a near null space that includes non-physical oscillatory modes and where it is not possible to span the near null space with a minimal set of locally supported basis vectors. Further discretization research is needed to understand the resulting trade-offs between accuracy, stability, and ease in solving the associated linear systems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Control logic to track the outputs of a command generator or randomly forced target

A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).

Trankle, T. L.↗
NASA NTRS1985

Performance of direct and iterative algorithms on an optical systolic processor

The frequency-multiplexed optical linear algebra processor (OLAP) is treated in detail with attention to its performance in the solution of systems of linear algebraic equations (LAEs). General guidelines suitable for most OLAPs, including digital-optical processors, are advanced concerning system and component error source models, guidelines for appropriate use of direct and iterative algorithms, the dominant error sources, and the effect of multiple simultaneous error sources. Specific results are advanced on the quantitative performance of both direct and iterative algorithms in the solution of systems of LAEs and in the solution of nonlinear matrix equations. Acoustic attenuation is found to dominate iterative algorithms and detector noise to dominate direct algorithms. The effect of multiple spatial errors is found to be additive. A theoretical expression for the amount of acoustic attenuation allowed is advanced and verified. Simulations and experimental data are included.

Ghosh, A. K.↗
NASA NTRS1981

Thermal infrared array, phase 1. Volume 1: Technical

The recommended design configuration for the focal plane array of a 1,000 element linear pushbroom system consists of 32 modules; the complete configuration is built by butting together two 1024 linear arrays. Each of the linear arrays is formed by edge butting 16 modules together. By staggering the modules of the two rows, the channel outages which occur where the modules are edge butted can be eliminated. Two stages TDI operation is performed by the post processing electronics, which reduces the design complexity of the focal plane. Systems studies show that: (1) a single focal plane design can satisfy both the LEO and SEOS mission configurations; (2) available optical designs can meet mission goals; (3) MTF can be traded with optical complexity in a future study; (4) a chopping mechanism can be devised to modifying modulate radiation to a 4-inch focal plane as well as insert two calibration sources at the required frequencies for chopping and calibration; (5) radiative cooling technology should be suitable for a future sensor in either mission configuration; and (6) cold shielding is not a requirement.

Source record↗
NASA NTRS1997

Nonlinear Behavior of a Typical Airfoil Section with Control Surface Freeplay: A Numerical and Experimental Study

A three degree-of-freedom aeroelastic typical section with control surface freeplay is modeled theoretically as a system of piecewise linear state-space models. The system response is determined by time marching of the governing equations using a standard Runge-Kutta algorithm in conjunction with Henon's method for integrating a system of equations to a prescribed surface of phase space section. Henon's method is used to locate the "switching points" accurately and efficiently as the system moves from one linear region into another. An experimental model which closely approximates the three degree-of-freedom, typical section in two-dimensional, incompressible flow has been created to validate the theoretical model. Consideration is given to modeling realistically the structural damping present in the experimental system. The effect of the freeplay on the system response is examined numerically and experimentally. The development of the state-space model offers a low-order, computationally efficient means of modeling fully the freeplay nonlinearity and may offer advantages in future research which will investigate the effects of freeplay on the control of flutter in the typical section.

Conner, M. D.↗
DOE OSTI2023

An electrified boom actuation system with energy regeneration capability driven by a novel electro-hydraulic unit

This paper presents a novel electrified solution for linear actuation systems, which has undergone a successful in-vehicle demonstration, marking a significant advancement in this field. Aligned with the growing trend towards electrification, this solution holds promise for a wide range of off-road applications. The showcased electrohydraulic actuation architecture enables efficient four-quadrant operation and incorporates energy recovery capabilities. At the core of the system lies a distinctive electro-hydraulic unit, integrating a fixed hydraulic pump and a variable-speed electric motor into a compact and powerful entity. A specialized hydraulic system is designed to efficiently transform electrical energy from the electro-hydraulic unit into boom cylinder actuation. The sizing of the system is determined by the boom operation of a commercial compact loader. The maximum power output of the electro-hydraulic system is approximately 15 kW. The components of the proposed system are integrated into the reference vehicle, and comprehensive performance tests are conducted. The results of the tests performed on the vehicle with the boom lifting and lowering cycle indicate an overall system efficiency of 60%. The electrified solution consumes only about one-third of the energy used by the conventional boom actuation system on the reference machine, while exhibiting energy savings exceeding 75% during specific work phases. The energy savings come mainly from energy regeneration and minimal loss from throttling through the specialized hydraulic circuit design. Finally, the successful demonstration on the reference vehicle underscores the practicality and effectiveness of the proposed electrified solution in current mobile hydraulic applications

42 ENGINEERING↗