Design of piecewise-linear switching functions for relay control systems.
Optimum design of piecewise-linear switching functions for linear, constant, lumped systems with single ideal relay controller
OPTIMAL CONTROL↗
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Results for “linearity”
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Linear problems for systems of nonlinear differential equations.
Linear problems involving linear and nonlinear systems of differential equations, proving theorems for nonlinear differential equation systems
Opial, Z.↗
Sub-optimal control of non-linear single input systems.
Suboptimal control generation for nonlinear single input systems by linear combination of states and repeated linearization of equations system
Aggarwal, J. K.↗
Linear voltage-to-frequency converter
Voltage-to-frequency converter, with ultra-high input impedance and linear response, is used in analog to digital data conversion systems. Voltage-to-current converter, using MOSFET devices and a multivibrator, has ultra-linear voltage-to-frequency characteristics. It replaces voltage sensitive magnetic-core oscillators.
Lokerson, D. C.↗
Electrothermal linear actuator
Converting electric power into powerful linear thrust without generation of magnetic fields is accomplished with an electrothermal linear actuator. When treated by an energized filament, a stack of bimetallic washers expands and drives the end of the shaft upward.
Derr, L. J.↗
On the Chebyshev solution of inconsistent linear equations.
Ascent algorithm for Chebyshev solution of inconsistent linear equations, noting use for linear programming
Tewarson, R. P.↗
On the design of optimal linear systems using only output-variable feedback.
Optimal control of linear systems with state variables generated by linear feedback from output variables, considering time variance
Athans, M.↗
On the linear smoothing problem.
Smoothing problem for linear discrete time system, converting problem to special case of standard linear filtering problem
Willman, W. W.↗
Ordinary differential equations in linear topological space. II.
Ordinary differential equations in linear topological space extended from Fattorini investigation, emphasizing use of linear operator
Fattorini, H. O.↗
Discrete control of linear distributed systems with application to the deformable primary mirror of a large orbiting telescope
One of the more significant technological problems associated with the orbital operation of large astronomical telescope's is the fabrication and maintenance of the primary mirror surface to the tolerance required for diffraction-limited performance. An interesting approach to the solution of this problem involves continuously measuring and automatically correcting the optical surface of a thin deformable mirror by means of discrete actuators located on its rear surface: The realization of diffraction-limited performance from a telescope in space by this method rests on the ability of the designer to achieve extremely accurate control of a highly complex, interacting, multivariable system. This paper presents the results of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is then exerted over a finite number (equal.to the number of actuators) of the most significant modes. Through the application of the modal expansion technique the mirror equation of motion is transformed tb a set of uncoupled, linear, time-invariant, ordinary differential equations. The desired dynamic response and static accuracy may then be achieved by the application of classical single-variable design techniques. The formulation of a quadratic performance index which incorporates a measure of image quality permits determination of the trade-off between the-number of actuators and optical purity. A criterion for defining actuator placement and pad size is presented which minimizes the tendency of the controller to excite the unmonitored modes.
Jeremiah F Creedon↗
Simplification in the computation of the sensitivity functions for constant coefficient linear systems
Constant coefficient linear systems sensitivity functions computational procedure using nth order differential equations linear transformations
Denery, D. G.↗
A linear programming manual
Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.
Tuey, R. C.↗
An efficient parallel algorithm for the solution of a tridiagonal linear system of equations
Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.
Stone, H. S.↗
A program for identification of linear systems
A program has been written for the identification of parameters in certain linear systems. These systems appear in biomedical problems, particularly in compartmental models of pharmacokinetics. The method presented here assumes that some of the state variables are regularly modified by jump conditions. This simulates administration of drugs following some prescribed drug regime. Parameters are identified by a least-square fit of the linear differential system to a set of experimental observations. The method is especially suited when the interval of observation of the system is very long.
Buell, J.↗
Synthesis procedure for linear time-varying feedback systems with large parameter ignorance
The development of synthesis procedures for linear time-varying feedback systems is considered. It is assumed that the plant can be described by linear differential equations with time-varying coefficients; however, ignorance is associated with the plant in that only the range of the time-variations are known instead of exact functional relationships. As a result of this plant ignorance the use of time-varying compensation is ineffective so that only time-invariant compensation is employed. In addition, there is a noise source at the plant output which feeds noise through the feedback elements to the plant input. Because of this noise source the gain of the feedback elements must be as small as possible. No attempt is made to develop a stability criterion for time-varying systems in this work.
Mcdonald, T. E., Jr.↗
Circuit model for characterizing the nearly linear behavior of avalanche diodes in amplifier circuits
A nonlinear circuit model for avalanche diodes is proposed. The model was derived by assuming that the bias dependence of the elements in a known small-signal equivalent-circuit model for existing diodes arises in a manner consistent with the theory of an idealized Read-type device. The model contains a nonlinear R-L branch, a controlled source, and a linear depletion capacitance. The model is used in the nearly linear sense to predict intermodulation distortion and gain compression in avalanche diode amplifiers. Computed results for amplifiers with existing diodes are shown to be in good agreement with experiment.
Penfield, P., Jr.↗
Viscel: A general purpose computer program for analysis of linear viscoelastic structures, volume 2
The VISCEL program is a general purpose computer program developed for equilibrium analysis of linear viscoelastic structures. The program is written in FORTRAN 5 language to operate on the Univac 1108 computer under the EXEC 8 operating system. The program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form written for the IBM 7094 computer. Finite element matrix displacement approach coupled with the synchronized material property concept, utilizing incremental time steps, was adopted for the solution presented. The step-by-step procedure involves solution of recursive equations in the time domain, which takes into account the memory of material properties. Incremental and accumulative displacements and stresses are obtained at the end of each time step. In order to minimize the extent of computations resulting from accumulative effects of material memory, the program provides an option which enables the employment of constant time steps in the logarithmic scale. Program documentation is presented.
Gupta, K. K.↗
A study of an advanced confined linear energy source
A literature survey and a test program to develop and evaluate an advanced confined linear energy source were conducted. The advanced confined linear energy source is an explosive or pyrotechnic X-Cord (mild detonating fuse) supported inside a confining tube capable of being hermetically sealed and retaining all products of combustion. The energy released by initiation of the X-Cord is transmitted through the support material to the walls of the confining tube causing an appreciable change in cross sectional configuration and expansion of the tube. When located in an assembly that can accept and use the energy of the tube expansion, useful work is accomplished through fracture of a structure, movement of a load, reposition of a pin, release of a restraint, or similar action. The tube assembly imparts that energy without release of debris or gases from the device itself. This facet of the function is important to the protection of men or equipment located in close proximity to the system during the time of function.
Anderson, M. C.↗