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A theorem and its corollary are presented in which conditions are stated for a global transformation of a nonlinear system to a linear system. An explicit method for constructing such a transformation is given, and the important noncharacteristic matrix is introduced. Examples illustrating the technique are presented.
It is known that an effective control system is the key condition for successful implementation of high-performance magnetic servo systems. Major issues to design such control systems are nonlinearity; unmodeled dynamics, such as secondary effects for copper resistance, stray fields, and saturation; and that disturbance rejection for the load effect reacts directly on the servo system without transmission elements. One typical approach to design control systems under these conditions is a special type of nonlinear feedback called gain scheduling. It accommodates linear regulators whose parameters are changed as a function of operating conditions in a preprogrammed way. In this paper, an on-line learning fuzzy control strategy is proposed. To inherit the wealth of linear control design, the relations between linear feedback and fuzzy logic controllers have been established. The exercise of engineering axioms of linear control design is thus transformed into tuning of appropriate fuzzy parameters. Furthermore, fuzzy logic control brings the domain of candidate control laws from linear into nonlinear, and brings new prospects into design of the local controllers. On the other hand, a self-learning scheme is utilized to automatically tune the fuzzy rule base. It is based on network learning infrastructure; statistical approximation to assign credit; animal learning method to update the reinforcement map with a fast learning rate; and temporal difference predictive scheme to optimize the control laws. Different from supervised and statistical unsupervised learning schemes, the proposed method learns on-line from past experience and information from the process and forms a rule base of an FLC system from randomly assigned initial control rules.
Nonstationary colored noise linear shaping filter to transform white noise into nonstationary random process with specified covariance function
Differential-pressure transducer includes a piston, helical springs, and a linear variable-differential transformer concentric with piston. Transducer senses motion of piston in response to changes in pressure differential. Eight seals within the transducer prevent fluid leakage from one pressure line to the other. Reliability and operating life of the new unit are superior to many conventional transducers.
Electrohydraulic servo controls moving elements of airflow valve. Position of moving element and attached piston is monitored by linear variable-differential transformer (LVDT). Single-stage servo valve lets fluid into and out of piston volume in response to feedback signals from the LVDT.
Radio astronomers have investigated spatial frequencies and their relationship to apertures with the objective to improve the resolution in radio observations. Welch (1965) has related Fourier transform theory developed for linear communications to aperture design problems, while Fakley (1959) has conducted a comparison between the performances of a time-averaged product array and an intraclass correlator. The present investigation is concerned with an approach which resembles very closely the intraclass correlator system considered by Fakley. A description is presented of a process whereby a thinned array of elements samples selected spatial frequencies from a uniform signal wave front incident on the array. The spatial frequencies are used to generate a set of synthetic spatial frequencies which behave as though they had been sampled by a fully filled array. Beam formation is obtained by summing the set of synthetic spatial frequencies.
Repetitive measurements simplified by tool based on LVDT operation. With fingers in open position, Gap-measuring tool rests on digital readout instrument. With fingers inserted in gap, separation alters inductance of linear variable-differential transformer in plastic handle. Originally developed for measuring gaps between surface tiles of Space Shuttle orbiter, tool reduces measurement time from 20 minutes per tile to 2 minutes. Also reduces possibility of damage to tiles during measurement. Tool has potential applications in mass production; helps ensure proper gap dimensions in assembly of refrigerator and car doors and also used to measure dimensions of components and to verify positional accuracy of components during progressive assembly operations.
System for checking levelness of machines and structures requires less time and labor than conventional optical systems. Measures differences in elevation to within 0.002 in. (0.05 mm). Floats at opposite ends of structure determine positions of cores in linear variable-differential transformers. Outputs of LVDT's carried by cables to control console, where displayed to operator as difference in core levels and therfore of ends of structure.
Electrical properties of solenoids imitated for tests of control circuits. Simulation circuit imitates voltage and current responses of two engine-controlling solenoids. Used in tests of programs of digital engine-control circuits, also provides electronic interface with circuits imitating electrical properties of pressure sensors and linear variable-differential transformers. Produces voltages, currents, delays, and discrete turnon and turnoff signals representing operation of solenoid in engine-control relay. Many such circuits used simulating overall engine circuitry.
A series of techniques are presented for analyzing airplane control and output characteristics. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled, modal coordinates. Techniques for analyzing the impacts of system inputs on the fundamental modes of motion and the appearance of these modes in the system outputs are explained. Scaled modal matrices are used to compute steady-state control inputs which optimize the steady-state response of selected system outputs. Graphics which promote quick understanding of the analysis are presented to display the resulting vectors and matrices. The defined analysis techniques are applied to an example airplane model, illustrating the insight which can be acquired using the described modal techniques.
The SKITTER 2 design is a monocoque version of the proposed lunar three-legged walker. By the definition of monocoque, the body and legs are a shell with no internal ribbing or supports added for absorbing stresses. The purpose of the monocoque is to encase the elements used for power transmission, power supply, and control of the motion. The material for the structure is a vinyl ester resin, Derakane 8084. This material is easily formable and locally obtainable. The body consists of a hexagonally shaped cylinder with truncated hexagonal pyramids on the top and botton. The legs are eight inch diameter cylinders. The legs are comprised of a tibia section and a femur section. The SKITTER 2 is powered by six actuators which provide linear forces that are transformed into rotary torques by a series of chains and sprockets. The joints connect the femur to the body and the tibia to the femur. Surrounding the joints are flexible rubber hoses that fully encase the chains and sprockets. The SKITTER 2 is capable of walking upside down, righting itself after being overturned, and has the ability to perform in many environments. Applications for this walker include lunar transport or drilling, undersea exploration, and operation in severe surroundings such as arctic temperatures or high radiation.
The progress to date on the analysis and design of a high power, digitally controlled spacecraft power system is described. Several battery discharger topologies were compared for use in the space platform application. Updated information has been provided on the battery voltage specification. Initially it was thought to be in the 30 to 40 V range. It is now specified to be 53 V to 84 V. This eliminated the tapped-boost and the current-fed auto-transformer converters from consideration. After consultations with NASA, it was decided to trade-off the following topologies: (1) boost converter; (2) multi-module, multi-phase boost converter; and (3) voltage-fed push-pull with auto-transformer. A non-linear design optimization software tool was employed to facilitate an objective comparison. Non-linear design optimization insures that the best design of each topology is compared. The results indicate that a four-module, boost converter with each module operating 90 degrees out of phase is the optimum converter for the space platform. Large-signal and small-signal models were generated for the shunt, charger, discharger, battery, and the mode controller. The models were first tested individually according to the space platform power system specifications supplied by NASA. The effect of battery voltage imbalance on parallel dischargers was investigated with respect to dc and small-signal responses. Similarly, the effects of paralleling dischargers and chargers were also investigated. A solar array and shunt model was included in these simulations. A model for the bus mode controller (power control unit) was also developed to interface the Orbital replacement Unit (ORU) model to the platform power system. Small signal models were used to generate the bus impedance plots in the various operating modes. The large signal models were integrated into a system model, and time domain simulations were performed to verify bus regulation during mode transitions. Some changes have subsequently been incorporated into the models. The changes include the use of a four module boost discharger, and a new model for the mode controller, which includes the effects of saturation. The new simulations for the boost discharger show the improvement in bus ripple that can be achieved by phase-shifted operation of each of the boost modules.
An engineering approach for analyzing airplane control and output characteristics is presented. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled coordinates. The scaling is accomplished by applying various transformations to the system to employ prior engineering knowledge of the airplane physics. Two different analysis techniques are then explained. Modal analysis techniques calculate the influence of each system input on each fundamental mode of motion and the distribution of each mode among the system outputs. The optimal steady state response technique computes the blending of steady state control inputs that optimize the steady state response of selected system outputs. Analysis of an example airplane model is presented to demonstrate the described engineering approach.
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Inertial linear actuators developed to suppress residual accelerations of nominally stationary or steadily moving platforms. Function like long-stroke version of voice coil in conventional loudspeaker, with superimposed linear variable-differential transformer. Basic concept also applicable to suppression of vibrations of terrestrial platforms. For example, laboratory table equipped with such actuators plus suitable vibration sensors and control circuits made to vibrate much less in presence of seismic, vehicular, and other environmental vibrational disturbances.
Instrumented hydraulic constrained blister-peel apparatus obtains data on degree of bonding between specimen of rubbery material and rigid plate. Growth of blister tracked by video camera, digital clock, pressure transducer, and piston-displacement sensor. Cylinder pressure controlled by hydraulic actuator system. Linear variable-differential transformer (LVDT) and float provide second, independent measure of change in blister volume used as more precise volume feedback in low-growth-rate test.
Thoriated tungsten extension rod fabricated to replace stainless-steel extension rod attached to linear variable-differential transformer in gap-measuring gauge. Threads formed on end of rod by machining with special fixtures and carefully chosen combination of speeds and feeds.
Report describes modifications of design of type of ball-screw linear actuator driven by dc motor, with linear-displacement feedback via linear variable-differential transformer (LVDT). Actuators used to position spacecraft engines to direct thrust. Modifications directed toward ensuring reliable and predictable operation during planned 12-year cruise and interval of hard use at end of cruise.