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Description of a general synthesis procedure for the compensation of linear multivariable systems through the combined use of dynamic feed-forward compensation and linear state variable feedback. Applications of the synthesis algorithm presented to problems of decoupling and exact model matching illustrate its use.
An on-line adaptive technique is developed to provide a self-contained redundant-sensor navigation system with a capability to utilize its full potentiality in reliability and performance. This adaptive system is structured as a multistage stochastic process of detection, identification, and compensation. It is shown that the detection system can be effectively constructed on the basis of a design value, specified by mission requirements, of the unknown parameter in the actual system, and of a degradation mode in the form of a constant bias jump. A suboptimal detection system on the basis of Wald's sequential analysis is developed using the concept of information value and information feedback. The developed system is easily implemented, and demonstrates a performance remarkably close to that of the optimal nonlinear detection system. An invariant transformation is derived to eliminate the effect of nuisance parameters such that the ambiguous identification system can be reduced to a set of disjoint simple hypotheses tests. By application of a technique of decoupled bias estimation in the compensation system the adaptive system can be operated without any complicated reorganization.
Multivariable control theory is applied to the design of a hierarchial attitude control system for the CARD space vehicle. The system selected uses reaction control jets (RCJ) and control moment gyros (CMG). The RCJ system uses linear signal mixing and a no-fire region similar to that used on the Skylab program; the y-axis and z-axis systems which are coupled use a sum and difference feedback scheme. The CMG system uses the optimum steering law and the same feedback signals as the RCJ system. When both systems are active the design is such that the torques from each system are never in opposition. A state-space analysis was made of the CMG system to determine the general structure of the input matrices (steering law) and feedback matrices that will decouple the axes. It is shown that the optimum steering law and proportional-plus-rate feedback are special cases. A derivation of the disturbing torques on the space vehicle due to the motion of the on-board television camera is presented. A procedure for computing an upper bound on these torques (given the system parameters) is included.
A low phase noise frequency divider composed of a grating arrangement is disclosed. The grating arrangement supplies selected portions of an input reference signal to be divided to a tuned circuit without any phase noise due to the grating action. The arrangement which in one embodiment consists of an FET is connected to the tuned circuit input to short out the input except when the input reference signal amplitude crosses ground level in a positive direction and a gate enabling signal is present at the gate electrode of the FET. The gate enabling signal alone does not decouple the tuned circuit input from ground, therefore phase noise, due to the leading and trailing edges of each gate-enabling signal, is substantially eliminated.
The spherical harmonic coefficients in the gravity field of Mars are determined using a two stage filtering process. In the first stage, a weighted least squares orbit determination processor is applied to Mariner 9 Doppler tracking data to estimate Kepler elements and rates. In the second stage, the Kepler element rates are used as input to another weighted least squares processor that estimates gravity coefficients using the Lagrange perturbation equations. The novelty in this method is the fitting of element rates rather than the elements themselves. This procedure decouples the results from the effects of internal spacecraft dynamics.
An autopilot logic is designed here for controlling a helicopter with a hanging load. A 16th order model for the system is decoupled into four subsystems: (1) a second order system for yawing motion, (2) a second order system for vertical motion, (3) a sixth order system for longitudinal motion, and (4) a sixth order system for lateral motion. A measuring scheme, which could be used in remote areas, is developed and filters are designed to estimate the state variables from these measurements. The autopilot can be used to move the load over short distances without retracting the cables. This is done by automatically shifting the autopilot modes from position-hold (hover) to acceleration-hold to velocity-hold (cruise) to deceleration-hold to velocity-hold (near hover) to position-hold (hover). Use of such an autopilot might save considerable turnaround time. The Sikorsky S-61 helicopter is chosen as an example vehicle. The performance of the controlled system is studied in the presence of longitudinal and lateral winds.
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of finite geometry solids and suggest a possible extension of this technique to nonlinear material behavior.
Heat pipe (HP) thermal control systems designed for possible space shuttle applications were built and tested under this program. They are: (1) a HP augmented cold rail, (2) a HP/phase change material (PCM) modular heat sink and (3) a HP radiating panel for compartment temperature control. The HP augmented cold rail is similar to a standard two-passage fluid cold rail except that it contains an integral, centrally located HP throughout its length. The central HP core helps to increase the local power density capability by spreading concentrated heat inputs over the entire rail. The HP/PCM modular heat sink system consists of a diode HP connected in series to a standard HP that has a PCM canister attached to its mid-section. It is designed to connect a heat source to a structural heat sink during normal operation, and to automatically decouple from it and sink to the PCM whenever structural temperatures are too high. The HP radiating panel is designed to conductively couple the panel feeder HPs directly to a fluid line that serves as a source of waste heat. It is a simple strap-on type of system that requires no internal or external line modifications to distribute the heat to a large radiating area.
Research was initiated to investigate certain facets of modern control theory and their integration with a digital computer to provide a tractable flight control system for a VTOL aircraft. Since the hover mode is the most demanding phase in the operation of a VTOL aircraft, the research efforts were concentrated in this mode of aircraft operation. Research work on three different aspects of the operation of the X-14B VTOL aircraft is discussed. A general theory for optimal, prespecified, closed-loop control is developed. The ultimate goal was optimal decoupling of the modes of the VTOL aircraft to simplify the pilot's task of handling the aircraft. Modern control theory is used to design deterministic state estimators which provide state variables not measured directly, but which are needed for state variable feedback control. The effect of atmospheric turbulence on the X-14B is investigated. A maximum magnitude gust envelope within which the aircraft could operate stably with the available control power is determined.
Design of multivariable systems is considered and design procedures are formulated in the light of the most recent work on model matching. The word model matching is used exclusively to mean matching the input-output behavior of two systems. The term is used in the frequency domain to indicate the comparison of two transfer matrices containing transfer functions as elements. Design methods where non-interaction is not used as a criteria were studied. Two design methods are considered. The first method of design is based solely upon the specification of generalized error coefficients for each individual transfer function of the overall system transfer matrix. The second design method is called the pole fixing method because all the system poles are fixed at preassigned positions. The zeros of terms either above or below the diagonal are partially fixed via steady state error coefficients. The advantages and disadvantages of each method are discussed and an example is worked to demonstrate their uses. The special cases of triangular decoupling and minimum constraints are discussed.
Review of some of the problems associated with the determination of epicenters and mechanisms of moonquakes with the aid of the four seismic stations now operating on the moon. No decoupling of compressional, transverse, and surface waves takes place there, no clear first arrivals can be found, and coherence between vertical and horizontal components on a seismograph stationed on the moon is poor. New techniques for locating epicenters are presented.
It is shown that the fields of velocity, eddy viscosity, potential temperature, and specific humidity in a planetary boundary layer are decoupled by the introduction of a free parameter, Q, which combines the effects of thermal and humidity stratification. Solutions of the whole system are shown to be obtainable by the method of trial and error on Q. Results show good agreement when both the thermal and humidity stratification are accounted for.
The morphological features of Mare Imbrium and Mare Serenitatis are discussed on the basis of Apollo, Ranger, and Orbiter photography. It is suggested that the mare basins were filled relatively slowly by interdigitating, overlapping lava flows, over an extended period of time. Mare wrinkle ridges were formed by localized compression of a relatively thin crust which is effectively decoupled from underlying topography and structure. Since the deformation took place shortly after the time the mare filling was completed, it is possible that this thin crust was underlain by still liquid lava.
Review of recent work in recasting the energy type of approximation to aircraft flight in terms of singular perturbation theory and in extending this theory to three-dimensional maneuvers. Singular perturbations for differential equations arising in optimal control are first examined for a system of fairly general form but low order. The attitude dynamics for optimal flight of a rocket in vacuum is then studied as an introductory, and fairly transparent, example. The question of the choice of variables is then discussed. Finally, optimal aircraft flight in various reduced-order approximations is investigated. In particular, the problem of three-dimensional aircraft flight is formulated for singular perturbation treatment, and possibilities for decoupling into several lower-order problems are illustrated. The use of reduced-order approximation facilitates numerical computations by reducing the number of multiplier initial values that must be determined simultaneously and by improving the conditioning of the differential equations.
A local-molecular-field description for the ground-state properties of the quantum solids is presented. The dynamical behavior of atoms contributing to the local field, which acts on an arbitrary pair of test particles, is incorporated by decoupling the pair correlations between these field atoms. The energy, pressure, compressibility, single-particle-distribution function, and the rms atomic deviations about the equilibrium lattice sites are calculated for H2, He-3, and He-4 over the volume range from 5 to 24.5 cu cm/mole. The results are in close agreement with existing Monte Carlo calculations wherever comparisons are possible. At very high pressure, the results agree with simplified descriptions which depend on negligible overlap of the system wave function between neighboring lattice sites.
A pattern in moonquakes, which correlates with the monthly tidal cycle, also correlates with a phase-shifted pattern of a 7-month tidal cycle. The lead of approximately 2 months in moonquake occurrence can be explained if local tidal forces are combined with a moonquake-driving force. This force, assumed to result from the 6-yr physical libration in latitude, would cause N-S sliding of an outer layer across a solid layer within a decoupled core in a lunar model. During 1969-1971, the sliding would be southward with a progression of monthly maxima in the combined forces. Where these forces control moonquakes, the reversal in direction of the 6-year cyclic force in early 1972 should cause a minimum in moonquake activity. Decreases toward such a minimum did occur simultaneously in the similar progressions of monthly moonquakes and maxima in the combined forces at the most active hypocenter. Repetition of the 1966-1971 force pattern in 1975-1977 should produce a corresponding repetition of the moonquake pattern.
Review of some results obtained in an effort to develop efficient, high-precision trajectory computation processes for artificial satellites by optimum selection of the form of the equations of motion of the satellite and the numerical integration method. In particular, the matching of a Gaussian variation-of-parameter (VOP) formulation is considered which is expressed in terms of equinoctial orbital elements and partially decouples the motion of the orbital frame from motion within the orbital frame. The performance of the resulting orbit generators is then compared with the popular classical Cowell/Gauss-Jackson formulation/integrator pair for two distinctly different orbit types - namely, the orbit of the ATS satellite at near-geosynchronous conditions and the near-circular orbit of the GEOS-C satellite at 1000 km.
On-line system identification of linear discrete systems for implementation in a digital adaptive flight controller is considered by the conventional extended Kalman filter and a decoupling process in which the linear state estimation problem and the linear parameter identification problem are each treated separately and alternately. Input requirements for parameter identifiability are established using the standard conditions of observability for a time variant system. Experimental results for simulated linearized lateral aircraft motion are included along with the effect of different initialization and updating procedures for the priming trajectory used by the filter.