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The use of a hybrid computer in the solution of trajectory optimization problems is described. The solution technique utilizes the indirect method and requires iterative computation of the initial condition vector of the co-state variables. Convergence of the iteration is assisted by feedback switching and contour modification. A simulation of the method in an on-line updating scheme is presented.
Manual tracking experiments were conducted to determine the suitability of tactual displays for presenting flight-control information in multitask situations. Although tracking error scores are considerably greater than scores obtained with a continuous visual display, preliminary results indicate that inter-task interference effects are substantially less with the tactual display in situations that impose high visual scanning workloads. The single-task performance degradation found with the tactual display appears to be a result of the coding scheme rather than the use of the tactual sensory mode per se. Analysis with the state-variable pilot/vehicle model shows that reliable predictions of tracking errors can be obtained for wide-band tracking systems once the pilot-related model parameters have been adjusted to reflect the pilot-display interaction.
An approach to display evaluation based on the optimal-control or state-variable model of the human operator is described. The approach evolved over the past several years, and is believed to have significant advantages for display evaluation. The foundations of the methodology are briefly described, and results are presented of its application to the analysis of vertical situation displays for STOL approach. This analysis includes the effects of both status and command displays on pilot workload and system performance.
Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.
A general procedure is presented for systematic development of rotorcraft models for use in systems identification, which includes fuselage and rotor degrees of freedom (DOF). Formulations for rigid blade flap and lag as well as the normal mode representation of an elastic blade are developed for hingeless and articulated rotor systems. The method of multiblade coordinates is used to obtain linear constant coefficient state variable models of various levels of approximation. Two of the approximate models, a 6 DOF, are identified from a nonlinear articulated helicopter computer simulation. The results demonstrate the accuracy attainable for each model. Advanced results outline the status of rotorcraft modeling and systems identification and indicate areas that require further investigation.
A linear system identification technique developed by Lion is adapted for use on a third-order system with six unknown parameters and noisy input-output measurements. A digital computer is employed so that rapid identification takes place with only two state variable filters. Bias in the parameter estimates is partially eliminated by a signal-to-noise ratio testing procedure.
The global distribution of temperature in the stratosphere from 100 to 10 mbar and the total ozone in the atmosphere are remotely sensed from the Nimbus-4 IRIS measurements for a period of about one year. The temperature and ozone data are presented in the form of monthly mean global maps. The standard deviations of temperature and ozone with respect to zonal averages are calculated. The mean and the variable state of the stratosphere are discussed with the help of these observations. The lower stratosphere in the tropical regions reveals a significant wave number one pattern in the circulation. The Arctic and Antarctic stratospheric winter circulation regimes display a different behavior apparently due to the ocean and orographic differences.
Several techniques for obtaining linear constant-coefficient airplane models from specified handling-quality time histories are discussed. One technique, the pseudodata method, solves the basic problem, yields specified eigenvalues, and accommodates state-variable transfer-function zero suppression. The method is fully illustrated for a fourth-order stability-axis small-motion model with three lateral handling-quality time histories specified. The FORTRAN program which obtains and verifies the model is included and fully documented.
Numerical results obtained in a simplified version of the one on one aerial combat problem are presented. The primary aim of the data is to specify the roles of pursuer and evader as functions of the relative geometry and of the significant physical parameters of the problem. Numerical results are given in a case in which the slower aircraft is more maneuverable than the faster aircraft. A third order dynamic model of the relative motion is described, for which the state variables are relative range, bearing, and heading. The ranges at termination are arbitary in the present version of the problem, so the weapon systems of both aircraft can be visualized as forward firing high velocity weapons, which must be aimed at the tail pipe of the evader. It was found that, for the great majority of the ralative geometries, each aircraft can evade the weapon system of the other.
A FORTRAN digital computer program which performs the general analysis of linearized control systems is described. State variable techniques are used to analyze continuous, discrete, and sampled data systems. Analysis options include the calculation of system eigenvalues, transfer functions, root loci, root contours, frequency responses, power spectra, and transient responses for open- and closed-loop systems. A flexible data input format allows the user to define systems in a variety of representations. Data may be entered by inputing explicit data matrices or matrices constructed in user written subroutines, by specifying transfer function block diagrams, or by using a combination of these methods.
A technique is presented for calculating feedback and feedforward gain matrices that enable a VTOL aircraft to track input commands of forward and vertical velocity while maintaining acceptable responses to pilot inputs. Leverrier's algorithm is used for determining a set of state-variable, feedback gains that force the closed-loop poles and zeros of one pilot-input transfer function to pre-selected positions in the s-plane. This set of feedback gains is then used to calculate the feedback and feedforward gains for the velocity-command controller. The method is computationally attractive since the gains are determined by solving systems of linear, simultaneous equations. The method is used in a digital simulation of the CH-47 helicopter to control longitudinal dynamics.
A technique has been developed for calculating feedback and feedforward gain matrices that stabilize a VTOL aircraft while enabling it to track input commands of forward and vertical velocity. Leverrier's algorithm is used in a procedure for determining a set of state variable, feedback gains that force the closed loop poles and zeroes of one pilot input transfer function to be at preselected positions in the s plane. This set of feedback gains is then used to calculate the feedback and feedforward gains for the velocity command controller. The method is computationally attractive since the gains are determined by solving systems of linear, simultaneous equations. Responses obtained using a digital simulation of the longitudinal dynamics of the CH-47 helicopter are presented.
Model reference adaptive controllers for multivariable plants are designed using only input and output signals rather than the complete state vector. The design is based on Liapunov's direct method, and the Meyer-Kalman-Yacubovich lemma. State variable filters are employed to avoid differentiating output signals. Augmented error signals are used in deriving stable adaptive control laws which assure that the normally used response error signals approach zero asymptotically.
The control of the flexible motion in a plane of two pinned beams is addressed with application to remote manipulators. Three types of linear feedback control schemes are considered: joint angle and velocity feedback with (GRC) and without (IJC) cross joint feedback, and feedback of flexible state variables (FFC). Two models of the distributed flexibility are presented along with some results obtained from them. The relative merit of the three control schemes is discussed.
A technique is presented for determining state variable feedback gains that will place both the poles and zeros of a selected transfer function of a dual-input control system at pre-determined locations in the s-plane. Leverrier's algorithm is used to determine the numerator and denominator coefficients of the closed-loop transfer function as functions of the feedback gains. The values of gain that match these coefficients to those of a pre-selected model are found by solving two systems of linear simultaneous equations. The algorithm has been used in a computer simulation of the CH-47 helicopter to control longitudinal dynamics.
Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.
The sampled-data optimal linear regulator problem provides a means whereby a control designer can use an understanding of continuous optimal regulator design to produce a digital state variable feedback control law which satisfies continuous system performance specifications. A basic difficulty in applying the sampled-data regulator theory is the requirement that certain digital performance index weighting matrices, expressed as complicated functions of system matrices, be computed. Infinite series representations are presented for the weighting matrices of the time-invariant version of the optimal linear sampled-data regulator problem. Error bounds are given for estimating the effect of truncating the series expressions after a finite number of terms, and a method is described for their computer implementation. A numerical example is given to illustrate the results.
State variable techniques are utilized to generate the RMS vertical load factors for the B-52H and B-1 bombers at low level, mission critical, cruise conditions. A ride quality index is proposed to provide meaningful comparisons between different controls or conditions. Ride quality is shown to be relatively invariant under various popular control laws. Handling quality variations are shown to be major contributors to ride quality variations on both vehicles. Relaxed static stability is artificially implemented on the study vehicles to investigate its effects on ride quality. The B-52H ride quality is generally degraded when handling characteristics are automatically restored by a feedback control to the original values from relaxed stability conditions. The B-1 airplane shows little ride quality sensitivity to the same analysis due to the small rigid body contribution to load factors at the flight condition investigated.