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NASA NTRS1987

Flight test of a digital controller used in a helicopter autoland system

This paper describes the flight test evaluation of an advanced digital helicopter flight control system. The controller was designed using an optimal control design procedure for a fully coupled lateral and longitudinal vehicle model. Explicit integrals of the guidance error were included to produce a type 1 characteristic. Gain scheduling was used to account for changes in the vehicle dynamics. The digital controller was exercised by combining it with state estimators, a trajectory generator, and a closed-loop guidance algorithm to form a helicopter autoland system. A CH-47 tandem rotor helicopter was equipped with sensors, on-board digital flight computers, and electrohydraulic actuators. The system was exercised by automatically flying straight-in descending decelerating trajectories typcial of VFR manual landing approaches. A description of the test-ground facilities, the flight hardware and software, and the velocity and position tracking performance is included.

Downing, David R.↗

NASA NTRS1983

Pilot modeling and closed-loop analysis of flexible aircraft in the pitch tracking task

The issue addressed in the appropriate modeling technique for pilot vehicle analysis of large flexible aircraft, when the frequency separation between the rigid-body mode and the dynamic aeroelastic modes is reduced. This situation was shown to have significant effects on pitch-tracking performance and subjective rating of the task, obtained via fixed base simulation. Further, the dynamics in these cases are not well modeled with a rigid-body-like model obtained by including only 'static elastic' effects, for example. It is shown that pilot/vehicle analysis of this data supports the hypothesis that an appropriate pilot-model structure is an optimal-control pilot model of full order. This is in contrast to the contention that a representative model is of reduced order when the subject is controlling high-order dynamics as in a flexible vehicle. The key appears to be in the correct assessment of the pilot's objective of attempting to control 'rigid-body' vehicle response, a response that must be estimated by the pilot from observations contaminated by aeroelastic dynamics. Finally, a model-based metric is shown to correlate well with the pilot's subjective ratings.

Schmidt, D. K.↗

NASA NTRS1987

An analysis of a candidate control algorithm for a ride quality augmentation system

This paper presents a detailed analysis of a candidate algorithm for a ride quality augmentation system. The algorithm consists of a full-state feedback control law based on optimal control output weighting, estimators for angle of attack and sideslip, and a maneuvering algorithm. The control law is shown to perform well by both frequency and time domain analysis. The rms vertical acceleration is reduced by about 40 percent over the whole mission flight envelope. The estimators for the angle of attack and sideslip avoid the often inaccurate or costly direct measurement of those angles. The maneuvering algorithm will allow the augmented airplane to respond to pilot inputs. The design characteristics and performance are documented by the closed-loop eigenvalues; rms levels of vertical, lateral, and longitudinal acceleration; and representative time histories and frequency response.

Suikat, Reiner↗

NASA NTRS1982

Design and flight testing of a digital optimal control general aviation autopilot

This paper presents the designs of Proportional-Integral-Filter (PIF) autopilots for a General Aviation (NAVION) aircraft. The PIF autopilots use modern control theory to determine heading select and altitude select and hold autopilot modes. The PIF control law uses typical General Aviation sensors for state feedback; command error integration for command tracking; digital complimentary filtering and analog prefiltering for sensor noise suppression; a control filter for computation delay accommodation; and the incremental form to eliminate trim values in implementation. Theoretical developments for the control law are described which combine the sampled-data regulator with command generator tracking for use as a digital flight control system. The digital PIF autopilots are evaluated using closed-loop eigenvalues and simulations. Successful flight test results for the PIF autopilots are presented for different turbulence conditions and quadratic weights.

Broussard, J. R.↗

NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗

NASA NTRS1987

Optimal control of large space structures via generalized inverse matrix

Independent Modal Space Control (IMSC) is a control scheme that decouples the space structure into n independent second-order subsystems according to n controlled modes and controls each mode independently. It is well-known that the IMSC eliminates control and observation spillover caused when the conventional coupled modal control scheme is employed. The independent control of each mode requires that the number of actuators be equal to the number of modelled modes, which is very high for a faithful modeling of large space structures. A control scheme is proposed that allows one to use a reduced number of actuators to control all modeled modes suboptimally. In particular, the method of generalized inverse matrices is employed to implement the actuators such that the eigenvalues of the closed-loop system are as closed as possible to those specified by the optimal IMSC. Computer simulation of the proposed control scheme on a simply supported beam is given.

Nguyen, Charles C.↗

NASA NTRS1988

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗

NASA NTRS1988

The 15-meter antenna performance optimization using an interdisciplinary approach

A 15-meter diameter deployable antenna has been built and is being used as an experimental test system with which to develop interdisciplinary controls, structures, and electromagnetics technology for large space antennas. The program objective is to study interdisciplinary issues important in optimizing large space antenna performance for a variety of potential users. The 15-meter antenna utilizes a hoop column structural concept with a gold-plated molybdenum mesh reflector. One feature of the design is the use of adjustable control cables to improve the paraboloid reflector shape. Manual adjustment of the cords after initial deployment improved surface smoothness relative to the build accuracy from 0.140 in. RMS to 0.070 in. Preliminary structural dynamics tests and near-field electromagnetic tests were made. The antenna is now being modified for further testing. Modifications include addition of a precise motorized control cord adjustment system to make the reflector surface smoother and an adaptive feed for electronic compensation of reflector surface distortions. Although the previous test results show good agreement between calculated and measured values, additional work is needed to study modelling limits for each discipline, evaluate the potential of adaptive feed compensation, and study closed-loop control performance in a dynamic environment.

Grantham, William L.↗

NASA NTRS1976

Trajectory optimization for the Atlas/Centaur launch vehicle

A state-of-art survey of computational techniques employed in design and optimization of trajectories for the Atlas/Centaur launch vehicle is presented. Attention is focused on the constrained optimization technique, related to Hestenes' (1969) method of multipliers, with various formulas used in updating the multipliers. Advantages of applying multiplier method to trajectory optimization, with gains in computing speed, are argued, and optimization of the HEAO-A (high energy astronomical observatory) is discussed. Open-loop atmospheric guidance strategy and closed-loop exoatmospheric pitch and yaw guidance equations are dealt with, and the full range of constraints to be observed during the flight is discussed.

Brusch, R. G.↗

NASA NTRS1977

Tracking performance of symbol synchronizers for Manchester coded data

The implementation and tracking performance of symbol synchronizers for Manchester coded data is presented with motivation provided by maximum a posteriori (MAP) estimation theory. Certain physically relizable closed-loop structures, readily implemented in practice, are suggested by the theory for uncoded data symbols with arbitrary data transition probabilities. The tracking performance of these loops is optimized and comparisons are made among the various configurations over a wide range of system parameters. Although not the major intent of the paper, the acquisition problem is briefly addressed.

Simon, M. K.↗

NASA NTRS1982

Robust Kalman filter design for active flutter suppression systems

Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.

Garrard, W. L.↗

NASA NTRS1984

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Broussard, J. R.↗

NASA NTRS1983

Closed-form solutions for feedback control with terminal constraints

The problem of closed-loop control of maneuvers between two states for linear dynamical systems, subject to an arbitrarily specified terminal state, is considered. The feedback controller design is based on finite-time quadratic regulator theory. Closed-form expressions for the optimal control law are developed. Solutions are presented for both conventional and smoothed control profiles with fixed and/or free end condition problems. In the maneuvers using control-rate penalties, smooth profiles are generated throughout the maneuvers, in the sense that the initial condition jump discontinuities have been eliminated. Several examples involving large-angle maneuvers of a spacecraft are demonstrated. Results include control maneuvers from one state to another such as rest to rest and spin to rest, which effectively justify the solutions developed in this paper.

Juang, J.-N.↗

NASA NTRS1986

Closed-loop, pilot/vehicle analysis of the approach and landing task

In the case of approach and landing, it is universally accepted that the pilot uses more than one vehicle response, or output, to close his control loops. Therefore, to model this task, a multi-loop analysis technique is required. The analysis problem has been in obtaining reasonable analytic estimates of the describing functions representing the pilot's loop compensation. Once these pilot describing functions are obtained, appropriate performance and workload metrics must then be developed for the landing task. The optimal control approach provides a powerful technique for obtaining the necessary describing functions, once the appropriate task objective is defined in terms of a quadratic objective function. An approach is presented through the use of a simple, reasonable objective function and model-based metrics to evaluate loop performance and pilot workload. The results of an analysis of the LAHOS (Landing and Approach of Higher Order Systems) study performed by R.E. Smith is also presented.

Anderson, M. R.↗

NASA NTRS1986

Integrated aeroservoelastic tailoring of lifting surfaces

An approach to the integration of two design activities, structural design and active control design, for a highly idealized aeroservoelastic system is presented. The particular design goal for this study is the maximization of the stable airspeed envelope of an idealized model of an aeroservoelastic system through rational and systematic variation of structural and control design parameters. The steady-state linear quadratic regulator is used to model the control subsystem; the structural subsystem is assigned characteristic design parameters, such as shear center position. The application of the procedure described here produces optimally controlled structures with stability characteristics superior to those of open-loop and initial closed-loop designs.

Zeiler, T. A.↗

NASA NTRS1986

An estimator-predictor approach to PLL loop filter design

An approach to the design of digital phase locked loops (DPLLs), using estimation theory concepts in the selection of a loop filter, is presented. The key concept is that the DPLL closed-loop transfer function is decomposed into an estimator and a predictor. The estimator provides recursive estimates of phase, frequency, and higher order derivatives, while the predictor compensates for the transport lag inherent in the loop. This decomposition results in a straightforward loop filter design procedure, enabling use of techniques from optimal and sub-optimal estimation theory. A design example for a particular choice of estimator is presented, followed by analysis of the associated bandwidth, gain margin, and steady state errors caused by unmodeled dynamics. This approach is under consideration for the design of the Deep Space Network (DSN) Advanced Receiver Carrier DPLL.

Statman, J. I.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS1988

The Mark III stellar interferometer

The Mark III interferometer is an operational long baseline stellar interferometer on Mt. Wilson with four-possible baseline configurations from 9m NE-SW to 20m N-S. The interferometer was designed to be a highly automated astronomical instrument to measure stellar positions and diameters to a magnitude limit of seven. Initial fringe observations were made in September 1986 with a 12-m N-S baseline. In the following months, semi-automated astrometric and stellar diameter measurements were also made. This paper describes the hardware and software components of the instrument and its operational characteristics. The interferometer has several novel features. One is the use of optimal estimation and control algorithms (e.g. Kalman filters) in the control loops. Another is the ability to operate both as a closed-loop phased interferometer and eventually as an open-loop or absolute coherent interferometer. High thermal stability and mechanical accuracy should permit the instrument to point blind at an astronomical object and maintain optical path equality to within the limits set by the atmosphere. In this absolute interferometric mode of operation, it should be possible to observe faint astronomical objects that are too dim for phase tracking. In theory, measurements of amplitude, group delay, and closure phase will be possible to 14 mag.

Shao, M.↗