Optimal paths through downbursts
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Zhao, Yiyuan↗
Engineering topics
Bryson, A. E., Jr.
Publications and source records attributed to Bryson, A. E., Jr..
Control of an aircraft in downbursts
Guidance schemes are designed to approximate the optimal survival and optimal performance paths through downbursts, which were determined in the previous paper. Specifically, climb-rate command following is used to achieve performance, and altitude command following is used to enhance survivability. Nonlinear simulations are conducted to investigate the effects of the climb-rate command and altitude command. Takeoff flight is considered and full thrust is assumed. In a mild to moderate downburst, an aircraft can follow a constant, smaller-than-nominal climb rate without stall. Better survival capability is achieved by climbing at a lower rate accompanied by lower altitude, and vice versa. In a severe downbursts, the aircraft must descend to avoid stall. The farther it descends, the higher the survival capability, but the poorer the performance. If the downburst is very severe, the best strategy is to descend immediately to the lowest safe altitude. Since the intensity of a downbursts is hard to evaluate prior to penetration, it is advisable to keep a high airspeed. Therefore, use of the survival strategy is recommended that employs maximum thrust and allows the aircraft to descend to a safe minimum altitude immediately upon entering a downburst on takeoff.
Zhao, Yiyuan↗
Optimal landing of a helicopter in autorotation
The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. A unique feature in the present formulation is the addition of path inequality constraints on both the control and the state vectors. The control variable inequality constraint is a reflection of the limitation on the rotor thrust coefficient. The state-variable inequality constraint is an upper bound on the vertical sink-rate of the helicopter during descent. Optimal trajectories are calculated for entry conditions well within the height-velocity (H-V) restriction curve, with the helicopter initially in hover or in forward flight. The optimal solutions exhibited control techniques similar to those used by helicopter pilots in actual autorotational landings. The study indicates that, subject to pilot acceptability, a substantial reduction could be made in the H-V restriction zone using optimal control techniques.
Lee, A. Y.↗
Modeling of flexible structures for active control
If a flexible structure has a plane of symmetry, the equations of motion can be split into two uncoupled sets, one for symmetrical motions and one for anti-symmetric motions. If there are m controls, it is often convenient to assign the linear combinations of controls that enter into the m lowest frequency modes and new controls. As an example the feed-support structure of a spacecraft antenna is considered. It is modeled as a tetrahedron made up of flexible bars and connected to the spacecraft by six short flexible legs containing force actuators and displacement sensors. Due to the three-sided symmetry of this structure, both the symmetric and the anti-symmetric equations of motion can be decoupled into two subsystems. The resulting four subsystems are: (1) pitch/fore-aft motions with four degrees of freedom (DOF), two controls, and one output (the fore-aft motion of the feed); (2) vertical motions with three DOF, one control, and one output (the vertical motion of the feed); (3) roll/lateral motions with four DOF, two controls, and one output (the lateral motions of the feed); and (4) yaw motion with one DOF, one control, and no output (the feed does not move during yaw motion).
Bryson, A. E., Jr.↗
Active stabilization of a flexible antenna feed tower
Active stabilization logic is synthesized to hold a feed at the focus of a spacecraft antenna dish. The feed support structure is modeled as a tetrahedron made up of flexible bars and connected to the dish by six short legs containing force actuators. Using the symmetry of the structure, the model can be decomposed into four uncoupled subsystems: pitch/forward motions with four degrees of freedom (DOF) and two controls; roll/lateral motions with four DOF and two controls; vertical motions with three DOF and one control; and yaw motion with one DOF and one control. This greatly simplifies the synthesis of control logic.
Bryson, A. E., Jr.↗
Disturbance estimation for a STOL transport during landing
Transport aircraft can experience dangerously high sink rates if wind shear or thrust loss are encountered during landing approach. This is of special concern for STOL aircraft that use engine thrust for lift augmentation. Such conditions must be detected quickly and available power increased promptly to avoid serious flight path deviations. This study demonstrates the feasibility of designing constant-gain estimators, which use on-board instrumentation, to detect such conditions with sufficient speed and accuracy to provide adequate warning. Estimator design techniques are discussed and simulation results presented.
Bossi, J. A.↗
Modeling and control of flexible space structures
The effects of actuator and sensor locations on transfer function zeros are investigated, using uniform bars and beams as generic models of flexible space structures. It is shown how finite element codes may be used directly to calculate transfer function zeros. The impulse response predicted by finite-dimensional models is compared with the exact impulse response predicted by the infinite dimensional models. It is shown that some flexible structures behave as if there were a direct transmission between actuator and sensor (equal numbers of zeros and poles in the transfer function). Finally, natural damping models for a vibrating beam are investigated since natural damping has a strong influence on the appropriate active control logic for a flexible structure.
Wie, B.↗
Modal methods in optimal control synthesis
Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.
Bryson, A. E., Jr.↗
Kalman filter divergence and aircraft motion estimators
Kalman filters designed for many aerospace systems turn out to be unsatisfactory. The estimate errors become large compared to the errors predicted by the theory ('divergence'). One of the principal causes of this failure is that the system model contains states or modes that are undisturbed by the modeled process noise, and are neutrally stable (NS). One cure for such problems is periodic restarting of a time-varying Kalman filter. Other cures include minimum variance observers with eigenvalue constraints, added noise, pole-shifting, and destabilization. Several examples are given, including effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several NS modes are undisturbed by wind gusts. An interpretation of these estimators as a 'strapdown IMU' without accelerometers, gimbaled gyros, or servos is given.
Bryson, A. E., Jr.↗
Attitude control of a flexible spacecraft
An algorithm is presented for designing optimal low order compensators for high order systems and it is applied to the title problem where many vibration modes are excited by the control torque. These low order compensators are compared with the full order optimal compensator and found to be less sensitive to modeling errors and to provide near optimal attitude regulation.
Martin, G. D.↗
On-line parameter estimation using a high sensitivity estimator
An on-line parameter identification method is presented. The method is based on a recursive formulation of the maximum likelihood method, with a significant modification on the gains of the state estimator. In the conventional maximum likelihood method, the Kalman gains are used in the state estimator. This produces unbiased, minimum variance parameter estimates in the presence of process noise and measurement noise, but it also slows the convergence rate when the identification is done on-line. Here we suggest choosing the gains to maximize a measure of the sensitivities of the state estimates to parameter variations. One such criterion is to minimize the trace of the inverse information matrix. This increases the convergence rate significantly. After one or two time constants, the gains are switched to the Kalman values to assure unbiased, minimum-variance estimates. The state estimate will initially be nonoptimal, and may not be adequate for control purposes. In this case, a parallel Kalman filter which uses the identifier's parameter estimates can be used. This method is applied here for the identification of a simple first-order system, and for the identification of short-period stability derivatives of an F-8 aircraft from simulated data.
Mishne, D.↗
Control logic to track the outputs of a command generator or randomly forced target
A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).
Trankle, T. L.↗
Active flutter control using generalized unsteady aerodynamic theory
This paper describes the application of generalized unsteady aerodynamic theory to the problem of active flutter control. The controllability of flutter modes is investigated. It is shown that the response of aeroelastic systems is composed of a portion due to a rational transform and a portion due to a nonrational transform. The oscillatory response characteristic of flutter is due to the rational portion, and a theorem is given concerning the construction of a linear, finite-dimensional model of this portion of the system. The resulting rational model is unique and does not require state augmentation. Active flutter control designs using optimal regulator synthesis are presented.
Edwards, J. W.↗
Near-hover control of a helicopter with a hanging load
Piloting a helicopter with a hanging load is a difficult task, especially when the mass of the load is a significant fraction of the mass of the vehicle and there are gusty winds. An autopilot logic is proposed here for controlling the helicopter in this configuration and for precision hover. It is proposed that the vehicle position be measured using a lightweight cable from the helicopter to a point on the ground near the desired hover point. Simulation with one version of S-61 Sikorsky helicopter shows satisfactory controller performance under both design conditions and for parameter changes from one mission to another. Assuming noise-free measurements for feedback is found to be far too optimistic in predicting performance, the sensor/estimator design is a key element in the controller.
Gupta, N. K.↗
Long-range energy-state maneuvers for minimum time to specified terminal conditions
The calculus of variations and energy-state approximation are used to determine the optimum maneuvers in three-dimensional minimum-time aircraft flight paths to a specified final point or line. Constraints on thrust, Mach number, angle of attack, dynamic pressure, and load factor are included. It is shown that when the initial range is sufficiently large that the maximum velocity constraint is encountered en route, the calculation of minimum-time maneuvers can be greatly simplified by a separation of arcs into two two-parameter problems. Suboptimal paths along which the bank angle is restricted to three discrete values (negative maximum angle, 0, positive maximum angle) compare favorably with the optimum, continuous bank angle solutions for transonic speeds and below.
Parsons, M. G.↗
Wind modeling and lateral control for automatic landing
For the purposes of aircraft control system design and analysis, the wind can be characterized by a mean component which varies with height and by turbulent components which are described by the von Karman correlation model. The aircraft aero-dynamic forces and moments depend linearly on uniform and gradient gust components obtained by averaging over the aircraft's length and span. The correlations of the averaged components are then approximated by the outputs of linear shaping filters forced by white noise. The resulting model of the crosswind shear and turbulence effects is used in the design of a lateral control system for the automatic landing of a DC-8 aircraft.
Holley, W. E.↗
The predicament of aeronautical engineering education and what we can do about it
An analysis of the aeronautical engineering situation and the relationship to the U.S. aircraft industry is presented. Some of the problems encountered in undergraduate aeronautical engineering education are explained. A reorganization of the educational structure for aeronautical engineering is proposed. The human factors aspect of aeronautical engineering discipline is described.
Bryson, A. E., Jr.↗
Multi-input, multi-output regulator design for constant disturbances and non-zero set points with application to automatic landing in a crosswind
Undesirable steady offsets result when a stationary, linear regulator using state feedback is subjected to constant disturbances and/or non-zero setspoints. To eliminate these offsets, the disturbances and non-zero setpoints can be fed forward to the control. Only when the number of outputs is less than or equal to the number of control inputs can the outputs be maintained at arbitrary non-zero setpoints. The state and the disturbance may be estimated using a constant gain Kalman filter or by modeling the constant disturbances as exponentially correlated processes with long correlation times.
Holley, W. E.↗