Engineering topics
Publications and source records attributed to Schmidt, Stanley F..
Paper presents historical view of adaptation of Kalman filtering techniques to aerospace applications and eventually to fields as diverse as exploration for oil and control of powerplants. Describes scientific breakthroughs and reformulations that transformed Kalman filtering techniques into fundamental tool for analyzing and solving broad class of estimation problems.
Concepts from statistical filter theory are applied to the problem of in-flight determination of the position and velocity of a space vehicle for the purposes of midcourse guidance. The source of information is assumed to be an arbitrary sequence of measurements of any desired set of "observables" (e.g., space angles), the measurements being corrupted by additive errors so that the position and velocity are never known perfectly. A state transition approach is employed which leads naturally to a computational scheme that is readily implemented by a digital computer. The scheme can be regarded as a dynamical time-varying filter which weights the incoming observations in an optimal sense for use in producing an up-to-date optimal estimate of position and velocity. The advantages of the scheme are (1) it provides the best possible estimate (minimum error) based upon ensemble statistics of injection conditions and measurement errors; (2) it is extremely versatile, not requiring adherence to a predetermined observation schedule or reference trajectory; and (3) the computations are sufficiently simple to be practical in an on-board computer. A digital computer simulation of the proposed system is employed to demonstrate the feasibility of an all on-board system and to illustrate the performance attainable in a hypothetical physical situation.
Statistical filter theory is employed to develop a method for determining the best possible estimate of the position and velocity of a space vehicle in the midcourse phase of flight. Results of a computer simulation are given to illustrate the performance attainable. An on-board system is visualized in which the source of information is an arbitrary sequence of observations of space angles, corrupted by measurement errors. The scheme is in effect a dynamical time-varying filter, implemented by a digital computer, which processes the incoming data to compute an up-to-date optimal estimate of position and velocity.
A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.
Sampled-data theory, using the Z transformation, is applied to the design of a digital controller for an aircraft-altitude autopilot. Particular attention is focused on the sensitivity of the design to parameter variations and the abruptness of the response, that is, the normal acceleration required to carry out a transient maneuver. Consideration of these two characteristics of the system has shown that the finite settling time design method produces an unacceptable system, primarily because of the high sensitivity of the response to parameter variations, although abruptness can be controlled by increasing the sampling period. Also demonstrated is the importance of having well-damped poles or zeros if cancellation is attempted in the design methods. A different method of smoothing the response and obtaining a design which is not excessively sensitive is proposed, and examples are carried through to demonstrate the validity of the procedure. This method is based on design concepts of continuous systems, and it is shown that if no pole-zero cancellations are allowed in the design, one can obtain a response which is not too abrupt, is relatively insensitive to parameter variations, and is not sensitive to practical limits on control-surface rate. This particular design also has the simplest possible pulse transfer function for the digital controller. Simulation techniques and root loci are used for the verification of the design philosophy.
The possibility of overshooting the anticipated normal acceleration as a result of the artificial-feel characteristics of the F-89C airplane at a condition of minimum static stability was investigated analytically by means of an electronic simulator. Several methods of improving the stick-force characteristics were studied. It is shown that, due to the lag in build-up of the portion of the stick force introduced by the bobweight, it would be possible for excessive overshoots of normal acceleration to occur in abrupt maneuvers with reasonable assumed control movements. The addition of a transient stick force proportional to pitching acceleration (which leads the normal acceleration) to prevent this occurring would not be practical due to the introduction of an oscillatory mode to the stick-position response. A device to introduce a viscous damping force would Improve the stick-force characteristics so that normal acceleration overshoots would not be likely, and the variation of the maximum stick force in rapid pulse-type maneuvers with duration of the maneuver then would have a favorable trend.