The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

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

Theoretical Investigation of the Effects of the Artificial-Feel System on the Maneuvering Characteristics of the F-89 Airplane

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

Application of Statistical Filter Theory to the Optimal Estimation of Position and Velocity on Board a Circumlunar Vehicle

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