Showing papers on "Describing function published in 1980"

Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty

Abstract: The optimal control of watershed systems requires accurate real-time short-term forecasts of river flows. For the first time, this paper formulates a large, nonlinear conceptual model (the National Weather Service catchment model) in a mode amenable to analysis of uncertainty and the utilization of real-time information (measurements, forecasts, guesses) to update system states and improve streamflow predictions. The proposed methodology is based on the state space formulation of the equations describing the hydrologic model and the assumption of sources of uncertainty in the data and in the model structure. The first two moments of random variables are estimated in a computationally efficient way using on-line linear estimation techniques. Linearization of functional relationships is performed with the uncommon but powerful multiple-input describing function technique for the most strongly nonlinear responses and Taylor expansion for the rest. The linear feedback rule developed is based on the Kalman filter.

A survey on non-linear oscillations

Abstract: This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariate systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-l...

Optimal and adaptive control in canine postural regulation

Abstract: For analytic purposes, dogs trained to stand quietly on an oscillating platform can be likened to a fixed-length inverted pendulum with a point mass. Describing function analysis permitted derivation of torque and error values as functions of phase and gain relative to platform movement. A phase criterion was determined for minimization of either control torque at a given error amplitude or error at a given control torque amplitude. Describing functions for dogs with and without vision approached optimal phase. Stretch reflex control involving proportional-plus-rate feedback is not sufficient to account for the approach to optimal phase. Blindfolded labyrinthectomized dogs did not exhibit optimal behavior and the phase constraint for stretch reflex control was satisfied at most frequencies. The observed behavior is best accounted for by a model involving both otolith and visual feedforward (pursuit-precognitive) control processes. Reductions in phase lag by blindfolded dogs during the first few cycles of platform motion provide evidence of adaptive control.

On Existence of Periodic Motions in Nonlinear Control Systems with Periodic Inputs

Abstract: The existence of periodic solutions of nonlinear control systems subjected to sinusoidal forcing functions, using the describing function method, is studied. The setting is general enough to allow systems with delays, systems with discontinuous nonlinearities, systems with hysteresis nonlinearities, and so forth. The present results state that if the linearized describing function problem can be solved and if certain bounds (which depend on the exact form of the solution of the describing function problem) can be satisfied, then there is a periodic solution of the exact problem. Furthermore, the present results provide relative error bounds between the response of the exact problem and the associated linearized describing function problem. To demonstrate the applicability of the method advanced, a specific example is considered.

A Statistical Method Applied to Pilot Behavior Analysis in Multiloop Systems

Abstract: A recently developed statistical method has been applied to the analysis of pilot control behavior in multiloop systems. The method utilizes the so-called autoregressive scheme, and produces analytical results in terms of root mean square values, power spectra, and pilot describing functions. The method is practical in that it manipulates operating records and it can check the validity of the assumed compensatory control system structure. To show the usage and feasibility of the method, the data from a series of moving-base simulator experiments have been analyzed by the method. Emphasis of the experiment was placed on the lateral-directional control of an aircraft in the landing approach phase under the influence of turbulence. The variation of pilot control behavior with respect to two experimental variables, the Dutch-roll damping ratio and the flight rules, is presented with the discussion as to the system structure and the limitations of the method. Since the application of the method to the field of pilot behavior analysis is quite new, the described method and the presented results are considered to help better analyze and understand pilot behavior in multiloop systems.

Periodic solutions of systems of ordinary differential equations

Abstract: Publisher Summary The existence or nonexistence of oscillations is of fundamental importance in the design and the evaluation of feedback systems. Mees and Bergen have recently proved some results on existence and nonexistence of periodic solutions of certain autonomous ordinary differential equations. This chapter presents an extension of some of their results to a class of interconnected systems and presents an analysis of feedback systems as the interconnection of simpler subsystems. Each subsystem is analyzed using describing function techniques. The results in the chapter address the most popular uses of describing functions, that is, it presents conditions that ensure that the system cannot sustain a π-symmetric oscillation. The conditions are computable in the sense that certain parameters are obtained for each subsystem by graphical methods. These parameters are combined with parameters that measure the strength of the interconnections to form a test matrix.

A new approach to the prediction of limit cycles

Abstract: The describing function method is commonly used for the prediction of limit cycles in non-linear systems. This method is based upon the representation of signals by a Fourier series, and assigning a gain to the non-linear component derived from its response to a sinusoidal input, In this paper we show that a different approach is feasible which in some respects is the dual of the describing function method. The signals are analysed into a Walsh scries, and a gain is assigned to the linear component of the system derived from its response to a square, wave. In many instances the method is likely to give more accurate predictions of limit cycling.

Human Operator Modeling for Aerial Tracking.

Abstract: : Modern Optimal Control techniques are employed to investigate and model human performance degradation under sustained positive linear acceleration stress. The study, which combines both experimental and analytical programs, reaffirms the hypothesis that target tracking performance under Gz-stress deteriorates significantly. The empirical data exhibit trends which manifest this contention: Gz-stress effects slow tracking error recovery, lower magnitude of the human describing function, increased variability in tracking errors, a large increase in the pilot's control remnant, and significantly larger RMS tracking scores. A normative performance G-model, based upon the Optimal Control Model (OCM), is developed. The model outputs include first- and second-order statistics of the various quantities in the tracking loop, such as tracking errors, control input time histories. Alternately, when a steady state situation is considered, the model predicts the human transfer function, control remnant and other related frequency measures. It is shown that under Gz-stress, the OCM is augmented with G-submodels and that model parameters depart from their nominal values. (Author)

Computer graphics methods for nonlinear multivariable systems

Abstract: This paper describes frequency domain programs developed for the study of nonlinear single and multivariable feedback control systems. The algorithms which require graphics facilities include absolute stability methods, describing function methods, techniques for the determination of limit cycles in relay control systems and criteria for the absence of limit cycles of a particular frequency. They can also be used to design compensators using conventional frequency domain methods. Two new theorems are proved which guarantee the absence of limit cycles of certain frequencies in a multivariable system.

Evaluation of a Describing Function Approach to Nonlinear Gust Loads Analysis

Abstract: Structural loads on the vertical tail of an aircraft with a limited authority yaw damper are calculated. The results of a random input describing function analysis are compared with those of a Monte Carlo simulation. Comparisons of exceedance rates and other statistics are presented. The mission analysis criterion for continuous turbulence is used to establish the design limit load. The describing function analysis consistently underestimates the design limit load for two different authority limits. The cause of this discrepancy is examined, and a simplified procedure is developed to assess the necessity for, and adequacy of, describing function analyses.