Showing papers on "Describing function published in 1985"

Nonlinear Compensator Synthesis via Sinusoidal-Input Describing Functions

Abstract: We describe a new nonlinear compensator synthesis approach and illustrate it with an application to a position servo design problem from robotics. The synthesis technique is based on a set of amplitude-dependent sinusoidal-input describing function (SIDF) models of the nonlinear plant. An intermediate step is the design of a linear compensator set based on these models; final synthesis of the nonlinear control system is accomplished by SIDE inversion to determine the required compensator nonlinearities. The major extension in comparison with earlier research is that the compensator so obtained is fully nonlinear; i.e., there is a nonlinear operator associated with each term (proportional, integral, derivative) in the compensator. This approach is capable of treating nonlinear plants of a very general type, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type, and can be extended readily to include other compensator types, e.g., lead/lag. The end result is a closed-loop nonlinear control system that is relatively insensitive to reference input amplitude.

A frequency domain stability analysis of a phase plane control system

Abstract: A describing function is used to model a phase plane controller which is part of the Space Shuttle on-orbit Reaction Control System autopilot. A frequency domain stability analysis of the closed-loop control system is applied to a study of potential flight control system interaction with the Orbiter and a class of payloads deployed from a tilt table. Phase-gain plot techniques are used to show that expansion of phase plane angular rate limits and stiffening of the tilt table pivot do not always enhance system stability. Instability region approximations are mapped as a function of rate limit, payload geometry, jet used, and natural frequency of the pivot. Comparison of the describing function analysis with simulation results shows excellent correlation.

Nonlinear Controller Design by an Inverse Random Input Describing Function Method

Abstract: An interactive Inverse Random Input Describing Function method is developed which is able to find an approximate nonlinear function from given Random Input Describing Function data. Using this technique, a nonlinear controller design method for nonlinear systems with random inputs is presented that keeps the transient and r.m.s. error response insensitive to the input r.m.s. value. The method is then applied to a second order servo system with actuator saturation. The analytical results show the advantage of the nonlinear controller over the linear one and these results are verified through Monte Carlo simulations.

Method of multiple scales and identification of nonlinear structuraldynamic systems

Abstract: A procedure has been developed t o identify the parameters of a nonlinear structural dynamic system with a single degree of freedom. A cubic nonlinearity has been assumed for purposes of illustration. In comparison t o the direct identification procedures, that depend on (a) either the availability of data on all four variables, namely, velocity, acceleration, displacement and the input t o the system or (b) the formulation of a numerical algorithm that can be used a t each iterative step, the developed procedure requires the data on only one of the field variables. The input t o the system is also treated a s an unknown. The results from the perturbation identification procedure have been compared with the results from two direct identification procedures.

An iterative procedure for nonlinear flutter analysis

Abstract: An iterative procedure in the frequency domain is presented for flutter analysis of large dynamic systems with multiple structural nonlinearities. The major components of the procedure are the describing function approach for system linearization, a structural dynamics modification method for shifting system mode shapes and frequencies, and a complex eigenvalue algorithm for solution of the flutter equation. The purpose of the procedure is to achieve alignment of the oscillatory amplitude in each nonlinear spring with the describing function prediction of stiffness before computing the final stability characteristics. The result is a system tuned to the flutter frequency at the time of instability. To support the development and validation of the procedure, several describing functions are formulated and a quantitative measure of the errors in each is presented. Validation of the iterative method is accomplished through examples involving dynamic systems of increasing complexity, coupled with various representations of the unsteady aerodynamic forces. Both numerical simulations and experimental data are used to compare with the iterative predictions. In the cases studied, the agreement is good to excellent, with the method accurately predicting the amplitude of a limit cycle flutter as well as the initial disturbance required to produce flutter.

Limit cycles in diesel/controllable pitch propeller propulsion systems using load control

Abstract: Marine diesel/controllable pitch propeller propulsion systems using load control can experience limit cycling or bunting. Simplified fourth-order and eight-order models are developed to study the properties of these control systems. The backlash inherent in mechanical-hydraulic type engine governors is taken as the principal non-linearity in the system. Describing function analysis and digital simulation are used to demonstrate the existence and characteristics of the limit cycles. The numerical example is based upon the characteristics of a 1000 foot Great Lakes bulk carrier with 8000 horsepower per shaft. It is shown that an active load control feature, which couples the pitch control to the engine governor, is a major cause of the limit cycles with 15 to 20 second period observed on these vessels. The describing function analysis with the fourth-order model is effective in predicting the limit cycle existence and period. The sensitivity of the limit cycle characteristics to the system parameters is presented. Results are presented for both describing function analysis and simulation for each model for comparison.

W-domain design of single- and double-valued relay control systems

Abstract: The design of relay control systems is presented having ideal, dead zone and rectangular hysteresis transfer characteristics. The choice of the appropriate describing function model is considered and examples are given of limit cycle prediction and digital compensation in the w-domain. The method described is particularly useful for the analysis of slowly sampled systems.

Computation of branching solutions of a non-linear control system via dual-input describing function and root locus techniques

Abstract: Dual-input describing function techniques combined with elementary root locus techniques are used to compute stationary and periodic bifurcation solutions of a non-linear control system and to determine their stability behaviour.

Sinusoidal input describing function analysis of nonlinear systems having a very general structure

Abstract: An iterative method, with examples of use, is presented for describing function analysis of nonlinear systems having a very general structure.

Response of Bayonet-type Heat Exchangers to Sinusoidal Flow Rate Changes of Large Amplitude

Abstract: A computational method is presented for obtaining the steady-state temperature responses of bayonet-type heat exchangers subject to sinusoidal flow rate changes of large amplitude The frequency- and amplitude-dependent describing functions between the input sinusoidal flow rate changes and the fundamental component of the steady-state response of the outlet temperature of tube-side of shell-side fluid are also derived Numerical examples are given and the effects of the amplitude of the flow rate changes on the frequency responses are shown: (1) The vector loci of the describing functions are illustrated (2) The dc-components of the periodic responses are plotted for various values of the amplitude Finally the responses calculated by the present method are confirmed by means of the Runge-Kutta-Gill method, and it is shown that the present method can reduce the computation time remarkably