Describing Function Analysis Research Articles

Nonlinear interaction of DC cables and magnetically controlled ship-steering autopilots

This paper presents new results on the interaction of DC cables and magnetically controlled ship-steering autopilots. Simulations with a nonlinear model show that a ship using a steering autopilot with a magnetic compass can be captured by a DC cable. That is, the ship tracks the cable, perhaps in an oscillatory fashion. A full-scale experimental study has been performed at the Kontiskan high voltage direct current link to verify calculations and simulation results. Good agreement was obtained between measurements and computer simulations. This paper presents the simulation study, the dynamic model used, and the test results. Simulation and field test show that if the ship is captured by the cable, it can, under certain conditions, track the cable with limit-cycle oscillation. Steady-state stability analysis explains why the ship does not find a stable capture course. Describing function analysis is used to find the limit-cycle amplitude and frequency.

Describing-function theory for flow excitation of resonators

A theory is presented for the mechanism by which resonators are excited by grazing flow. The theory allows prediction of oscillation characteristics for the range of Reynolds numbers, frequencies, and resonator amplitudes for which the acoustically excited mean flow rolls up into discrete vortices. The resonator-flow system is treated as an autonomous nonlinear system. Limit cycles of the system are found using describing-function analysis, in which each component of a nonlinear oscillating system is represented by an associated frequency-response function. This mathematical approach is shown to be a generalization of models in which the resonator and flow are considered parts of a feedback system. The theory’s predictions for the frequencies of oscillation compare favorably with experiment. The results indicate that both ‘‘edge’’ and ‘‘resonator’’ feedback contribute to the mechanism of self-excited oscillations of the resonator-flow system.

A modified relay-based technique for improved critical point estimation in process control

In this paper, we present a modified relay-based technique for estimating the critical point in process control systems with improved accuracy over existing relay-based methods. The proposed technique addresses the accuracy of the conventional approach by eliminating the errors introduced in the usual describing function analysis of nonlinear systems. The analytical basis of the technique is described in the paper, and it is also shown that it is theoretically possible to obtain an exact estimate of the process critical point under ideal conditions. The effectiveness of the proposed technique is verified by simulation results and also by real-time experimental results in the level control of a coupled-tanks system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Describing function matrix for multivariable systems and its use in multiloop PI design

The describing function analysis for single-input single-output systems (SISO) is extended to multivariable plants under multiloop relay feedback control. Both necessary and sufficient conditions for limit cycle oscillations are given in terms of eigenvalues of the open loop system. The stability of such limit cycles is also established. Finally, the use of the describing function matrix in the design of multiloop PI controllers is demonstrated through some simulation examples.

Pulse-modulated control synthesis for a flexible spacecraft

The describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. The method provides a means of characterizing the pulse modulator in terms of its gain and phase for structural mode limit cycle analysis. Although the describing function method is inherently inexact and is not widely used in practice, a new way of utilizing it for practical control design problems is presented. It is shown that the approximations inherent in the method can be accounted as a modeling uncertainty for the nonlinear control robustness analysis. The pulse modulated control system of the INTELSAT 5 spacecraft is used as an example to illustrate the concept and methodology developed in the gaper. The nonlinear stability margins predicted by the describing function analysis are verified from nonlinear simulations.

A Study of Islanding in Utility-Connected Residential Photovoltaic Systems Part II--case Studies

The phenomenon wherein a group of residential, utility-connected, photovoltaic inverters continue to operate even after loss of the utility source is known as 'islanding.' Islanded operation is undesirable since it can jeopardize the safety of utility personnel as well as cause damage to connected equipment. Analytical methods for the study of islanding have been presented in the companion paper [1]. It has been shown therein that a power-flow analysis type of method can be effectively used to identify the electrical frequency at which a power balance can be achieved in an islanded system. If such a frequency exists then islanding is possible. At this predicted frequency, largesignal Describing Function analysis and small-signal stability analysis can be used to determine if islanding will actually occur. In the present paper the methods are extended to the analysis of systems containing multiple power conditioning systems (PCS). Beginning with a general state-variable format, models are defined for power-flow analysis, describing functions analysis, and small-signal stability analysis. The methods above are used to study islanding in several test systems. Three types of PCSs are studied-the Gemini manufactured by Windworks, Inc., the Teslaco manufactured by Teslaco, Inc., and

Jump Resonance Phenomena in Multivariable Nonlinear Systems of a General Structure

Abstract A new numerical method, based on an iterative technique using describing functions, has been developed for calculating and plotting jump resonance curves for single-input single-output and multi-input multi-output feedback systems. The system structure can be of a general form provided that describing function analysis remains valid. The algorithms are described and three examples given. Multiple jump resonance phenomena are detected in the multi input multi output examples.

Estimation of Maximum Amplitudes of Conductor Galloping by Describing Function Analysis

Estimates of maximum amplitudes of conductor galloping are needed in order to determine appropriate phase-to-phase clearances on overhead lines. A new method for computing these estimates is presented. The method gives estimates of the amplitude and frequency of galloping limit cycles along with the wind speed at which they occur. These features make the method useful as a design guide and also allow it to be used to gain further insight into he mechanisms of conductor galloping.

Estimation of Maximum Amplitudes of Conductor Galloping by Describing Function Analysis

Estimates of maximum amplitudes of conductor galloping are needed in order to determine appropriate phase-to-phase clearances on overhead lines. A new method for computing these estimates is presented. The method gives estimates of the amplitude and frequency of galloping limit cycles along with the wind speed at which they occur. These features make the method useful as a design guide and also allow it to be used to gain further insight into he mechanisms of conductor galloping.

Limit cycles in diesel/controllable pitch propeller propulsion systems using load control1

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.

Book Review: Non-Linear Control Engineering: Describing Function Analysis and Design

Book Review: Non-Linear Control Engineering: Describing Function Analysis and Design

Analysis of oscillations in systems with polynomial-type nonlinearities using describing functions

Sufficient conditions for the existence of oscillations are obtained in the case of an autonomous single-loop feedback system when the nonlinear elements belong to a class of polynomials. Both a graphical procedure and an algebraic technique are presented for use with describing function analysis, and a graphical procedure is given for use with multiple input describing functions. Graphing is done in a parameter space of the solution, rather than in the complex plane.

Validity of describing function analysis for 3-phase power systems

Validity of describing function analysis for 3-phase power systems

Describing-function analysis of slow-drift oscillations of vessels moored in random-sea conditions

Slow-drift oscillations of moored vessels in the open sea have become a topic of some importance in recent years. In this study we make use of the describing-function technique, which has been well-developed and much used in the analysis of nonlinear

A describing-function approach to antiskid design

A describing-function approach is employed in the design of an antiskid braking system. This includes the specification of the dynamics of a braking vehicle, a proposed system employing a feedback compensator to provide antiskid behavior, and the determination of the design parameters by a describing-function analysis. A wide range of tire-roadway conditions was considered in the latter. The resulting design was implemented and evaluated in field tests. The observed antiskid braking performance was approximately that predicted from the design. Thus the describing-function approach, especially in view of its ease of application and the insights it provides, appears to be a useful one for the control aspect of antiskid design.

Limit Cycle Analysis of Hydroelectric Systems

Describing function analysis is used to predict limit cycles in a single-area hydroelectric power system. Backlash, rate limits, and a detailed hydrogovernor turbine model are considered in the analysis. The results provide evidence of the existence and nature of very low frequency limit cycles. Such theoretical evidence contrasts with early simulation studies and helps clarify anomalies among more recent observations and simulation studies.

Influence of combined visual and vestibular cues on human perception and control of horizontal rotation.

Measurements are made of manual control performance in the closed-loop task of nulling perceived self-rotation velocity about an earth-vertical axis. Self-velocity estimation is modeled as a function of the simultaneous presentation of vestibular and peripheral visual field motion cues. Based on measured low-frequency operator behavior in three visual field environments, a parallel channel linear model is proposed which has separate visual and vestibular pathways summing in a complementary manner. A dual-input describing function analysis supports the complementary model; vestibular cues dominate sensation at higher frequencies. The describing function model is extended by the proposal of a non-linear cue conflict model, in which cue weighting depends on the level of agreement between visual and vestibular cues.

Describing function analysis of ship steering system nonlinearities

Describing function analysis of ship steering system nonlinearities

Optimal and adaptive control in canine postural regulation.

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.

Evaluation of a Describing Function Approach to Nonlinear Gust Loads Analysis

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.