Showing papers on "Describing function published in 1991"

Application of the time varying transfer function for exact small-signal analysis

Abstract: An analysis method for determining the control-to-output linearized describing function of time-interval-modulated switched networks using time-varying system theory was previously proposed by the author. A simplification is now presented which eases the analysis considerably. Use of the simplified approach is demonstrated in the derivation of the control-to-output frequency response of pulse-width-modulated (PWM) DC-to-DC switching power converters operating in discontinuous conduction mode (DCM) and current programmed converters operating in continuous conduction mode (CCM) as well as in DCM. Experimental results are presented which verify the modeling approach. >

Describing functions, Volterra series, and the analysis of non-linear systems in the frequency domain

Abstract: A relationship between the higher-order frequency response functions of the Volterra series model and the well-known describing function representation for non-linear systems is derived. It is shown that a large class of generalized describing functions can be derived from the Volterra model and that this approach removes the restriction to specific inputs. The concept of a worst case transfer function is introduced, and examples are included to illustrate the results.

Analysis and design of fuzzy PID control systems

Abstract: The describing function (DF) approach is employed to analyze the stability of a fuzzy PID control system. The fuzzy PID controller is composed of the memory component due to its integral action and the dynamic component due to its derivative action. Its DF is amplitude- and frequency dependent which is different from that of static nonlinear controllers. Two algorithms are developed to calculate the DF. A stability criterion is presented to predict the closed-loop stability approximately. The design of fuzzy PID controllers is briefly discussed based on this criterion. Numerical simulations are also carried out.

Design of nonlinear controllers for nonlinear plants

Abstract: The paper describes three methods for designing nonlinear phase lead/lag controllers to be used in cascade with nonlinear plants to provide closed loop responses which are essentially amplitude independent. The approach requires amplitude dependent frequency response descriptions of the nonlinear plants, makes use of the describing function method and requires the solution of an inverse describing function problem to determine the nonlinear elements of the controller.

Harmonic characterisation of feedback systems incorporating saturation nonlinearities

Abstract: Discrepancies in the prediction of jump-resonance frequency responses by describing functions are resolved by introducing harmonics. The effects of saturation asymmetry and offset in the nonlinear characteristic are illustrated for a simple bandpass active filter.

Limit cycles in periodically switched circuits

Abstract: Examines the existence, uniqueness, and stability of limit cycles in periodically switched circuits, such as those used in power electronic and power conditioning applications. The main results relate the existence and uniqueness of limit cycles in these switched circuits to the analogous properties of equilibrium points in nonswitched averaged models for these circuits. The results are applicable to two types of circuits. First, the author considers circuits built from incrementally passive (or locally passive) elements including DC sources and ideal switches in which the switches are operated periodically in an open-loop manner. Second, the author introduces an averaging procedure based on the describing function method. This procedure is then used to study limit cycle stability in closed-loop DC-DC converters. >

Method for the control of a special class of non-linear systems

Abstract: A method For the numerical synthesis of compensators for non-linear control systems is proposed. The non-linear systems investigated are the type in which the system can be represented by two separate parts: a linear element and a non-linear element, as shown in Fig, 1. The approach adopted is called the method of inequalities, in which the problem is formulated as a set of inequalities, which represent the specified closed loop performance of the system as well as constraints of an engineering and financial kind. The non-linear part of the system is linearized using an exponential input describing function. An inequality is then formulated concerning the non-linear element to ensure that every point in the admissible space represents a closed loop system which does not exhibit autonomous limit cycle oscillation. This inequality is defined by using an enhanced sinusoidal describing function which takes account of the effects of higher harmonic signal components as well as of a fundamental sinusoi...

Application of the RIDF's to the Evaluation of Monopulse Errors Under Saturating ECM Enviroments

Abstract: It is usually supposed that monopulse systems are immune to noise- jamming ECM's because of its internal ellimination of external amplitude and phase modulations. In the paper is proved that this is not true under saturating conditions and an analysis scheme based on the RIDF's (Random Input Describing Functions) is proposed. The main advantage of this method is its numeric efficiency which allows subsystem's saturation behaviour be included in dynamic simulators.

Modeling and digital nonlinear control of active magnetic bearing (abstract)

Abstract: In the first part of the paper we propose a complete nonlinear dynamic model of a magnetic bearing. The bearing is made up to two controlled axes and three passive axes. This model takes into account the changeover of the power between the two coils of each controlled axis in order to control each axis without exciting currents. In this case, the model is not linear anymore. In the second part we compute a linear regulator taking into account the nonlinearity of the model. For that, we use the ‘‘describing function approach’’ (the nonlinearity is approximated by a complex gain which is a function of the magnitude of the input signal). The stability of the control is assumed first by using the frequency response of the linear part of the model and second by using the describing function of the nonlinearity. In the third part, the regulator is implemented on a digital computer with a sampling period of 0.4 ms. The matching between simulation results and experimental trials shows the accuracy of both the mod...

Application of an Adaptive Clustering Network to Flight Control of a Fighter Aircraft. Phase 1

Abstract: : An artificial neural net controller was developed for a typical fighter aircraft's longitudinal Stability and Control Augmentation System (SCAS) , using elevator and thrust-vector-angle controls, and operating at high angle of attack. The 'baseline' neurocontroller (NC) was in the feedforward loop (Kawato Type-C), with inputs from the pilot's pitch rate commands and rates and SCAS feedback error. An Adaptive Clustering Network algorithm was used to train the radial-basis-function neurons. Significant improvements in performance resulted from the NC action and these effects were analyzed by frequency domain describing functions. Thrust vector failures were handled satisfactorily, but reconfiguration of the SCAS was not possible within the simplified aircraft and NC effects. Phase II recommendations are included, such as: ways to choose signals for the neural net to more efficiently identify and separate failures of correlated control effectors; the further use of frequency domain describing functions to identity neurocontroller dynamic processes; and the development of a Neuro-controller Analysis Toolbox with diagnostic forcing functions, methods, analyses, and benchmark criteria for evaluation to a common NC standard.

Transmitter Power System Equipment

Abstract: Publisher Summary The paper describes software written for the investigation of the stability of, and limit cycles in, nonlinear sampled-data systems. The software uses a new approach based on the z-transform describing function and includes two sections, A numerical section which consists of solving numerically the system characteristic equation and a graphical section which plots the ZDF of the nonlinearity and the Nyquist locus of the linear plant on a z-or a w-plane. Both methods investigate automatically the different limit cycles that may occur at the same frequency but with different waveshapes at the output of a two segment nonlinearity.