Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this article, a hybrid mode shape based modal superposition method was proposed for the determination of steady state vibration response of nonlinear structures, where the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system.
32 citations
••
TL;DR: In this article, a design method is proposed for pulse-width modulation (PWM) control systems, where magnitude of control input is e xed but pulse width is adjustable.
Abstract: A design method is proposed for pulse-width modulation (PWM) control systems, where magnitude of control input is e xed but pulse width is adjustable. In the proposed method, e rst a discrete-time (DT) control system of the amplitude modulation type is designed, and then it is converted into a PWM control system. Pulse width and delay time for PWM input are determined at each sampling time so that the state error between the DT and PWM control systems can be small. The DT controller is determined by digital redesign of a given continuous-time (CT) controller. The digital redesign method previously proposed by the authors is based on the principle of equivalent area. Thus, in spiteof theinherent nonlinearity of PWM input, inasmuch as linear control theory can be employed in design of the baseline DT or CT controller, the PWM control system is obtained without using nonlinear control theory. In addition, because the proposed methods are described in state-space representation, they are applicable to multi-input/multi-output systems. The effectiveness of the methods is illustrated through computer simulation using a e exible spacecraft model.
32 citations
••
TL;DR: In this article, the generalized transfer function of the Laplace and discrete operator is introduced to describe simultaneously the continuous and discrete time nature of the system, and the mixed description includes the transfer functions of continuous-time and discrete-time systems as limiting cases.
Abstract: A new description of linear periodically time-varying systems is proposed. To describe simultaneously the continuous and discrete time nature of the system, the generalized transfer function of the Laplace and discrete operator is introduced. This mixed description includes the transfer functions of continuous time and discrete time systems as limiting cases. Special attention is paid to two-phase switched circuits and results of computer simulations are presented.
32 citations
••
TL;DR: In this manuscript a very accurate analytic expression of the phase deviation equation is derived via the joint application of the describing function technique and of Malkin's theorem.
Abstract: Oscillatory nonlinear networks represent a circuit architecture for image and information processing. In particular they have associative properties and can be exploited for dynamic pattern recognition. In this manuscript the global dynamic behavior of weakly connected cellular networks of oscillators is investigated. It is assumed that each cell admits of a Lur'e description. In case of weak coupling the main dynamic features of the network are revealed by the phase deviation equation (i.e., the equation that describes the phase deviation due to the weak coupling). Firstly a very accurate analytic expression of the phase deviation equation is derived via the joint application of the describing function technique and of Malkin's Theorem. Then a complete analysis of the phase-deviation equation is carried out for 1-D arrays of oscillators. It is shown that the total number of periodic limit cycles with their stability properties can be estimated. Finally, in order to show the accuracy of the proposed approach, two networks containing second-order and third-order oscillators, respectively, are studied in detail.
32 citations
••
TL;DR: In this article, a novel guidance law that is dependent on the conditional probability density function of the estimated states is presented, which is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command.
Abstract: A novel missile guidance law that is dependent on the conditional probability density function of the estimated states is presented. The guidance law is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command. The nonlinear saturation function is represented by the equivalent random input describing function. Since for the investigated problem the certainty equivalence property is not valid, the resulting controller depends on the measurement noise level and on the saturation limit. In comparison to the classical optimal guidance law (OGL), the maximal value of the effective navigation gain is achieved during the engagement instead of near the terminal time. Thus, the saturation limit is reached earlier so as to have enough time to reduce the guidance errors. Using Monte-Carlo simulations, the superiority of the new guidance law over the classical OGL is shown. This validates the new approach of designing an estimation statistics dependent guidance law by using a random input describing function to approximate the missile's acceleration saturation.
32 citations