Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

Suppression of limit cycle and improvement of robust performance in two-mass resonant systems with nonlinearity

Abstract: Two-mass systems are shown as a model of two masses connected by a spring and often seen in mechanical systems. PID control, resonance ratio control, H/sup /spl infin// control, and etc. have been applied to the two-mass systems. Conventional controllers that use a disturbance observer for two-inertia systems are adopted. A systematic parameter design method for the systems is proposed, where a load variation, Coulomb friction, and fast and precise control are considered. For limit cycle due to friction, a suppression condition of limit cycle is derived by an analysis using a describing function method. For load variation, robust stability for time varying system with structured uncertainty is guaranteed by the quadratic stability. Moreover, nominal performance is improved by maximizing the smallest eigen value of control system under the above restrictions. Effectiveness is confirmed by some simulations and experiments.

Design of a Fuzzy Gain Scheduling Controller Having Input Saturation: A Comparative Study

Abstract: A fuzzy gain scheduling proportional controllers that exhibits the improved performance than the conventional linear fixed gain controller having input saturation is proposed in this paper. We proposed an adaptive anti-windup control system in which the gain of a proportional controller is dynamically tuned by a fuzzy PD system. The methodology employed in the analysis is based on the describing function (DF), which is determined the range of the universal discourse for the output of the fuzzy PD system. Other approaches are the linear quadratic regulator (LQR) method and combined back-calculation and generalized conditioning anti-windup. In this paper, a comparison study of these three approaches for design anti-windup controller is made. The simulation results show the differences and confirm the availability of the proposed design approaches.

Iterative method based on CFD data for the assessment of seakeeping control effects, considering amplitude and rate saturation

Abstract: An iterative procedure for the frequency domain evaluation of control effects in nonlinear loops is introduced. The article focuses on ship seakeeping control, to attenuate ship motions. There is no model of the ship, only CFD tabulated data. The proposed procedure could be used for design or empirical tuning of a controller. The actuators have angle and rate limits. In the case of a ship, the actuators are submerged moving wings: flaps, fins and T-foil. The control evaluation procedure uses a describing function approach. The paper considers amplitude and rate saturation in series. The results are validated with experiments using a scaled ship in a towing tank facility. Copyright © 2010 John Wiley & Sons, Ltd.

A Three-Sample-Based PLL-Less Hysteresis Current Control and Stability Analysis of a Single-Phase Active Distribution System

Abstract: This article proposes a computationally simple strategy by using a three-sample-based technique for a grid-connected inverter in a single-phase active distribution system. The proposed control is to improve the performance during varying grid conditions such as voltage sag, swell, and frequency swing. A comparative analysis between the proposed controller and the conventional second-order generalized integrator phase-locked loop (PLL) based controller for dynamic grid conditions in weak-grid scenario has been presented. Additionally, a frequency domain analysis via describing function method is used to model the dynamics of nonlinear hysteresis current controller to analyze the closed-loop stability of the system. Further validation of the proposed control algorithm is simulated in MATLAB/SIMULINK environment for various scenarios. To establish the effectiveness of the proposed approach in real time, the proposed control strategy is tested in a 1 kVA based experimental setup.

Particle Swarm Optimization of Matsuoka's oscillator parameters in human-like control of rhythmic movements

Abstract: In the field of neuroscience, the Matsuoka's nonlinear neural oscillator is commonly used to model Central Pattern Generator (CPG) in humans/animals. How the parameters of such structure should be selected is not always clear. It was generally done in past studies thanks to a trial-and-error method that needs to be reiterated each time the task changes. Recent studies using a Describing Function Analysis (DFA) of this CPG model provide interesting analytical tuning methods. Nevertheless, as they are based on a linear approximation, they might have a limited efficiency in the particular case of timing-sensitive task, such as the ball-bouncing task considered in this study. A Particle Swarm Optimization (PSO) is thus proposed to select the parameters of a novel neural oscillator-based human-like control architecture able to face disturbances and to adapt to new reference set-points during the ball-bouncing task. The general method presented in the present paper can also be used for other Matsuoka's oscillator tunings and other tasks.