Describing function

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

Design of Robust Controller for Flexible Joint Robot with Nonlinear Friction Characteristics

Abstract: A robust controller method for flexible joint robot considering the effect caused by nonlinear friction was presented.The nonlinear friction was denoted as inverse additive output uncertainty relative to the nominal model in our work,based on which the describing function was analyzed in frequency domain,and the weighting function of nonlinear friction was further calculated as well. By combining the friction uncertainty,the mixed sensitivity H∞optimization was proposed as the benchmark for controller design, which also leaded to good performance of robustness. Furthermore,unstructured perturbation to the system was analyzed so that the stability was guaranteed. Simulation results show that the proposed controller can provide excellent tracking and regulation performance.

Coupled modal sliding mode control of vibration in flexible structures

Abstract: The sliding mode control algorithm is developed for the coupled modal space control of a flexible structure when the bounds on the system parameters' errors are known. An explicit method to construct the desired sliding hyperplanes for the coupled modal sliding mode control is formulated. A boundary layer is used around each sliding hyperplane to eliminate the chattering phenomenon. Three types of steady-state solutions for the closed-loop system inside the boundary layers are found: the zero solution (origin of the state space), the constant nonzero solution, and the limit cycle. The amplitudes, phase angles, and the frequency of the limit cycle have been estimated by the describing function approach. The modal displacements corresponding to the constant nonzero solution have been obtained analytically. The stability of the zero solution has been examined by the linearized system analysis. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analyses.

Contribution to the theory of weakly nonlinear oscillators: Part I. An estimation of amplitude and frequency

Abstract: Steady state signal in an oscillator is described by a nonlinear integral equation. A new theorem on the existence of an isolated number ω, for which the equation has a periodic eigensolution of period 2π/ω is given in the paper. An approximate value ω and approximate eigensolution can be easily obtained by the describing function method. The main result of the paper is the presentation of an effective estimation of the error of this approximation for weakly nonlinear oscillators.

Stability of fuzzy control systems

Abstract: Stability of a class of fuzzy control systems is analyzed by replacing the fuzzy controller with an appropriate describing function. Nonlinear analytical expressions for fuzzy controllers are derived. These expressions are numerically approximated by describing functions. The Nyquist stability criterion is used to determine the stability of the fuzzy control system. Numerical examples illustrate the methodology. >