Describing function

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

Periodic motion of underactuated mechanical systems self-generated by variable structure controllers: Design and experiments

Abstract: A new approach in generating a periodic motion for underactuated mechanical systems using variable structure controllers without computing a reference trajectory is proposed in this paper. The design procedure, in order to find explicit expressions of the controller gain parameters in terms of the desired frequency and amplitude, is made through frequency-domain tool, particularly with describing function method. Performance issue of a self-excited system, applied to a double pendulum, is illustrated by experiments.

Robust Stability and Nonlinear Loop-Shaping Design for Hybrid Integrator-Gain-Based Control Systems

Abstract: In this paper, the use of quasi-linear tools for the closed-loop design and analysis of Hybrid Integrator-Gain Systems (HIGS) is considered. A nonlinear motion control design procedure is proposed in which quasi-linear loop-shaping methods, based on describing functions, are combined with rigorous conditions for closed-loop stability. The latter are established by means of multiple piecewise quadratic Lyapunov functions. Admissible functions are found by solving a set of numerically tractable linear matrix inequalities (LMIs). The potential of the robust design method is illustrated by simulation results of a two-mass-spring-damper system.