Describing function

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

H∞-Constrained Quasi-Linear Quadratic Gaussian Control with Loop Transfer Recovery

Abstract: In this paper we propose a new nonlinear controller design method, called quasi-linear quadratic Gaussian/H-infinity/loop transfer recovery (QLQG/H∞/LTR), for nonlinear multivariable, systems with hard nonlinearities such as Coulomb friction and dead-zones. We consider H∞-constraints for the optimization of statistically linearized systems, by replacing the covariance Lyapunov equation by a modified Riccati equation, whose solution leads to an upper bound QLQG performance. As a result, the nonlinear correction term is included in the Riccati equation which, in general, is excessively difficult to solve numerically. To solve this problem, we use the modified loop shaping technique and derive analytic proofs of the LTR condition. Finally, the H∞-constrained, nonlinear controller is synthesized by an inverse random input describing function technique (IRIDF). The proposed design method for a hard nonlinear multivariable systems has better robustness to unstructured uncertainty and hard nonlinearities than the QLQG/LTR method. A flexible link system with Coulomb frictions serves as a design example for our methodology.

Detection of limit cycles in discrete systems with backlash and resolution

Abstract: In this paper, a discretization-oriented describing function is derived for nonlinear devices combining backlash and quantization (resolution) while being subject to discretization through a sampler and zero-order hold. Such a describing function is frequency-dependent so that the overall nonlinearity, which includes both resolution and backlash, is interpreted as one possessing nonlinear inertia. That inertia is generated by the sampling process since it does not appear if the system is continuous. The presence of limit cycles is investigated through simulated examples. >

Frequency Domain Nonlinear Modeling and Analysis of Liquid-Filled Column Dampers

Abstract: Tuned liquid column dampers (TLCDs) have an extensive usage as effective vibration absorbers to enhance the structure response under the effect of seismic or wind loads. In this study, parameter optimization of nonlinear model of a TLCD in frequency domain under harmonic excitation is proposed in order to improve the performance of TLCDs. The nonlinearity in the model is due to the head-loss caused by the orifice resulting in velocity squared damping. A six-story building with a TLCD is considered as a case study. Describing function method (DFM) is used to model the nonlinear effects in frequency domain which results in a set of nonlinear algebraic equations. The resulting set of nonlinear equations is solved by Newton’s method utilizing Homotopy Continuation. The effect of change of TLCD parameters (cross-sectional area, head loss coefficient, total length, horizontal length) on the overall system response is investigated through the developed nonlinear model. TLCD parameters are optimized utilizing genetic algorithm and gradient descent optimization methods. Response of the optimized and non-optimized models is compared in frequency domain. The linear and nonlinear models are also compared, and the necessity of introducing nonlinearity to the frequency domain model is addressed.

A describing function for the multiple nonlinearities present in 2-stage electrohydraulic control valves

Abstract: AN EARLIER PAPER1 introduced a method for handling multiple nonlinearities through describing functions, and developed such describing functions for single-stage electrohydraulic control valves. This work is extended in this paper to 2-stage valves of the type shown in Fig. 1. Most of the essential nonlinearities are included in the describing function which is brought to a form similar to that for the single-stage valve.1 Precalculated charts are utilized which help to make reasonable the amount of labor of computing the describing function for a specific valve. An example in the paper illustrates the use of the describing function, and very good agreement with analog computer studies is demonstrated.