Describing function

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

On the limit cycle of the underwater vehicle control system

Abstract: Underwater vehicle control systems usually experience the limit cycle due to inherent nonlinear properties. Two major nonlinearities existing in such a system are the fluid drag force and the thruster dynamics. Solution of the limit cycle for the underwater vehicle control system using the describing function approach is presented in this paper. It appears that the proportional controller gain to excite the limit cycle has a lower bound. Simulation study is conducted to investigate characteristics of the limit cycle for an underwater vehicle position control system. Prediction performance of the limit cycle using the proposed method is evaluated by comparing with actual amplitude and frequency of the limit cycle measured from step responses of a complete dynamics model. Simulation results demonstrate excellent performance of prediction. Effect of model linearization on the limit cycle will also be examined.

Limit cycle analysis of PID controller design

Abstract: The main purpose of this paper is to predict limit cycles of nonlinear PID control systems with adjustable parameters by the approaches of stability equation, describing function and parameter plane. First, nonlinear elements are linearized by the classical describing function method. The stability of equivalent linearized system with adjustable parameters is then analyzed by using the stability equations and the parameter plane method. According to our study, the characteristics of limit cycles with PID control design in current literature can be improved. Finally, this approach is also extended to a sampled-data control system with broken line nonlinearity.

Gust Response Computations with Control Surface Freeplay Using Random Input Describing Functions

Abstract: An analytical and computational investigation of the effect of control surface freeplay on aeroelastic behavior, including random gust response and limit cycle oscillations (LCO), is presented. An ...

An Improved Describing Function With Applications for OTA-Based Circuits

Abstract: Electronic systems make extensive use of operational transconductance amplifiers (OTAs) to build filters and oscillators. Studying the effects of the saturation nonlinearity on these OTA-based circuits is difficult and often requires lengthy simulations to check the system’s performance under large-signal operation. The describing function (DF) theory allows to circumvent these simulations by deriving a signal-dependent linearized gain, which predicts the effects of the nonlinearity. However, its use is limited since the state-of-the-art DFs deviate significantly from the real saturating behavior of OTAs. This paper proposes an improved DF, which can be directly derived from the static nonlinear characteristic of the transconductance amplifier. The performance of the proposed methodology is demonstrated for both an OTA-based filter and oscillator. It is shown that the proposed DF has a better nonlinear prediction capability than the state-of-the-art solutions.

Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method

Abstract: In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.