Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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TL;DR: In this paper, the authors present a method to analyze limit cycle phenomenon for underwater vehicle control systems subject to inherent nonlinearities, characterized by using their corresponding describing functions, and the stability equations decomposed from characteristic equation establish a necessary condition to sustain a limit cycle with respect to the selection of controller coefficients.
01 Jan 1970
TL;DR: This communication illustrates a simple technique for identifying the pilot/vehicle describing functions from routine flight test records and provides a straightforward method of analyzing and comparing the dynamics of closed-loop attitude control tasks from actual flight test operations.
Abstract: This communication illustrates a simple technique for identifying the pilot/vehicle describing functions from routine flight test records. This technique provides a straightforward method of analyzing and comparing the dynamics of closed-loop attitude control tasks from actual flight test operations. Some results from the Gemini and X-15 flight test records tend to confirm previous findings that the pilot tries to adjust his dynamics such that the combined pilot/vehicle describing function can be described by a simple crossover model.
23 May 2015
TL;DR: In this paper, a multivariable PD controller is designed to decrease the vertical acceleration associated with pitch and heave, and parameters of the controllers are optimized according to the H 2 norm of the worst vertical acceleration (WVA) output.
Abstract: To decrease the vertical acceleration associated with pitch and heave, a multivariable PD controller is firstly designed in the paper, then parameters of the controllers are optimized according to the H 2 norm of the worst vertical acceleration (WVA) output. The non-linearity of the actuators (flaps and T-foil) is considered and included into the simulation process. In order to assess the closed-loop performance of the nonlinear system, an evaluation method based on the describing function and the variance gain is proposed. This evaluation approach provides, in the frequency domain, a clear picture of the closed-loop performance on the vertical acceleration. By using this evaluation approach to a specific example, it is indicated that this frequency domain closed-loop performance computation approach can more reasonably explain the simulation results of the system. This evaluation method can not only be used to quantitatively access the WVA reduction percentage, but also can be used to estimate the degree of Input/Output non-linearity of the closed-loop system.
TL;DR: In this article, an improved describing function method was used to estimate the number, stability and parameters of oscillations for the coupled nonlinear system by its amplitude-phase characteristics and pole placement.
Abstract: The phenomena of oscillations in sliding mode control system usually cause potential damage or danger in engineering applications. This paper focuses on the estimation and adjustment of oscillation parameters (frequency and amplitude) using an improved describing function method and the characterization of the influence of the reduced-order sliding surface coefficients on the performance of the nonlinear system. The model of series connection of the zero-order holder and switching function is established in frequency domain. The improved describing function method could intuitively estimate the number, stability and parameters of oscillations for the coupled nonlinear system by its amplitude-phase characteristics and pole placement. The stability, parameters and attraction zones of three oscillations in a fourth-order plant are analyzed and simulated. The analytical results show that the reduced-order sliding mode controller possesses complex and colorful nonlinear behaviors. Besides, a coefficient tuning method is presented to eliminate the undesired oscillation which may lead to poor precision or break the stability. The simulations demonstrate that appropriate tuning on sliding surface may greatly improve the efficiency and robustness of the sliding mode control system.
01 Nov 2018
TL;DR: An analytical small-signal model applied for Hybrid Hysteretic Charge (HHC) control has been proposed and analyzed and shown that the proposed analytical transfer functions are valuable and can be applied for the practical power design to achieve good prediction result.
Abstract: In this paper, an analytical small-signal model applied for Hybrid Hysteretic Charge (HHC) control has been proposed and analyzed based on the improved analytical Direct Frequency Control (DFC) model which is based on the extended describing function method. For the first time, the systematical analytical open loop transfer functions from control to output, input to output, output impedance and the closed transfer functions of overall loop, audio susceptibility and output impedance are proposed and verified through simulation. Finally, the experiments on a design example of 12V& I2A are conducted and verified. It has been shown that the calculations match well with the results from both the simulation results and experimental results, which has shown that the proposed analytical transfer functions are valuable and can be applied for the practical power design to achieve good prediction result.