Describing function

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

Spline-based behavioural model for efficient analysis of large front-ends for W-CDMA systems

Abstract: A new behavioural model suitable for the analysis of RF front-ends for W-CDMA systems is described. The model fully accounts for both linear and nonlinear dispersion effects, so that relatively by a band digitally modulated signals can be accurately dealt with. The linear front-end response is computed by means of the conversion admittance matrix. The relationship between the linear and nonlinear responses is characterised by a voltage and frequency-dependent describing function. The latter is evaluated by a cubic-spline-based two-dimensional interpolation scheme starting from a database generated by harmonic-balance analysis. In this way, front-end simulations that would require months of CPU time even by modern envelope-oriented techniques, can be performed in a matter of seconds without significant loss of accuracy.

A method of analysis for the dodco optimal controller.

Abstract: : An approximate representation of the DODCO Optimum Limited Information Adaptive Controller (DOLIAC) is formulated by a describing function approach. The describing function approximation of the DODCO controller coupled with conventional servo-analysis techniques is found to give reasonably accurate estimates of the stability characteristics of such systems. Results are verified by application to a specific plant and by digital computer simulation of the resulting system. (Author)

On Parametric Uncertainty in Dynamically Perturbed Sliding Mode Controlled Systems

Abstract: The unmodeled dynamics inside an SMC control loop such as actuators, sensors, time-delays, etc, dynamically perturb their close-loop response, inducing chattering Dynamically perturbed SMC systems have been widely analyzed in the frequency domain via the Describing Function (DF), Tzypkin method, Locus of a Perturbed Relay System (LPRS), and others, that require a linear representation of the plant (usually given as a transfer function) to later estimate the resulting chattering parameters However, if parametric variation/uncertainty is present, a unique value of the chattering parameters cannot be guaranteed In this paper, a method to analyze dynamically perturbed SMC with parametric uncertainty is presented Parametric uncertainty is addressed as a family of interval second-order transfer functions, formed by cascading a first-order actuator with a plant with relative-degree of one The proposed method identifies (in closed-form) the member system among the interval, corresponding with the marginal chattering parameters Hence, leading to the worst-case condition for the whole systems' family and enabling direct design criteria Analytic and simulated examples to validate the proposed methods are presented

Non-linear proportional and rate feedback design for highly non-linear systems

Abstract: A new procedure for the design of non-linear proportional and rate feedback controllers based on a previously proposed concept is developed. The procedure is to obtain the sinusoidal-input describing function models of the system, followed by determination of the amplitude-dependent rate feedback gains. Then, this amplitude-dependent gain function is inverted to obtain the non-linear function describing a non-linear rate feedback gain. Then, the amplitude-dependent proportional gains that desensitize the overall open-loop system are determined via optimization. Finally, the obtained amplitude-dependent proportional gains are inverted to obtain the actual non-linear function describing the required non-linear behaviour of the proportional gain. Bounded-input–bounded-output stability is demonstrated by successful generation of the closed-loop describing function models, and the procedure is applied to a servo problem; the results are compared with four other non-linear controller design procedures that were...

The Second Describing Function and Removal of Jump Resonance by Signal Stabilization

Abstract: Describing function for analysis of feedback control systems with time-invariant nonlinear elements, simplifying derivation by taking derivative of output of nonlinear element with respect to input