Describing function

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

Reduced-Order Modeling and Design of Single-Stage LCL Compensated IPT System for Low Voltage Vehicle Charging Applications

Abstract: In this paper, single-stage LCL inductive power transfer (IPT) system is proposed in low voltage vehicle charging applications to minimize the system complexity, and its reduced-order modeling and design approach is presented. To deal with the high-order resonant tank, the reduced-order methodology is applied throughout the paper, with which the behavior of resonant tank is investigated under multiple scales. Using the reduced-order time-domain model, the resonant waveform within switching period is accurately described with only one cycle's numerical computation. A novel parameter design principle for realizing ZVS condition and high averaged efficiency within full load range is then proposed and serves as parametric basis. Next, the low-order linear frequency-domain model is deduced using Extended Describing Function (EDF). It is found that six-order LCL-type system behaves as second-order underdamped system within frequency range of interest. Compared to existing models, the proposed reduced-order model features much more simplicity as it provides intuitive understanding into both steady and dynamic characteristic of the converter while facilitating the parameter and controller design. Through above work, the overall design consideration towards a single-stage LCL IPT system is elaborated. Finally, experimental results are given to verify accuracy of the models as well as the effectiveness of designed parameters and controller.

Analysis of Limit Cycle Oscillations in Maximum Power Point

Abstract: This paper analyses the limit cycle oscillations (LCOs) that characterize some of the most commonly adopted maximum power point tracking (MPPT) digital algorithms. The paper identifies necessary conditions for the LCO existence and clarifies the relationship between some of its characteristics, namely amplitude and frequency, and some relevant system parameters, e.g. DC-DC converter control strategy, adopted MPPT algorithm and iteration frequency, A/D converter resolution. The theoretical study is based on the derivation of an equivalent small signal model of a complete photovoltaic system, where the MPPT algorithm is modelled by its describing function. The final goal is to allow the designer to predict the frequency and amplitude of the LCO and so to drive the design of key system parameters. The correctness of the results has been verified performing computer simulations as well as experimental tests on a 1 kWp PV generator.

Generating self-excited oscillations for underactuated mechanical systems via two-relay controller

Abstract: A tool for the design of a periodic motion in an underactuated mechanical system via generating a self-excited oscillation of a desired amplitude and frequency by means of the variable structure control is proposed First, an approximate approach based on the describing function method is given, which requires that the mechanical plant should be a linear low-pass filter–the hypothesis that usually holds when the oscillations are relatively fast The method based on the locus of a perturbed relay systems provides an exact model of the oscillations when the plant is linear Finally, the Poincare map's design provides the value of the controller parameters ensuring the locally orbitally stable periodic motions for an arbitrary mechanical plant The proposed approach is shown by the controller design and experiments on the Furuta pendulum

Nonlinearities in Industrial motion stages - detection and classification

Abstract: Detection and classification of nonlinearities in motion systems becomes of increasing importance with high demands on (closed loop) performance. In this paper two methods are compared that aim to measure both the linearized dynamics and the influence of nonlinearities. First, a broadband signal is used to measure a linear approximation of the systems dynamics. This method uses multisine signals with identical amplitude spectrum, but randomly distributed phases. Averaging over multiple periodic responses to the same signal and over multiple realizations of the random phase multisine allows the computation of the level of nonlinearities and external disturbances separately. This yields both a linear approximation of the systems dynamics and the amount of nonlinear ‘disturbance’ as a function of frequency. Second, single sine based measurements are used to measure the Higher Order Sinusoidal Input Describing Functions (HOSIDF) of the system under test. HOSIDFs describe the response of the system by describing not only the ‘direct’ response (gain and phase shift) of the system at the input frequency, but by describing the response at higher harmonics of the input frequency as well. This yields a quantitative measure of the power generated by nonlinearities at harmonics of the input frequency as a function of this frequency and the signal amplitude. In the paper these methods are utilized to acquire a non-parametric model for an industrial high precision stage. The effects of and sources for nonlinear influences are discussed for this particular case as well.