Showing papers on "Describing function published in 2006"
TL;DR: A study of this problem, which relates the maximum achievable object stiffness to the elements of the control loop, examines how the sampling rate, quantization, computational delay, and amplifier dynamics interact with the inertia, natural viscous, and Coulomb damping of the haptic device.
Abstract: Rendering stiff virtual objects remains a core challenge in the field of haptics. A study of this problem is presented, which relates the maximum achievable object stiffness to the elements of the control loop. In particular, we examine how the sampling rate, quantization, computational delay, and amplifier dynamics interact with the inertia, natural viscous, and Coulomb damping of the haptic device. Nonlinear effects create distinct stability regions, and many common devices operate stably, yet in violation of passivity criteria. An energy-based approach provides theoretical insights, supported by simulations, experimental data, and a describing function analysis. The presented results subsume previously known stability conditions
295 citations
TL;DR: The chattering can be caused by fast dynamics which were neglected in the ideal model, and these `unmodeled' dynamics with small time constants are usually disregarded in models of servomechanisms, sensors and data processors.
167 citations
TL;DR: The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter and Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters.
Abstract: In this paper, the commonly used switching schemes for sliding mode control of power converters is analyzed and designed in the frequency domain. Particular application of a distribution static compensator (DSTATCOM) in voltage control mode is investigated in a power distribution system. Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters. Magnitude conditions of carrier signals are developed for robust switching of the inverter under carrier-based modulation scheme of sliding mode control. The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter. The load bus voltage of an unbalanced three-phase nonstiff radial distribution system is controlled using the proposed carrier-based design. The results are validated using PSCAD/EMTDC simulation studies and through a scaled laboratory model of DSTATCOM that is developed for experimental verification
103 citations
TL;DR: In this paper, an extension to higher-order describing functions is realized by introducing the concept of the harmonics generator, which relates the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude of a sinusoidal excitation.
100 citations
TL;DR: It is investigated how the parameters of a 2-SMC algorithm affect the frequency and the magnitude of the limit cycles that occur when the overall relative degree of the plant plus the actuator is three or more and it is shown that the estimated chattering parameters are in good agreement with the actual ones.
68 citations
TL;DR: In this article, the authors developed a simple real-time transient performance model for jet engine control, where the control system specifications are formulated to specify the maximal variance of the fuel flow command (from idle to maximum power level).
Abstract: The main objective of this paper is development of a simple real-time transient performance model for jet engine control. A jet engine arrives to its most dangerous condition during transient operation that may be triggered by fast changes of the input fuel command signal. Thus, the control system specifications are formulated to specify the maximal variance of the fuel flow command (from idle to maximum power level) during transient maneuver. Linear and piecewise-linear techniques are not always convenient and appropriate for turbine engine controller design. An alternative quasilinear simple/ fast engine model is discussed in this paper. This model has maximum accuracy for maximal variance of the fuel flow input command in accordance to the jet engine control system specifications. The fast model is obtained using the Novel Generalized Describing Function, proposed for investigation of nonlinear control systems. The paper presents the Novel Generalized Describing Function definition and then discusses the application of this technique for the development a fast turbine engine simulation suitable for control and real-time applications. Simulation results are compared between the conventional and fast models and found to provide good agreement.
64 citations
TL;DR: A new type of sigma-delta modulator that operates in a special mode named limit-cycle mode (LCM) is proposed, which brings several very attractive advantages: a reduction of the required power consumption per converted bandwidth, an immunity to excessive loop delays and to digital-analog converter waveform asymmetry and a higher tolerance to clock imperfections.
Abstract: A new type of sigma-delta modulator that operates in a special mode named limit-cycle mode (LCM) is proposed. In this mode, most of the SDM building blocks operate at a frequency that is an integer fraction of the applied sampling frequency. That brings several very attractive advantages: a reduction of the required power consumption per converted bandwidth, an immunity to excessive loop delays and to digital-analog converter waveform asymmetry and a higher tolerance to clock imperfections. The LCMs are studied via a graphical application of the describing function theory. A second-order continuous time SDM with 5 MHz conversion bandwidth, 1 GHz sampling frequency and 125 MHz limit-cycle frequency is used as a test case for the evaluation of the performance of the proposed type of modulators. High level and transistor simulations are presented and compared with the traditional SDM designs.
48 citations
Dissertation•
01 Jan 2006
TL;DR: It is shown in this thesis that describing functions can be used to calculate not only the large-Signal behavior, but also the small-signal behavior using the method of impulse sensitivity functions.
Abstract: Oscillators are present in most electronic equipment where they provide timing information, for example as sampling clocks in analog-to-digital converters or as radio carriers in wireless communications. To design an oscillator, we must have knowledge of the properties and the operation of oscillators. Since oscillators are inherently nonlinear and are subject to noise, we have a system that is difficult to analyze since the large wanted signal and the small unwanted signal interact. It is shown in this thesis that describing functions can be used to calculate not only the large-signal behavior, but also the small-signal behavior using the method of impulse sensitivity functions. Based on theoretical results from this method, a design methodology for harmonic oscillators is derived and analyzed. The design methodology aims at the design of harmonic oscillators fulfilling phase-noise requirements with minimized power consumption subject to constraints from the other requirements set by the specification and the technology used to implement the oscillator. The design methodology has been used to design oscillators meeting quite different specifications, both discrete and integrated implementations and with either inductors and capacitors or crystals as frequency-determining elements.
35 citations
TL;DR: In this article, a comprehensive experimental and computational study of the dynamical behavior of the tapping mode atomic force microscope (AFM) probe in interaction with the force field of a sample surface is presented.
Abstract: In this work we report a comprehensive experimental and computational study of the dynamical behavior of the tapping mode atomic force microscope (AFM) probe in interaction with the force field of a sample surface. To address the nonlinear nature of the probe dynamics, we apply describing function method. We established that the corner frequency of the low pass describing function of the probe is sensitive to the modulation amplitude and is generally higher than predicted by linear --- force gradient --- approximation. We show that large tip apex radii and high values of surface Young's moduli can introduce a resonant amplitude transfer, which could lead to image distortion and system instabilities. We demonstrate that the oscillating amplitude of the probe far from the surface and during imaging, and the ratio of these two (setpoint) have an influence on the describing function of the probe similar to that of the quality factor. Accordingly, expert control of these parameters is as effective as active $Q$ control in improving the imaging bandwidth of the tapping mode AFM.
34 citations
TL;DR: A fundamental limitations-based analysis to quantify limits on obtainable performance for active control of combustion (thermoacoustic) instability and explains analytically the peak-splitting phenomenon observed in experiments.
Abstract: This paper presents a fundamental limitations-based analysis to quantify limits on obtainable performance for active control of combustion (thermoacoustic) instability. Experimental data from combustor rigs and physics-based models are used to motivate the relevance of both the linear and nonlinear thermoacoustic models. For linear models, Bode integral-based analysis is used to explain peak-splitting observed in experiments. It is shown that large delay in the feedback loop and limited actuator bandwidth are the primary factors that limits the effectiveness of the active control. Explicit bounds on obtainable performance in the presence of delay, unstable dynamics, and limited controller bandwidth are obtained. A multi-input describing function framework is proposed to extend this analysis to the study of nonlinear models that also incorporate the effects of noise. The fundamental limitations are interpreted for a modified sensitivity function defined with respect to noise balance. The framework is applied to the analysis of linear thermoacoustic models with nonlinear on-off actuators and Gaussian noise. The results of the analysis are well-supported by experiments and model simulations. In particular, we reproduce in model simulations and explain analytically the peak-splitting phenomenon observed in experiments
31 citations
TL;DR: The goal is to design an output feedback system that is a solution to a robust design such that sensitivity of the feedback control system with respect to amplitude of the excitation signal and the operating regimes would be at a minimum.
14 Jun 2006
TL;DR: In this article, a number of second order sliding mode (SOSM) control algorithms are analyzed in the frequency domain via the describing function method and it is shown that in the presence of parasitic dynamics the system driven by a SOSM algorithm would exhibit chattering.
Abstract: A number of second order sliding mode (SOSM) control algorithms are analyzed in the frequency domain via the describing function method. It is shown that in the presence of parasitic dynamics the system driven by a SOSM algorithm would exhibit chattering. The mechanism of chattering generation is analyzed. Further, it is substantiated why chattering is an inherent feature of the sliding mode principle and therefore unavoidable.
Proceedings Article•
01 Jan 2006
TL;DR: It is shown that in the presence of parasitic dynamics the system driven by a SOSM algorithm would exhibit chattering and substantiated why chattering is an inherent feature of the sliding mode principle and therefore unavoidable.
Abstract: A number of second order sliding mode (SOSM) control algorithms are analyzed in the frequency domain via the describing function method. It is shown that in the presence of parasitic dynamics the system driven by a SOSM algorithm would exhibit chattering. The mechanism of chattering generation is analyzed. Further, it is substantiated why chattering is an inherent feature of the sliding mode principle and therefore unavoidable.
TL;DR: For nonlinear controlled optical storage drives, a frequency-domain measurement approach is shown to be effective in demonstrating both stability and performance and the motivation for applying such an approach is illuminated.
Abstract: For nonlinear controlled optical storage drives, a frequency-domain measurement approach is shown to be effective in demonstrating both stability and performance. In an experimental setting based on an industrial optical playback (CD drive) device, the motivation for applying such an approach is illuminated. It is shown that performance can efficiently be assessed using a describing function approach on a model level and using swept-sine measurements on an experimental level. The validity and effectiveness of the approach is extensively shown via closed-loop measurements.
TL;DR: In this article, a technique for the explicit formulation of frequency response functions (FRFs) for nonlinear MDOF systems, yielding closed-form analytical expressions, is presented, which produces FRFs at selected coordinates only, regardless of the system's size or the type of nonlinearity.
14 Jun 2006
TL;DR: In this article, a simple underactuated manipulator, named Pendubot, is made through second-order sliding mode (SOSM) algorithms, particularly with twisting algorithm.
Abstract: The generation of periodic motion for a simple underactuated manipulator, named Pendubot is made through second-order sliding-mode (SOSM) algorithms, particularly with twisting algorithm. This study is motivated by the fact that in the presence of an actuator, the transient process converge to a periodic solution. To obtain the desired amplitude and velocity of oscillations we use describing function and locus of a perturbed relay system approach to provide the corresponding gain parameters. Performance issue of the controller is illustrated in a simulation study.
14 Jun 2006
TL;DR: In this article, the NARMAX (Nonlinear Auto Regressive Moving Average with eXogenous inputs) system identification method is applied to develop a nonlinear flow model and low-pass filtering is introduced as an effective method to facilitate a quasi-linear approximation of the nonlinear fluidic system including synthetic jet actuation in the frequency domain.
Abstract: This research aims to facilitate feedback control of flow separation using synthetic jets. The effects of synthetic jets on flow separation are assessed via CFD simulations on a rounded backward-facing step. The NARMAX (Nonlinear Auto Regressive Moving Average with eXogenous inputs) system identification method is applied to develop a nonlinear flow model. Low-pass filtering is introduced as an effective method to facilitate a quasi-linear approximation of the nonlinear fluidic system including synthetic jet actuation in the frequency domain. Employing the describing function method, the approximate frequency response of the system is analyzed and implemented for the synthesis of a linear feedback controller. Finally, a PI controller is demonstrated to achieve tracking of a desired pressure with an improvement in the transient response over the open loop system.
TL;DR: This consistent approach to modelling CSs presented here aims to improve the computational efficiency, which in cases when nonlinearities are included, is a major problem when CSs with many degrees of freedom are modelled.
01 Jan 2006
TL;DR: It is shown that limit cycle Floquet's multipliers and the related bifurcation phenomena can be estimated through a spectral approach, entirely based on the describing function technique, and yields more accurate results than the other describing function-based approaches proposed in the literature.
27 Mar 2006
TL;DR: This work presents an exploratory study on the ability of oscillation-based test (OBT) for testing continuous-time low-pass ladder filters, particularly, fifth and seventh order Butterworth and elliptic filters.
Abstract: In this work, we present an exploratory study on the ability of Oscillation-Based Test (OBT) for testing continuous- time low-pass ladder filters. Particularly, fifth and seventh order Butterworth and elliptic filters are addressed. We devote our effort in determining the efficiency of OBT for detecting deviation-faults in the filters components, using signal-flow graphs for modeling the filters. For implementing the OBT oscillators, we use non-linear elements in the feedback paths. The describing function approach is adopted for the mathematical treatment of the non-linear elements. Additionally, the oscillation conditions are established with a very good precision using Bode Plots. For characterizing our OBT schemes, we inject arbitrary deviation-faults and then establish the fault coverage. An alternative approach is also suggested in the paper, based in the assessment of the lowest deviations in each circuit parameter able to be detected using the proposed oscillators. In this way, it is possible to determine the hard-to-verify components.
TL;DR: In this article, the authors studied the describing function (DF) of systems constituted by a mass subjected to nonlinear friction and decomposed the friction force into viscous, Coulomb and static forces.
TL;DR: In this paper, a single-range controller synthesis procedure for use with nonlinear, multivariable, and time-varying liquid propellant engines is developed based on one describing function model of the nonlinear plant coupled with two different linear algebraic controller design procedures.
TL;DR: An arctangent function is suggested as a suitable parameterisation for the soft-limiting gain characteristic frequently encountered in models of biomedical systems and this function is shown, as an example, to fit the neural arc component of the baroreflex.
Abstract: This paper suggests an arctangent function as a suitable parameterisation for the soft-limiting gain characteristic frequently encountered in models of biomedical systems. This function is shown, as an example, to fit the neural arc component of the baroreflex with the main contribution of the paper being the development of a simple describing function (DF) characteristic for the arctangent. The simple form of the DF allows transparency of the physiological parameters in, for example, stability analysis. For illustration, the derived DF is used to examine low-frequency limit cycles in blood pressure, sometimes termed Mayer waves.
TL;DR: In this article, the authors discuss and compare three different approaches for L2-gain estimation of Hammerstein systems, where the objective is to find the input signal that maximizes the gain.
01 Dec 2006
TL;DR: A phase lead reset compensator that has a flat gain characteristic is proposed to be used together with the common feedback control design to enlarge the servo bandwidth by increasing the phase stability margin.
Abstract: This paper investigates a time-dependent phase lead reset control (PLRC) scheme which resets the sub-set of states of the systems at a predefined time. A phase lead reset compensator that has a flat gain characteristic is proposed to be used together with the common feedback control design to enlarge the servo bandwidth by increasing the phase stability margin. We also propose to have a reset time slightly earlier than the instants of input zero-crossing in the usual reset control to solve the impulsive effect in the control signal that leads to control signal saturation. Sinusoidal describing function analysis of the proposed control scheme shows that it can relax the Bode's gain-phase constraint. The application of the proposed PLRC to the Hard Disk Drive (HDD) servo system shows that the performance improvement. Our results also show that the large sharp peaks in the control voltage which may lead to track following controller saturation is also avoided.
TL;DR: In this article, a new phase-noise measurement technique based on inter-injection locking of two similar oscillators is proposed, which is shown that in the case of zero phase of coupling coefficient, the system is in the optimum state where the only required parameter for the measurement is the locking bandwidth.
Abstract: Phase noise in two mutually coupled oscillators is analyzed by the describing function method, and the after-lock phase noise of the oscillators is calculated in terms of their free-running phase noise. A new phase-noise measurement technique based on inter-injection locking of two similar oscillators is proposed. Experimental results are presented, which confirm the theory. It is shown that in the case of zero phase of coupling coefficient, the system is in the optimum state where the only required parameter for the measurement is the locking bandwidth. In this optimum state, as far as the locking bandwidth is measured correctly, imperfections such as the frequency drift, parameters discrepancy, and nonlinear susceptance of the oscillators have no serious effect on the measurement accuracy. The proposed method is compared to the conventional ones.
14 Jun 2006
TL;DR: In this paper, a robust limit cycle controller for autonomous systems with separable single-input-single-output nonlinearities is proposed, where the objective is to design a controller such that the variation in limit cycle amplitude and frequency due the uncertainty is as small as possible in the controlled system for the worst uncertainty considered.
Abstract: The design of robust limit cycle controllers introduced here can be used for autonomous systems with separable single-input-single-output nonlinearities. Considering a system with unavoidable limit cycle and an uncertain linear subsystem, the objective is to design a controller such that the variation in limit cycle amplitude and frequency due the uncertainty is as small as possible in the controlled system for the worst uncertainty considered. The method consists of quasi-linearization of the nonlinear element via a describing function (DF) approach and then shaping the loop to reach desired limit cycle characteristics. As the DF method is used, loop shaping takes place in the Nyquist plot.
14 Jun 2006
TL;DR: In this article, the second-order sliding mode observer dynamics were analyzed in the frequency domain, based on the describing function method and the concept of the equivalent gains of nonlinear functions of the super-twisting algorithm.
Abstract: The second order sliding mode observer dynamics are analyzed in the frequency domain. The so-called super-twisting algorithm is utilized for generating the second-order sliding mode in the observer dynamical system. The frequency response of the actuator dynamics is obtained and used as a characteristic of the observer. The analysis proposed is based on the describing function method and the concept of the equivalent gains of nonlinear functions of the super-twisting algorithm.
Book Chapter•
01 Jan 2006
TL;DR: In this paper, the background of the describing function for a single sinusoidal signal and how it can be used in the analysis and possibly the design of a nonlinear feedback system are discussed.
Abstract: This section is primarily concerned with developing the background of the describing function for a single sinusoidal signal and showing how it can be used in the analysis and possibly the design of a nonlinear feedback system. After the definition of the describing function, its value is obtained for several specific nonlinear characteristics and then it is shown how the information can be used to explore the possibility of limit cycles in a nonlinear feedback loop. It is shown how the stability of any limit cycles may be ascertained and two examples of use of the DF in control systems problems are given. Uses of the DF for evaluating the closed loop frequency response and for designing compensators to eliminate limit cycles are discussed. The latter part of the presentation discusses describing functions for other signals, including those consisting of more than one component, and their possible uses in studying some aspects of feedback loop analysis and design.