Showing papers on "Describing function published in 2011"

Nonlinear mode triggering in a multiple flame combustor

Abstract: A nonlinear analysis of combustion instability is carried out by making use of the Flame Describing Function (FDF) framework. Predictions are compared with data obtained from experiments on a multipoint injection combustor. The burner comprises a premixer manifold of variable length, an injection system and a flame tube. This device features several types of self-sustained oscillation and its dynamics is characterized by nonlinearities like transient frequency shifting, mode switching, mode triggering and hysteresis phenomena which cannot be anticipated from a classical linear stability analysis. It is shown that many of these phenomena can be suitably predicted by including the amplitude dependent response of the flame in a matrix analysis of the system dynamics. More specifically, the present work centers on processes which cannot be anticipated from linear analysis such as mode switching linked to a triggering by the nonlinear flame response.

Characterization of traffic oscillation propagation under nonlinear car-following laws

Abstract: Unlike linear car-following models, nonlinear models generally can generate more realistic traffic oscillation phenomenon, but nonlinearity makes analytical quantification of oscillation characteristics (e.g, periodicity and amplitude) significantly more difficult. This paper proposes a novel mathematical framework that accurately quantifies oscillation characteristics for a general class of nonlinear car-following laws. This framework builds on the describing function technique from nonlinear control theory and is comprised of three modules: expression of car-following models in terms of oscillation components, analyses of local and asymptotic stabilities, and quantification of oscillation propagation characteristics. Numerical experiments with a range of well-known nonlinear car-following laws show that the proposed approach is capable of accurately predicting oscillation characteristics under realistic physical constraints and complex driving behaviors. This framework not only helps further understand the root causes of the traffic oscillation phenomenon but also paves a solid foundation for the design and calibration of realistic nonlinear car-following models that can reproduce empirical oscillation characteristics.

Modeling Wide-Frequency-Range Pilot Equalization for Control of Aircraft Pitch Dynamics

Abstract: In continuous manual control tasks, human controllers adapt their control strategy to the dynamics of the controlled element. This compensation for the controlled-element dynamics is performed around the pilot–vehicle system crossover frequency, in order to obtain satisfactory performance of the combined pilot–vehicle system, but is also seen to extend to frequencies well above crossover. For a controlled element representing the linearized pitch dynamics of a small conventional jet aircraft, an extension to the models for pilot equalization described in the literature was found to be needed for the modeling of the adopted pilot equalization dynamics over a wide frequency range. Measured pilot describing functions revealed that pilots use a combination of low-frequency lag and high-frequency lead equalization to compensate for the characteristics of these typical aircraft pitch dynamics around the short-period mode. An additional high-frequency lead term in the pilot equalization transfer function was found to allow for the modeling of these adopted equalization dynamics over a wide frequency range, thereby also yielding a significant increase in the percentage of measured control inputs that is explained by the pilot model. Furthermore, for this controlled element the extended model for the equalization dynamics was found to be important for the interpretation of the changes in pilot control behavior that occur due to the presence of physical motion feedback.

A small signal model for average current mode control based on describing function approach

Abstract: A small signal model for average current mode control based on describing function method is proposed. Modeling of average current mode control is more complicated than peak current mode control due to the additional current compensator. In this paper, two commonly used current compensators are considered as examples. The structure of average current mode control is compared with V2 control to find the similarity. Previous modeling result about V2 control is borrowed and modified for average current mode control. The proposed small signal model can be accurate up to switching frequency. The proposed model is verified using Simplis simulation and measurement.

Robust Control of Flight Simulator Motion Base

Abstract: simulator motion system. Imperfect compensation of the inverse dynamic control is intentionally introduced in order to simplify the implementation of this approach. Two control strategies are applied in the outer loop of the inverse dynamic control to counteract the eects of imperfect compensation. The rst one is designed using Laypunov stability theory (LST) and the second one is designed using H1 theory. Forward and inverse kinematics and full dynamic model of six degrees of freedom motion base driven by electromechanical actuators are briey presented. Describing function, dynamic threshold and some maneuvers computed from the washout lter were used to evaluate the performance of the controllers.

Reset Control Systems with Reset Band: Well-posedness and Limit Cycles Analysis

Abstract: Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed: anticipation of the condition with the so-called reset band, relaxation of the action applying partial reset, etc. There is a lack of analysis tools for reset systems with reset band. In this paper we address the problem of existence, detection and stability of limit cycles by means of Poincare maps. The results give also information on pathologies such as Zenoness. The presented approach is complementary to describing function analysis, in order to reveal the ability of reset controllers for overcoming fundamental limitations in the frequency domain.

Describing function model of series resonant inverter with current limiting diode-clamp

Abstract: An equivalent circuit model for predicting the steady-state behaviour of the series resonant inverter with a current limiting diode-clamp is derived using describing function techniques. An iterative procedure is employed to determine the conduction point of the diode-clamp. Experimental results taken from a prototype inverter are presented to validate the model.

Analysis and experimental investigation for switching frequency characterisation of a three-level ac-dc converter using frequency domain approach

Abstract: In this study, a relay with hysteresis-based control technique is analysed for a three-phase three-level neutral point clamped (NPC) ac-dc converter. The converter draws sinusoidal current with unity power factor from the supply grid and keeps total dc-link voltage constant. The hysteresis-based current control has good dynamic response but suffers from variable switching frequency. The switching frequency characterisation of hysteresis current control based on time domain approach is more complicated for the multilevel converters. Therefore there is a need to address the characterisation based on frequency domain approach. Here, describing function method and Tsypkin's method are proposed for the switching frequency characterisation of the relay with hysteresis-based system. The proposed methods determine the maximum switching frequency and amplitude of the current tracking error and permit the calculation of maximum switching frequency in simple algebraic equations. The closed-loop control scheme of the relay with hysteresis-based current control is implemented for a three-phase three-level NPC ac-dc converter system. The performance of the proposed frequency domain characterisation has been studied using MATLAB/Simulink, and a laboratory model is developed for experimental verification.

Comparative study of X-parameters and nonlinear scattering functions

Abstract: S-parameters have been used in analyzing linear networks for more than half a century. Despite the great success of S-parameters, they are severely limited. In fact in real world, all systems are nonlinear. It's a hard work to characterizing the nonlinear network and thus it becomes a hot issue today. This article introduces two methods of nonlinear modeling, X-parameters and scattering functions. We give a conclusion on the relation of these two methods after comparing their basic concept and extraction systems. At the end of this paper, we present an extraction system which can adopt either X-parameters or Scattering functions for the nonlinear characterizing and modeling.

A Low-Order Modelling of Ducted Flames With Temporally Varying Equivalence Ratio in Realistic Geometries

Abstract: The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the so-called G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies.Copyright © 2011 by ASME

Identification of Weakly Nonlinear Systems Using Describing Function Inversion

Abstract: In this paper describing functions inversion is used and the restoring force of a nonlinear element in a MDOF system is characterized. The describing functions can be obtained using linearized frequency response functions (FRFs). The response of the system to harmonic excitation forces at distinct frequencies close to the resonant frequency results in linearized FRFs. The nonlinear system can be approximated at each excitation frequency by an equivalent linear system. This approximation leads to calculation of the first-order describing functions. By having the experimental describing functions calculated and the system's responses corresponding to the nonlinear element (measured or interpolated), nonlinear parameter identification can be performed. Two numerical and experimental case studies are provided to show the applicability of this method.

Iterative method based on CFD data for the assessment of seakeeping control effects, considering amplitude and rate saturation

Abstract: An iterative procedure for the frequency domain evaluation of control effects in nonlinear loops is introduced. The article focuses on ship seakeeping control, to attenuate ship motions. There is no model of the ship, only CFD tabulated data. The proposed procedure could be used for design or empirical tuning of a controller. The actuators have angle and rate limits. In the case of a ship, the actuators are submerged moving wings: flaps, fins and T-foil. The control evaluation procedure uses a describing function approach. The paper considers amplitude and rate saturation in series. The results are validated with experiments using a scaled ship in a towing tank facility. Copyright © 2010 John Wiley & Sons, Ltd.

Designing the Non-Linear PID Controller for a Missile

Abstract: PID controllers are the most prevailing & operative controllers in industry in recent 50 years. NPID Method that is an optimized method of usual PID, leads to get better operation in response quickness and, also overshoot simultaneously. In this paper, it is used NPID method that is an efficient method for control. NPID includes a non-Linear gain and a defined linear gain that connected serial. Using this method results in setting responses based on closed loop system control operation, that kd (.), Ki (.) and Kp (.) are control gains varies with time and have constant values in linear proportional, integral, derivative controller. The missile control system contains a linear system to non-linear one. The missile control System responses to PID and NPID controller are shown at the end to compare their behaviors & effects.

Statistical Analysis of Self-Oscillating Power Amplifiers

Abstract: Self-oscillating power amplifiers (SOPA) are promising solutions for amplification of high crest factor signals, with good linearity and efficiency, as a result of using a switch mode amplifier inside the oscillating loop. The lack of comprehensive and statistical analysis method complicates the design and analysis procedure. In this paper, a new statistical approach is presented to analyze the nonlinear behavior of SOPA, to predict the required system metrics like EVM and ACPR. The approach is an extension to the describing function concept and is suitable for a general class of complex Gaussian input signals. The approach is validated through comparison with transistor level simulations and measurements performed on a single chip SOPA realized in 65 nm CMOS technology, for three types of input signal.

Computation of multiple limit cycles in nonlinear control systems - a describing function approach

Abstract: Limit cycles play an important role in nonlinear systems, provided that many control loops with common nonlinearities like relay, hysteresis, and saturation can present them Thus, a proper description of this nonlinear phenomenon is highly desirable A strategy for the linearized analysis is the describing function method, which is a frequency domain approach that allows the limit cycle prediction and stability analysis Some papers had discussed the method for the simplified analysis; however, they are concentrated in the prediction of only one limit cycle even for systems with multiple conditions This paper proposes a systematic way of multiple limit cycle determination, as well as the stability analysis of each one All theoretical/computational issues involved in the approach are also discussed

Third harmonic distortion calculation of a self-oscillating power amplifier

Abstract: It is difficult to analyze the harmonic distortion of a self-oscillating power amplifier (SOPA), because the SOPA is a hard nonlinear system without an external clock. The single or multiple sinusoidal inputs describing function (DF) method is commonly used to linearize a nonlinear element, but this method considers only the components at the same frequencies as the input signals (i.e., fundamental components) at the nonlinear element’s output. In this paper, besides the fundamental components, the third harmonic components are also calculated at the output of a comparator with three sinusoidal inputs, to create a linearized model of the comparator, and thus of the SOPA. The third harmonic distortion of the SOPA is calculated. The models of the zeroth and the first order SOPA are verified by behavioral simulation using MATLAB.

Identification and robust limit-cycle-oscillation analysis of uncertain aeroelastic system

Abstract: Model uncertainty directly affects the accuracy of robust flutter and limit-cycle-oscillation (LCO) analysis. Using a data-based method, the bounds of an uncertain block-oriented aeroelastic system with nonlinearity are obtained in the time domain. Then robust LCO analysis of the identified model set is performed. First, the proper orthonormal basis is constructed based on the on-line dynamic poles of the aeroelastic system. Accordingly, the identification problem of uncertain model is converted to a nonlinear optimization of the upper and lower bounds for uncertain parameters estimation. By replacing the identified memoryless nonlinear operators by its related sinusoidal-input describing function, the Linear Fractional Transformation (LFT) technique is applied to the modeling process. Finally, the structured singular value (µ) method is applied to robust LCO analysis. An example of a two-degree wing section is carried out to validate the framework above. Results indicate that the dynamic characteristics and model uncertainties of the aeroelastic system can be depicted by the identified uncertain model set. The robust LCO magnitude of pitch angle for the identified uncertain model is lower than that of the nominal model at the same velocity. This method can be applied to robust flutter and LCO prediction.

Thermal-electrical modeling and simulation of resonantly operated DC-DC converters based on extended describing function method

Abstract: Due to the very large difference between electrical and thermal time constants, stimulation for resonantly operated DC-DC converters using physical or ideal switching model is very time-consuming or impossible with limited computational resources. In order to overcome this problem a novel thermal-electrical averaging model of resonantly operated DC-DC converters is proposed in this contribution. The electrical model is based on extended describing function method. All required parameters for the thermal model can be obtained from datasheets. As examples thermal-electrical models of series-parallel resonant converters with LC- and C-type output filters are given and verified by comparison with a standard simulation tool. The thermal-electrical modeling procedure proposed in this contribution can of course also be applied for other types of resonant converters.

Recording of Model Frequency Responses and Describing Functions in Modelica

Abstract: An assistant Modelica package is introduced which supports the determination of model frequency responses or describing functions of Modelica models, as the case may be. The result is frequency response data which can be used for further analysis such as stability properties of the system in closed loop control or the derivation of linear time invariant (LTI) model approximations. The paper addresses inter alia proper scheduling of excitation frequency and amplitude, a brief theory of describing functions (harmonic linearization), the Modelica classes implemented in the package, and some application examples.

The effect of backlash nonlinear on resonance frequency of electric actuator transmission system

Abstract: In order to study the effect of backlash nonlinear on resonance frequency of electric actuator transmission system, in the premise of meeting the stability, it establishes balanced equation of dynamics system with backlash, and does some theory research and dynamic analysis of backlash nonlinearity and system natural frequency and resonance frequency. First, according to describing function to theoretically model the backlash nonlinear, the relation between describing function and the amount of backlash and input amplitude is analyzed; then, the dynamic equilibrium equation of transmission system with backlash is established, the effect of backlash on system natural frequency and resonance frequency; Finally, it makes dynamic simulation analysis for the transmission system based on virtual prototype technology, and the theoretical values and simulation values are compared. Theoretical analysis and simulation results show that the theoretical analysis is basically consistent with simulation results when it is zero backlash, and the error of theoretical analysis and simulation results is within 10%. Therefore, it can be concluded that considering the transmission system theoretical analysis of backlash nonlinearity is feasible, and it is much closer to the actual system with instructive significance.

Small-Signal Modeling of Resonant Converters

Abstract: Ayachit, Agasthya. M.S.Egr, Department of Electrical Engineering, Wright State University, 2011. Small-Signal Modeling of Resonant Converters. Resonant DC-DC converters play an important role in applications that operate at high-frequencies (HF). Their advantages over those of pulse-width modulated (PWM) DC-DC converters have led to the invention of several topologies over the traditional forms of these converters. Series resonant converter is the subject of study in this thesis. By variation in the switching frequency of the transistor switches, the optimum operating points can be achieved. Hence, the steady-state frequency-domain analysis of the series resonant converter is performed. The operational and characteristic differences between the series resonant and parallel resonant and series-parallel resonant configurations are highlighted. In order to understand the converter response for fluctuations in their input or control parameters, modeling of these converters becomes essential. Many modeling techniques perform analysis only in frequency-domain. In this thesis, the extended describing function method is used, which implements both frequency-domain and time-domain analysis. Based on the first harmonic approximation, the steady-state variables are derived. Perturbing the steady-state model about their operating point, a large-signal model is developed. Linearization is performed on the large-signal model extracting the small-signal converter state variables. The small-signal converter state variables are expressed in the form of the transfer matrix. Finally, a design example is provided in order to evaluate the steady-state parameters. The converter is simulated using SABER Sketch circuit simulation software and the steady-state parameters are plotted to validate the steady-state parameters. It is observed that the theoretical steady-state values agrees with the simulated results obtained using SABER Sketch.

Design of self-tuning controllers for highly non-linear mechatronic systems

Abstract: A new procedure for design of self-tuning adaptive controllers (e.g., PID, lead-lag and in general n th order linear controllers) for use with highly non-linear mechatronic systems of the sort encountered in robotic and servomechanism control is developed. The procedure is presented in an algorithmic format. Describing function models, using analytical or experimental techniques, are used to determine the structure of the approximating linear plant at various operating regimes. The parameters of this linear structure are identified (using any available identification scheme) followed by obtaining the parameters of the linear controller by solving a set of simultaneous linear algebraic equations in real time. The procedure is demonstrated for design of self-tuning PID and lead-lag controllers for a non-linear plant of the sort encountered in servomechanism. It is shown that results are better than a fixed gain linear PID controller, and they compete with designs involving a non-linear PID and a non-linear ...

Quantification of valve stiction and dead band in control loops based on harmonic balance method

Abstract: The presence of stiction in control valves often causes oscillations in control loops, with negative effects on quality and cost of goods. Step that follows diagnosis is to quantify this stiction, in order to decide about maintenance or to implement compensators that can improve control loop performance until next plant stop. The describing function method is a well known scheme to predict the period and amplitude of limit cycles in control loops, requiring the knowledge of linear and nonlinear parameters of system model. Here, a method is proposed to estimate these nonlinear parameters using the parameters of linear model and amplitude and period of limit cycle produced by nonlinearity. The result is a simple and efficient algorithm that can be easily extended to other nonlinearities. The conditions for existence and uniqueness of solution for dead band and stiction estimations are obtained. Also, the error from estimations is related to total harmonic distortion of control signal. The usefulness of the proposed method is demonstrated through its application to two examples.

A Sliding Mode Controller of Rudder Angle Servomechanism in Steer-by-Wire System of Pleasure Boat

Abstract: For rudder angle servo mechanism in steer-by-wire (SBW) system of pleasure boats, this paper presents a sliding mode controller with continuous control input. The sliding mode control theory is applied to the controller so as to have high robustness against the normal pressure of a rudder, which is regarded as an unknown disturbance. Designed with the twisting algorithm and the describing function method, a switching input of the proposed controller could enforce a switching function into a limit cycle. As a price of abandoning the perfect sliding mode, the proposed controller can bring not infinite-frequency switching input but continuous control input. As a result, the improvement of the load of the actuator in SBW system can be achieved.