Showing papers on "Describing function published in 2002"

Linear and Nonlinear Aeroelastic Analysis of Fighter-Type Wing with Control Surface

Abstract: Linear and nonlinear aeroelastic analyses of a fighter-type wing with a control surface have been performed by using frequency-domain and time-domain analyses. Modes from free vibration analysis and a doublet-hybrid method are used for the computation of subsonic unsteady aerodynamic forces. The fictitious mass modal approach is used to reduce the problem size and the computation time in the linear and nonlinear flutter analyses. For the nonlinear flutter analysis, the control surface hinge is represented by a free-play spring and is linearized by using the describing function method. The linear and nonlinear flutter analyses indicate that the flapping mode of the control surface and the hinge stiffness have significant effects on the flutter characteristics. From the nonlinear flutter analysis, limit-cycle oscillation and chaotic motion are observed in a wide range of air speed below the linear flutter boundary, and a jump of limit-cycle oscillation amplitude is observed.

Active Engine Vibration Isolation using Feedback Control

Abstract: Broad band active vibration isolation of automobile engine using linear and nonlinear feedback control is considered. The objective is to reduce the forces transmitted to the chassis and body, and, thus, reducing vibrations and structure borne noise inside the vehicle compartment when the engine is subjected to different excitations. Moreover, the ability of the original passive suspension system to deal with high load transient excitation, e.g. due to a dropped clutch operation, has to be preserved. Engine excitations corresponding to idle and driving engine operating conditions as well as internal and external transient excitations have been investigated.Solutions based on classical control and LQG (Linear Quadratic Gaussian) control methodologies have, to some extent, been treated. However, it turns out that the desired loop gain requires a control design method more suitable for shaping the loop gain and, at the same time, obtaining closed-loop stability. Using H2 control theory and Gain Scheduling, a MIMO (multi-input multi-output) control algorithm dealing with the above mentioned excitations when taking system nonlinearities into account, is developed.The active engine suspension system design has been performed making use of a virtual simulation, analysis, and verification environment providing powerful opportunities to deal with time varying system characteristics.Except for some restrictions originating from non-linearities, feedback loop shaping technique is found to be a suitable way to achieve desired closed-loop characteristics when dealing with such MIMO system. Where all engine excitations except those corresponding to high ramping speed or extremely high nominal engine torque, are successfully dealt with. However, to guarantee closed-loop stability, two kinds of non-linearities, reflecting the time varying system characteristics, have to be taken into account. Those are non-linear material characteristics of the engine mounts and large angular engine displacements. This requires the linear H2 control theory to be extended using a non-linear Gain Scheduling control scheme.The effects of input saturation have been investigated using describing function analysis for two different controller implementations, using computed and applied control force for state observation. It has, unexpectedly, been found that, avoiding closed-loop self-oscillations due to input saturation requires computed control force to be used for state observation.

Limitations of the describing function for limit cycle prediction

Abstract: We consider comparator-based nonlinear feedback systems, and use Tsypkin's method to develop a strategy with which to find systems with low-pass linear part for which the describing function technique erroneously predicts limit cycles. We produce an infinite set of examples of systems with very low-pass linear parts for which the describing function technique predicts spurious limit cycles, and also provide a more practical example in which limit cycles are erroneously predicted.

Describing Function Analysis of Systems with Impacts and Backlash

Abstract: This paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional-order dynamics is illustrated using the Nyquist plot and the results are compared with those of standard models.

A new family of neural network-based bidirectional and dispersive behavioral models for nonlinear RF/microwave subsystems(invited paper)

Abstract: The article introduces a new approach to the ANN-based behavioral modeling of nonlinear RF/microwave systems or subsystems. The proposed model accounts for both the linear and the nonlinear distortion of modulated signals. The former is introduced by the two-port frequency-dependent admittance matrix. The latter is described by the means of a couple of describing functions (which may also be frequency-dependent), relating the two-port linear and the nonlinear responses. The describing functions are approximated by artificial neural networks (ANN) trained by harmonic-balance results. The resulting model is fast to compute, can accurately handle broadband modulated signals, and is fully bilateral. This means that the model can be routinely used to analyze systems where bidirectional signal flow takes place, e.g., due to mismatches between the interconnected subsystems, or even due to the presence of filters operating in the stopband. © 2002 John Wiley & Sons, Inc. Int J RF and Microwave CAE 12: 51–70, 2002.

Steady-State Analysis for a Class of Sliding Mode Controlled Systems Using Describing Function Method

Abstract: In this paper, the analysis of the steady-state response of the slidingmode control system is presented. The nonlinearity of the switching termin the control law is approximately characterized by using itsequivalent describing function. The parasitic dynamics is modeled as afirst-order lag transfer function, and a possible transport delay isconsidered. Subsequently, a frequency domain method is used for theprediction of limit cycles. The stability-equation method together withthe parameter plane method is proposed to predict graphically limitcycles in the system coefficient plane. Four common types of switchingfunctions are investigated. This analysis further provides an approachof switching control gain selection for suppressing the limit cycle inthe sliding mode.

Dynamic characterization of hysteresis elements in mechanical systems

Abstract: This paper considers the dynamic behavior of single degree of freedom systems consisting of a mass on a "non-linear hysteretic spring". Elements in common engineering use, in the form of plain or rolling element bearings for a variety of applications such as linear guideways in machine tools, exhibit predominately such "non-linear hysteretic spring" behavior. The highly non-linear effect caused by such elements has hitherto not been taken into consideration, by designers, in the control design for such machine tools. However, since more accurate and faster machines are required, these non-linear hysteresis effects should be identified and incorporated in the control design. The properties of this type of static hysteresis are first outlined. Thereafter, the dynamics of autonomous systems are deduced by an analytic solution. The problem of forced response is discussed and treated by using the approximate describing function approach, which is then validated by direct simulation. This analysis shows that for small excitation amplitudes an approximate linear behavior is obtained. For excitation amplitudes around the saturation value of the hysteretic spring, there is a region that is marked by high sensitivity of the displacement amplitude for a given excitation amplitude in which no satisfactory results are obtained, while concordant results are obtained over the greatest part of the Amplitude-Frequency plain. The results of the analysis are intended for use as input for the design process of appropriate controllers.

A harmonic model for the nonlinearities of single-phase transformer with describing functions

Abstract: In a transformer, the harmonic model is essential for the filter design and analysis of harmonic power flow. Among all of the harmonic analyses of nonlinear devices, the core nonlinearity caused by the transformer hysteresis has received the most interest. Although many harmonic models have been proposed to interpret the nonlinearity of the transformer core, most of them require complex calculations. In this study, we derive the mathematical formulas of the exciting current for a single-phase transformer by the describing function methods. The mathematical expression allows us to obtain the Fourier series for the exciting current; and, then, it provides the various order harmonic magnitudes and phase angles of the exciting current. This work also presents a mathematical model characterized by simple calculation and with high precision for the harmonics of exciting current. The transformer is under no load condition. Actual measuring verifies the effectiveness of the proposed model.

Theoretical and experimental analysis of nonlinear dynamics in a linear compressor

Abstract: Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically and experimentally. In the theoretical approach, motions of not only piston but also cylinder are considered and dynamic models for steady-state response predictions are formulated by applying the describing function method. Effects of piston mass on the jump phenomena are predicted by the derived models as an example of design parameter variation and compared with actual experimental results.

Large-signal modelling of the PRC-LCC resonant topology with a capacitor as output filter

Abstract: In this paper, two mathematical models are presented to approximate, accurately enough, the large signal dynamical behaviour and the steady state behaviour of the PRC-LCC resonant topology with a capacitor as output filter. The method used to obtain these models is based on applying the extended describing function and the generalised averaging modelling techniques. Therefore, the evolution of the topology waveforms, most of them sinusoidal, is approximated by their corresponding envelope. These envelopes are expressed by a set of nonlinear differential equations which are solved numerically with the help of a computer. The resulting algorithm is faster than a straight PSpice simulation and free of convergence problems. Finally, the good concordance between the models and the practice is verified with a wide set of experimental results.

Modelling of the PRC-LCC resonant topology with a capacitor as output filter using EDF

Abstract: In this paper, the extended describing function (EDF) and the generalised averaging modelling techniques have been applied to a PRC-LCC resonant AC/DC power conversion topology with a capacitor as output filter. In this way, a mathematical large signal model has been obtained to describe the topology dynamic behaviour. This large signal model consists of a set of nonlinear differential equations which are solved numerically with the help of a computer. The resulting algorithm is faster than a straight PSpice simulation and free of convergence problems. From this dynamical model, a very simple steady state model has also been deduced. In the paper it is shown and particularised for the operation along the optimum switching tine. Finally, the accuracy of the presented models is verified with a wide set of experimental results.

Driver Follower Control Model with Vehicle Target Velocity Based on Preview Follower Theory

Abstract: According to the strong nonlinear character of vehicle dynamic control system,the transfer function of partial equivalent linearization,which can describe dynamic nonlinear character of vehicle velocity control,is established by the method of non linear system describing function and ARMA(Auto Regressive Moving Average)model.Then based on preview follower theory,a driver velocity control model that describes how the driver follows and controls vehicle velocity under the precondition of the given target velocity is presented.The results of simulation show that this model effectively simulates driver′s behavior of controlling the velocity by taking road velocity information,driver′s delay character and vehicle dynamic character into account,and provide an effective way for the research of vehicle velocity automatic control and advanced vehicle control system in ITS(Intelligent Transportation System).

Fractional Describing Function Analysis of Systems with Backlash and Impact Phenomena

Abstract: This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional-order dynamics is illustrated using the Nyquist plot and the results are compared with those of standard models. I. INTRODUCTION The area of Fractional Calculus (FC) deals with the operators of integration and differentiation to an arbitrary (including noninteger) order and is as old as the theory of classical differential calculus. The theory of FC is a well- adapted tool to the modelling of many physical phenomena, allowing the description to take into account some peculiarities that classical integer-order models simply neglect. For this reason, the first studies and applications involving FC had been developed in the domain of fundamental sciences, namely in physics (5) and chemistry (20). Besides the in tensive research carried out

Design of Fuzzy Regulator for Power System Secondary Load Frequency Control

Abstract: The stability analysis of nonlinear system that is harmonically linearised is given[10, 3, 11]. With the introduction of fuzzy regulator the nonlinear system consists of linear part and two nonlinear parts. The stability analysis is conducted by use of describing function method and Hurwitz stability criterion. Proportional and derivative parameters of Mamdani type fuzzy regulator gains were preliminary tuned (pre-tuned) by Cohen-Coon and Ziegler-Nichols methods [1, 13]. Stability analysis was conducted for the power system secondary load-frequency control model. The proposed stability analysis presents a good starting point for the design of fuzzy regulator for nonlinear systems.

Bifurcations in Systems with a Rate Limiter

Abstract: Limit cycles analysis of feedback systems with rate limiters in the actuator can be implemented by a classical method in the frequency domain, the harmonic balance method. In this paper, the rate limiter describing function is obtained and applied to the search for limit cycles in such control systems. Three examples with three different bifurcations (saddle-node bifurcation of limit cycles, subcritical Hopf bifurcation at infinity and supercritical Hopf-like bifurcation) are included. The method is approximate but its main advantage is that intuition is gained into a difficult problem.

Nonlinear identification of thermoacoustic instabilities with limit cycles in a Rijke tube

Abstract: This paper deals with the development of a model of thermoacoustic instabilities, observed in a laboratory scale Rijke tube. The model is built via a thorough description of both the gas dynamics and the heat release process, which is concisely outlined. The validation is carried out on the basis of real experimental data, and it is founded on a mixed linear/nonlinear identification method with the support of the describing function theory for the detection of limit cycle behavior.

A large-signal model for the PRC-LCC resonant topology with a capacitor as output filter

Abstract: In this paper, two mathematical models are presented to approximate, accurately enough, the large signal dynamical behaviour and the steady state behaviour of the PRC-LCC resonant topology with a capacitor as output filter The method used to obtain these models is based on applying of the extended describing function and the generalised averaging modelling techniques Therefore, the evolution of the topology waveforms, most of them sinusoidal, is approximated by their corresponding envelope These envelopes are expressed by a set of nonlinear differential equations which are solved numerically with the help of a computer The resulting algorithm is faster than a straight PSpice simulation and free of convergence problems Finally, the good concordance between the models and the practice is verified with a wide set of experimental results

Modeling and Analysis of Binary ABR Flow Control

Abstract: ATM networks provide pure QoS(Quality of Service)for diversified services through a series of traffic management mechanism, and the ABR(Available Bit Rate) flow control is especially important. In the binary flow control scheme, cell rate and queue length oscillate with great magnitude to reduce link utilization, and make a negative impact on switch performance, so the standard EFCI algorithm is regard as ineffecient, however, its simplicity is attractive to high performance switch design. In this paper, the model of the binary ABR flow control is deduced based on fluid flow theory, and the correctness of this model is validated through comparing the analytical solution with the simulation results. Then, the second order system presenting the source end system how to regulate the cell rate, is obtained by local linearization about the equilibrium point, moreover, the standard EFCI algorithm and the improved p EFCI algorithm are approximated as the typical nonlinear components, and they are relay with hysteresis loop and saturated component respectively. Subsequently, we investigate the stability of the two algorithms using the describing function approach, which is very mature and effective and widely used in analysis and design of classical nonlinear control system. The conclusion is that the p EFCI scheme is more robust than the standard EFCI algorithm because the relay with hysteresis loop has negative imaginary part of the negative of the inverse of the relative describing function, which provides more chances to intersect with the Nyquist diagram. It is intersection that leads to the self oscillation occurred in queue and ACR. However, for the saturated component included in p EFCI algorithm, the imaginary part is equal to zero. Finally, we emphasize that theoretical analysis is rather important during algorithm design because the performance of heuristic algorithms depended on intuition, just like EFCI, is not always reliable, and point out the farther studying direction, i.e., optimizing the binary ABR flow control applying with the design approach in control system.

Limit cycle analysis for electro‐hydraulic systems with friction

Abstract: In this paper, a graphical prediction method is developed to effectively predict the existence of the limit cycles induced by nonlinear friction force in an electro‐hydraulic control system. The friction‐induced nonlinearity is linearized by its corresponding describing function. Then the stability equation method, accompanied by the parameter plane method, provides a useful tool for the establishment of necessary conditions to sustain a limit cycle in the controller coefficient plane. Henceforth, the limit cycles are predicted in a graphical way, and simulations are carried out to verify the accuracy of the prediction method.

Limit-cycle oscillations of an airfoil with piece-wise linear restoring forces

Abstract: Nonlinear airfoil motion for incompressible airflow with a piece-wise linear restoring spring force is investigated. It is possible to obtain stable, divergent, limit-cycle oscillations and chaotic motions depending on airfoil parameters and initial conditions. Two numerical time-marching schemes are described and the accuracy is examined. A new method based on a point transformation theory to handle piece-wise linear functions in nonlinear aeroelastic problems is outlined. The results from this technique are used to assess the accuracy and limitations of the numerical schemes and the describing function technique.

Stability of RED Algorithm: Analysis Based on Nonlinear Control Theory

Abstract: This paper analyzes the attributes of RED(Random Early Detection) and gentle-RED algorithms using the describing function approach, which is a classical analysis approach in nonlinear control theory. In fact, authors conclude that the essential reason that queue periodic motion is the self-oscillation caused by the nonlinear component in the packet dropping probability profile, this point is neglected by most of the existed schemes, and then deduce a more accurate criterion with which the stable operation region of RED scheme will be estimated, on the other hand, although gentle-RED is more powerful than RED to keep queues stable, this ability is very limited because it only extends the stable operation region with different nonlinear characteristic, but doesn't thoroughly eliminate it. The ideal solution should be to design more robust linear controller for AQM scheme.