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Showing papers on "Describing function published in 1995"


Proceedings ArticleDOI
18 Jun 1995
TL;DR: In this article, a phase-shift-controlled series-resonant inverter operating at zerovoltage switching (ZVS) is used as the power supply for an induction heating system.
Abstract: A phase-shift-controlled series-resonant inverter operating at zero-voltage-switching (ZVS) is used as the power supply for an induction heating system. This system has two control loops: the phase-shift control loop regulates the output power; and the frequency control loop ensures ZVS for all load conditions. The design and implementation of these control loops are explained. The complete closed-loop small-signal model is obtained using the extended describing function method. The model predictions are compared with experimental data measured from a lab prototype. >

74 citations


Journal ArticleDOI
TL;DR: In this article, a theory for the mechanism by which resonators are excited by grazing flow is presented, which allows prediction of oscillation characteristics for the range of Reynolds numbers, frequencies, and resonator amplitudes for which the acoustically excited mean flow rolls up into discrete vortices.
Abstract: A theory is presented for the mechanism by which resonators are excited by grazing flow. The theory allows prediction of oscillation characteristics for the range of Reynolds numbers, frequencies, and resonator amplitudes for which the acoustically excited mean flow rolls up into discrete vortices. The resonator‐flow system is treated as an autonomous nonlinear system. Limit cycles of the system are found using describing‐function analysis, in which each component of a nonlinear oscillating system is represented by an associated frequency‐response function. This mathematical approach is shown to be a generalization of models in which the resonator and flow are considered parts of a feedback system. The theory’s predictions for the frequencies of oscillation compare favorably with experiment. The results indicate that both ‘‘edge’’ and ‘‘resonator’’ feedback contribute to the mechanism of self‐excited oscillations of the resonator‐flow system.

49 citations


Journal ArticleDOI
TL;DR: In this article, the effect of high order harmonics on the limit cycle response to the aeroelasticity system is investigated in a two-dimensional model of a wing/store with free play in the junction.

33 citations


Journal ArticleDOI
TL;DR: A modified relay- based technique for estimating the critical point in process control systems with improved accuracy over existing relay-based methods is presented and it is theoretically possible to obtain an exact estimate of the process critical point under ideal conditions.
Abstract: In this paper, we present a modified relay-based technique for estimating the critical point in process control systems with improved accuracy over existing relay-based methods. The proposed technique addresses the accuracy of the conventional approach by eliminating the errors introduced in the usual describing function analysis of nonlinear systems. The analytical basis of the technique is described in the paper, and it is also shown that it is theoretically possible to obtain an exact estimate of the process critical point under ideal conditions. The effectiveness of the proposed technique is verified by simulation results and also by real-time experimental results in the level control of a coupled-tanks system. >

33 citations


Journal ArticleDOI
TL;DR: In this article, the μ analysis method is applied to a class of multivariable separable autonomous nonlinear feedback systems, where the nonlinear element is replaced by its sinusoidal input describing function (SIDF) to develop a quasilinear nominal model for control analysis and design.
Abstract: The μ analysis method is applied to a class of multivariable separable autonomous nonlinear feedback systems. The nonlinear element is replaced by its sinusoidal input describing function (SIDF) to develop a quasilinear nominal model for control analysis and design. Some properties of the ∞ -norm and structured singular values (SSVs) are shown to hold for the type of systems where the output is a function of control input-signal amplitude and frequency. The model uncertainty induced by the SDIF approximation is calculated and incorporated in the control design as an input multiplicative perturbation to the quasilinear nominal model. The μ analysis technique is then employed to study the stability and performance robustness of the nonlinear control system. Using small gain theorem, the condition for the absence of limit cycle is derived. The information obtained from this analysis is then used to design a bank of controllers using the H ∞ optimization-based μ synthesis technique. These controllers are desi...

28 citations


Journal ArticleDOI
01 Sep 1995
TL;DR: In this article, a robust controller is designed for the series parallel resonant DC/DC converter based on the linear quadratic Gaussian/loop transfer recovery (LQG/LTR) methodology.
Abstract: A robust controller is designed for the series parallel resonant DC/DC converter based on the linear quadratic Gaussian/loop transfer recovery (LQG/LTR) methodology. The controller structure, comprising a servo-compensator with an internal model, reference state observer, plant and disturbance state observer, ensures tracking of the reference voltage and rejection of system disturbances. The controller performance is insensitive to converter parametric and operational variations. The controller design is based on a converter small-signal model derived using the principles of the describing function and harmonic balance on the nonlinear time-varying converter equations. The controlled converter is shown by computer simulation to perform excellently well, with very good tracking and disturbance capabilities in the presence of changes of load and input voltage.

20 citations


Journal ArticleDOI
TL;DR: In this article, a spectral technique for studying and predicting chaos in a one-dimensional array of Chua's circuits is proposed, where the network is reduced to a scalar Lur'e system to which the describing function technique is applied for discovering the existence and the characteristics of periodic waves.
Abstract: A spectral technique is proposed for studying and predicting chaos in a one-dimensional array of Chua's circuits. By use of a suitable double transform, the network is reduced to a scalar Lur'e system to which the describing function technique is applied for discovering the existence and the characteristics of periodic waves. Finally, by the computation of the distortion index, an approximate tool is given for detecting the occurrence of chaos. >

20 citations


Proceedings ArticleDOI
21 Jun 1995
TL;DR: In this article, the authors combine well known Kharitonov theorems with the describing function to test the stability of uncertain systems, and the results are obtained graphically or analytically by determining the intersection of the frequency for the linear subsystem and the described function.
Abstract: The describing function method is used to predict the existence of limit cycles in a system with a separable nonlinearity. The results are obtained graphically or analytically by determining the intersection of the frequency for the linear subsystem and the describing function. Here, the authors combine well known Kharitonov theorems with the describing function to test the stability of uncertain systems. An example is provided to illustrate the new method.

18 citations


Proceedings ArticleDOI
21 May 1995
TL;DR: A multiple term lead-lag controller is designed and implemented to quench the limit cycle and improve the rise time of the force control by more than an order of magnitude.
Abstract: The characteristics and the nonlinear dynamics of a high performance hydraulic actuator produced by ASI Inc. are described and modeled. When a feedback is applied for the regulation of output force, a limit cycle is observed. The existence of the limit cycle can a priori be attributed to one, or to a combination of, the four dominant nonlinear effect that were identified in these actuators. In order to pinpoint its origin, successive approximations are made to apply the describing function principle, so as to predict the onset of the limit cycle as function of the feedback gain. Given the experimental data, this method allows us to attribute beyond any doubt its origin to the electromagnetic hysteresis in the valve, which is based on jet-pipe technology. A multiple term lead-lag controller is designed and implemented to quench the limit cycle and improve the rise time of the force control by more than an order of magnitude.

16 citations


Proceedings ArticleDOI
Henrik Olsson1
28 Sep 1995
TL;DR: This paper discusses different approaches when using the describing function method for the prediction of limit cycles in control systems and in particular the author uses it together with a new dynamic friction model.
Abstract: This paper discusses different approaches when using the describing function method for the prediction of limit cycles in control systems. The method and friction modeling is briefly reviewed. A simple example showing stick-slip motion is given. Using different friction models the describing function is applied to the example. In particular the author uses it together with a new dynamic friction model. Determining the describing function for the friction nonlinearity itself will not predict existing limit cycles but combining part of the plant with the friction model yields a describing function which captures the behavior of friction for zero velocity. This, however, needs a dual-input describing function which depends on three parameters as compared to the normal two. The results are presented in a three dimensional plot.

15 citations


Proceedings ArticleDOI
21 Jun 1995
TL;DR: In this paper, a method for force guided assembly of complex parts using dither as a perturbation input is described, where the authors take positive actions by actively shaking the end effector and observing the reaction forces to the perturbations in order to obtain rich, reliable information.
Abstract: This paper describes a novel method for force guided assembly of complex parts using dither as a perturbation input. In the robotic assembly of parts with poor surface finish, simple force measurement does not provide reliable information for guiding the parts. Due to friction at burrs and irregular surfaces, force signals are very noisy and erratic, preventing reliable sensing and monitoring of the assembly process. In this paper, instead of simply measuring contact forces, the authors take positive actions by actively shaking the end effector and observing the reaction forces to the perturbation in order to obtain rich, reliable information. By taking the correlation between the input perturbation and the resultant reaction forces, the authors can determine the direction of robot motion correctly despite burrs and poor surface finish. First, the principle of force-guided assembly using the dither and correlation technique is described. The control algorithm is formulated as a type of direct adaptive control where the optimal point of a cost function is searched by perturbing the input. The assembly process is then analyzed by using describing functions for modeling the nonlinearity associated with mechanical contacts. Stability conditions and guidelines for tuning the dither and control parameters are obtained. The proposed method is then applied to a practical task, i.e. assembly of sheet metals. Experiments and simulation verify the analytical results as well as demonstrate the usefulness of the method.


Journal ArticleDOI
TL;DR: In this article, an investigation concerning the prediction and control of observed limit cycling behavior in a boosting rocket is considered, where a classical sinusoidal describing function analysis is used to accurately recreate and predict the observed oscillatory characteristic.
Abstract: An investigation concerning the prediction and control of observed limit cycling behavior in a boosting rocket is considered. The suspected source of the nonlinear behavior is the presence of Coulomb friction in the nozzle pivot mechanism. A classical sinusoidal describing function analysis is used to accurately recreate and predict the observed oscillatory characteristic. From this analysis, insight is offered into the limit cycling mechanism and confidence is gained in the closed-loop system design. Nonlinear simulation is used to support and verify the results obtained from describing function theory. Insight into the limit cycling behavior is, in turn, used to adjust control system parameters to indirectly control the oscillatory tendencies. Tradeoffs with the guidance and control system stability/performance are also noted. Finally, active control of the limit cycling behavior, using a novel feedback algorithm to adjust the inherent nozzle sticking-unsticking characteristics, is considered. HE ballistic tactical target vehicle (BTT V) is a suborbital rocket whose re-entry vehicle serves as a target for advanced air defense and theater defense systems under development.1'2 Flight telemetry results from the first two missions indicate the presence of low-amplitude, low-frequency steady oscillations in both the vehicle attitude and actuator piston displacement.3'4 Figure 1 illustrates this characteristic in the vehicle pitch attitude response during second stage boost of the first mission. Note the flight data has been post processed. The impact of the oscillatory motions on the guidance and control objectives appear to have been minor; however, their presence was unexpected and is of concern, especially with regards concerning the origins of the oscillatory behavior and the physical mechanism by which they occur. The hardware in question is the decommissioned Minuteman I Stage 3 system which is used as the second stage for the BTTV vehicle. After discussions with individuals intimately familiar with the Minuteman I Stage 3 characteristics, it became known that this system has a long history of exhibiting small, slow periodic motions during the boost phase. These characteristics are, in fact, so common that routine preflight analysis is used in estimating the oscillatory motion for the specific flight vehicle/control system in question. The results are then compared with an existing database to deter- mine whether the oscillatory motions will impact the guidance and control mission objectives. This database suggests the oscillatory motions are limit cycling behavior due to nonlinearities present in the actuator-nozzle system, a conventional hydraulic actuator driv- ing vectorable nozzles. Coulomb or dry friction present in the nozzle pivot is the primary culprit. Additional nonlinearities are present but are not considered here. The first goal of this research is to provide an accurate prediction, if possible, of the oscillatory behavior experienced by the BTTV flight vehicle.5 This analysis should provide insight as to the ori- gin of and the mechanism by which the characteristics occur. Si- nusoidal describing function theory and nonlinear simulation are to be employed in achieving this goal. A second goal of this re- search is to explore means by which the oscillatory motions may be controlled to lessen the impact upon the guidance and control performance.5 The implemented control systems should also have minimal impact on the performance of the guidance and control feedback loops, while simultaneously providing sufficient robust- ness against reasonably expected modeling uncertainties and errors.

Journal ArticleDOI
TL;DR: A new appoach based on the use of describing functions to obtain approximate symbolic expressions for the fundamental frequency component as well as for the second- and third-order harmonics for a single soft or hard transconductance non-linearity embedded in an arbitrary linear network is presented.
Abstract: This paper presents a new appoach based on the use of describing functions to obtain approximate symbolic expressions for the fundamental frequency component as well as for the second- and third-order harmonics. A single soft or hard transconductance non-linearity embedded in an arbitrary linear network is studied. Three examples are considered.

Journal ArticleDOI
TL;DR: In this paper, an algebraic relationship is derived which enables the generalized amplitude dependent describing function to be expressed in terms of the parameters of a general nonlinear integro-differential equation.
Abstract: An algebraic relationship is derived which enables the generalized amplitude dependent describing function to be expressed in terms of the parameters of a general nonlinear integro-differential equation. The algorithm is not restricted to a specific input, but treats the whole class of harmonically related, phase independent, sinusoidal inputs, and is illustrated by a number of examples.

Journal ArticleDOI
TL;DR: In this article, the feasibility of expanding the flight envelope of a modified VISTA F-16 to higher angles of attack through forebody vortex flow control was explored, and it was shown that additional yaw control power from the blowing control system provided significant improvement in high-a performance.

Journal ArticleDOI
TL;DR: In this article, the internal nonlinear mechanism of a class of current-mode active elements used in sinusoidal oscillators is analyzed and it is shown how it must operate to guarantee the stability of the oscillation amplitude.
Abstract: In this work the internal nonlinear mechanism of a class of current-mode active elements used in sinusoidal oscillators is analysed. By means of the describing function formalism it is shown how it must operate to guarantee the stability of the oscillation amplitude. An illustrative example is given.

Journal ArticleDOI
TL;DR: In this article, a new analytical describing-function based method which utilizes the phenomenon of attractors to predict the existence of stable, unstable and strange attractors in autonomous nonlinear systems is presented.
Abstract: This paper presents a new analytical describing-function based method which utilizes the phenomenon of attractors to predict the existence of stable, unstable and strange attractors in autonomous nonlinear systems. This method serves as a criterion for a route to chaos, which is an extension to the traditional criteria for limit cycle stability, thus bridging a gap between two apparently separate worlds in dissipative systems theory, namely traditional harmonic linearization techniques and the relatively new theory of strange attractors. An illustration of the procedure is presented by applying this method to documented examples of chaotic systems. Although the method is based on harmonic linearization, a comparison of analytical results with simulation results looks promising, especially in systems with a strong low-pass filter characteristic. The main advantage, however, remains the easy application compared to complicated and exact methods. The application of this tool in diverse areas of nonlinear con...

Journal ArticleDOI
TL;DR: In this paper, a quantitative design theory is presented to satisfy given frequency domain tolerances in motion control systems with dry friction and high-order uncertain plants, which can be predicted with describing function theory.
Abstract: Motion control systems with dry friction and high-order uncertain plants suffer from one or more limit cycles which can be predicted with describing function theory. In this paper quantitative design theory is presented to satisfy given frequency domain tolerances in these systems. The case of linear time-invariant (LTI) compensation is studied first. Then it is shown how, in those systems with a limit cycle, self-oscillating design with an adaptive loop (SOAL) can be used to reduce the LTI compensator bandwidth for a large class of problems.

01 Jan 1995
TL;DR: Stability and handling qualities analysis using the Neal-Smith Criterion were performed according to basically unstable aircraft with limiters in the closed loop and in the forward path of the flight control system.
Abstract: Due to frequency domain analysis the describing function of a rate limiting element is derived using the Fourier transformation. A method is derived to calculate the describing function of the complete highly augmented aircraft system. The method is verified by a comparison with non-linear simulations in the time domain. The influence of rate limiting elements on handling qualities of augmented aircraft is discussed using five characteristic examples. Stability and handling qualities analysis using the Neal-Smith Criterion were performed according to basically unstable aircraft with limiters in the closed loop and in the forward path of the flight control system. A new handling qualities criterion is proposed.


Book ChapterDOI
01 Jan 1995
TL;DR: In this article, a stability analysis of a first order plant driven by a Bang-Bang actuator is performed using simplicial algorithms, where gains are used as the H∞ weighting functions.
Abstract: This paper presents a new method for designing H∞ optimal or suboptimal controllers for nonlinear systems. A stability analysis is conducted using simplicial algorithms. In this example gains are used as the H∞ weighting functions. The system is a unstable first order plant, driven by a Bang-Bang actuator. A describing function model of the actuator is used in this analysis.

Book ChapterDOI
01 Jan 1995
TL;DR: In this article, the authors consider the use of describing function techniques in the s and w domains to predict limit cycling conditions and closed loop performance of an electric current transducer and an accelerometer.
Abstract: The control system aspects of digital transducers, based upon the application of sigma-delta modulation to a closed-loop structure, is discussed. Such a system is a nonlinear, discrete data, control system and consequently is a challenging task for the design engineer. In this paper the authors consider the use of describing function techniques in the s and w-domains to predict limit cycling conditions and closed loop performance. Simple examples of an electric current transducer and an accelerometer are used to illustrate the approach.

Book ChapterDOI
01 Jan 1995
TL;DR: In this article, the stability analysis of a nonlinear system using simplicial algorithms is presented, where the system analyzed is a unstable first order plant driven by a Bang-Bang actuator, stabilized by a non-linear adaptive perturbation filter.
Abstract: This paper discusses a new method for the stability analysis of a nonlinear system using simplicial algorithms. The system analyzed is a unstable first order plant, driven by a Bang-Bang actuator, stabilized by a nonlinear adaptive perturbation filter. A describing function model of the actuator is used in this analysis. This system is implemented on a digital computer, and in analog circuit form, to demonstrate the practicality of the method.

Journal ArticleDOI
TL;DR: In this article, an algebraic relationship is derived which enables the generalised amplitude dependent describing function to be expressed in terms of the parameters of a general nonlinear difference or differential equation, and the algorithm is not restricted to a specific input, but treats the whole class of harmonically related, phase independent, sinusoidal inputs.

Proceedings ArticleDOI
28 Apr 1995
TL;DR: A spectral technique is proposed for studying and predicting chaos in a one-dimensional array of Chua's circuits by use of a double Fourier transform and an approximate tool is given for detecting the occurrence of chaos.
Abstract: A spectral technique is proposed for studying and predicting chaos in a one-dimensional array of Chua's circuits. By use of a double Fourier transform the network is reduced to a scalar Lur'e system to which the describing function technique is applied for discovering the existence of periodic wave. Finally, by the computation of the distortion index an approximate tool is given for detecting the occurrence of chaos.

Proceedings ArticleDOI
06 Nov 1995
TL;DR: In this article, a new method for calculating the input-tooutput and control-to-output characteristics of DC-DC converters is formulated, based on a Fourier analysis technique, relating the input and output spectrums of the converter.
Abstract: A new method for calculating the input-to-output and control-to-output characteristics of DC-DC converters is formulated. The approach is based on a Fourier analysis technique, relating the input and output spectrums of the converter. For small perturbations in either the input line voltage or the control signal, describing functions are defined. At the frequency of interest, which is given by the frequency of the injected sinusoidal perturbation, the zeroth term of the time-varying transfer function of the circuit is determined and the describing functions are evaluated, giving the required small-signal AC characteristics of the converters. The method is integrated with an original algorithm for calculating the time-domain response of the regulator by monitoring the switches' position, which allows the simulator to find automatically the transition instants and the switching sequence, assuring the generality of the method. The method is exemplified by the simulation of a traditional boost PWM DC-to-DC converter. The results are favorably compared to those obtained in literature by using other approaches and to the experimental results.

Proceedings ArticleDOI
25 Oct 1995
TL;DR: In this paper, a large-signal quasi-static MESFET microwave power amplifier with bias dependent elements was designed using the describing function technique and the maximum bias device conditions in C class were obtained for maximum gain.
Abstract: A MESFET microwave power amplifier has been designed using a large-signal quasi-static model with bias dependent elements. This model has been derived from experimental S parameters and dc measurements. The analysis and gain optimization of the amplifier is performed by using the describing function technique. Optimum bias device conditions in C class are obtained for maximum gain. Experimental results show an excellent agreement with the theoretical analysis.