Showing papers on "Describing function published in 1974"
TL;DR: In this article, the authors investigated the use of the nonlinear device known as the Clegg integrator in the design of a nonlinear feedback system, which minimizes the effect of white sensor noise on the input to the plant.
Abstract: The problem considered is the design of a feedback system containing a linear, time invariant, minimum phase plant, whose parameters are known only within given bounds, such that the time response of the system remains within specified limits. A quasi-optimal design, for given design constraints, is one which minimizes the effect of white sensor noise on the input to the plant. An investigation was conducted on the use of the non linear device known as the Clegg integrator in the design of such a system. The describing function of the Clegg integrator has the same magnitude characteristic, apart from a scale factor, as the linear integrator, but has 52 deg less phase-lag, at all frequencies, than the linear integrator; thus, when used in a feedback system, it provides a larger stability margin than the linear integrator. This property allows the nonlinear feedback system to be designed so that the sensor noise is attenuated more than in the linear design.
182 citations
01 Jul 1974
TL;DR: In this article, the authors investigated the stability of limit cycles in nonlinear feedback systems with several describing function (d.f.) predicted limit cycle solutions and showed that for a single-frequency limit cycle the necessary conditions for stability of Loeb and Gelb could be satisfied yet the limit cycle was unstable.
Abstract: This paper investigates the stability of limit cycles in nonlinear feedback systems with several describing function (d.f.) predicted limit cycle solutions. The investigations showed that for a single-frequency limit cycle the necessary conditions for stability of Loeb and Gelb could be satisfied yet the limit cycle was unstable. Also the simple and often used graphical criterion was found to be incorrect. On the other hand, the incremental-describing function (i.d.f.) method used for both asynchronous and synchronous perturbations gave sufficient conditions, within the expected d.f. accuracy, for all the situations. It is further shown that the synchronous i.d.f. and the Loeb criterion are normally identical. The combined mode limit cycle oscillations were also satisfactorily predicted by a twoinput d.f. and i.d.f.
24 citations
TL;DR: In this paper, the locking equation for single-stage LC injection-locked oscillators is derived for subharmonic, fundamental, and harmonic locking, the dc transfer characteristic of a nonlinear device being approximated, at the dc operating point, by a third-order polynomial.
Abstract: By combining the instantaneous phase shift of a twosinusoid-input describing function with a phase response of the tuned circuit it has been possible to develop the locking equation for single-stage LC injection-locked oscillators ILO. The locking range as well as steady-state phase shift of an ILO are calculated for subharmonic, fundamental, and harmonic locking, the dc transfer characteristic of a nonlinear device being approximated, at the dc operating point, by a third-order polynomial. The phase plane representation is included. Experimental results are given to support some of the theoretical relations derived.
21 citations
TL;DR: In this paper, explicit expressions for the current reponse under a sinusoidal potential input (with and without amplitude modulation) are derived based on the operator formalism developed earlier, and the results are valid for several chemical reactions and for mass transfer models of varied forms like the diffuse-layer coupling with diffusion, spherical diffusion etc.
19 citations
01 Aug 1974
TL;DR: In this paper, the existence and characteristics of self-sustained oscillations in the dynamic behavior of the LST system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMGs).
Abstract: The purpose of the investigation reported upon is to study the existence and characteristics of self-sustained oscillations in the dynamic behavior of the Large Space Telescope (LST) system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMGs). A continuous-data single-axis model of the LST is considered. A solid friction model is used to represent CMG gimbal friction. A rigorous mathematical model is derived for use in a continuous describing function analysis. Conditions for self-sustained oscillations are then determined.
4 citations
TL;DR: In this article, the results of describing function measurement for dynamically or statically unstable second-order systems were presented, and the results indicated that the pilot pays attention only to the unstable first-order mode so that his describing function coincides with that for the firstorder unstable system control.
Abstract: In designing V/STOL and high-speed flight vehicles, knowledge of the human pilot's controllability limit may be needed. Measurement of the pilot's describing function for his control of the system with marginal levels of static stability or damping, or both, is important to determine the controllability limit. This report includes the results of describing function measurement for dynamically or statically unstable second-order systems. Also included is a brief explanation of an improved time domain analysis method. When the system is dynamically unstable, the results show that the pilot employs a modified describing function that contains a second-order lead term with a particular time constant associated with the undamped natural frequency of the system. For the statically unstable case, the results indicate that the pilot pays attention only to the unstable first-order mode so that his describing function coincides with that for the first-order unstable system control.
4 citations
TL;DR: In this paper, a new criterion on the stability of the limit cycle of a general third-order non-linear system is proposed, where the linear part transfer function can be either stable or unstable and the nonlinear element has a real describing function.
Abstract: The purpose of this paper is to show a new criterion on the stability of the limit cycle for a general third-order non-linear system : that the linear-part transfer function can be either stable or unstable and the non-linear element has a real describing function. The presented method is purely analytic. Combining with an analytic method for predicting the amplitudes and frequencies of limit cycles, an analytic process for determining the stable limit cycles of a general third-order non-linear system is completed. Many examples are given.
4 citations
TL;DR: In this paper, the authors describe function techniques for the analysis of nonlinear multivariable systems and the condition det G + N ˆ ≠ 0, sufficient for the absence of limit cycles.
4 citations
TL;DR: In this article, the diea of constructing non-linear electronic networks with describing functions which are constant complex quantities is applied to the dynamic displacement of the Nyquist critical point in the complex plane.
Abstract: Some techniques for the dynamic displacement of the Nyquist critical point are presented here. The diea of constructing non-linear electronic networks with describing functions which are. constant complex quantities is applied here. With the aid of such networks the Nyquist critical point can be located in such a point in the complex plane that a system with better dynamic response can result.
4 citations
01 Jul 1974
TL;DR: In this article, an analysis of ferro-oscillations in capacitor voltage transformers and series-compensated e.h.v. lines is presented, where the dual-input describing function is adopted to show the regions of existence and the influence of system parameters on such oscillations.
Abstract: The paper presents an analysis of ferro-oscillations in capacitor voltage transformers and series-compensated e.h.v. lines. The dual-input describing function is adopted to show the regions of existence and the influence of system parameters on such oscillations. A complete analytical method suitable for digital computation has been developed for determining the amplitudes of these oscillations.
3 citations
TL;DR: A solution to the problem of evaluating a nonlinearity that yields a given random describing function is given and approximate methods are discussed for cases where the describe function is only known graphically.
Abstract: A solution to the problem of evaluating a nonlinearity that yields a given random describing function is given. Approximate methods are discussed for cases where the describing function is only known graphically.
TL;DR: In this article, a new asymmetrical oscillatory transient describing function, AOTDF, is derived and its properties are discussed. But it is shown that the new function is optimal in the sense that it minimizes a weighted mean-square-error criterion.
Abstract: The paper investigates asymmetrical transient osciliations in non-linear systems. The Krylov—Bogoliubov asymptotic method is extended to cover the asymmetrical transient case. A new asymmetrical oscillatory transient describing function, AOTDF, is derived and its properties are discussed. It is shown that the new function is optimal in the sense that it minimizes a weighted mean-square-error criterion. The AOTDF is utilized to evaluate asymmetrical oscillatory transient behaviour in nonlinear systems. Two illustrative examples are given.
TL;DR: In this article, a criterion for the investigation of the stability of a certain class of non-linear systems with sinusoidal input is proposed, derived from the concepts of the describing function method and the circle criterion.
Abstract: A criterion for the investigation of the stability of a certain class of non-linear system with sinusoidal input is proposed. It is derived from the concepts of the describing function method and the circle criterion. If the non-linear system satisfies the restrictions of describing function analysis and if the characteristic of the non-linearity is bound in a sectory/ee[a, b], there exists a critical region in the G inverse polar plane which contains ail possible describing functions of non-linearities bounded in this sector. Sufficient condition for the stability of the system is assured if the locus of the linear element does not intersect the critical region.
TL;DR: By this method the real and imaginary part of a given describing function (DF) can be separately realized by nonlinear characteristics which can be selected for control systems compensation.
Abstract: A method of constructing nonlinear characteristics from given describing functions data is proposed here. By this method the real and imaginary part of a given describing function (DF) can be separately realized by nonlinear characteristics which can be selected for control systems compensation. Also a method for synthesis of imaginary and polynomial type DF is proposed. The network for the construction of such nonlinearities and its use for compensation of a nonlinear system having limit cycles is also presented.
TL;DR: In this article, a semi-graphic solution was proposed to analyze the stability of a closed-loop digital servo system with more than two nonlinearities such as DA conversion nonlinearity, nonlinear friction, and nonlinear differences between spool displacement in servo valve hydraulic motor input pressure and flow rate.
Abstract: Stability analysis of a feed drive servo system of numerically controlled machine tools is important for improving its performance but very difficult since an actual system has a lot of nonlinearities. In this paper, we propose two methods. One is a simple identification method of the nonlinearities and the dynamics of hydraulic closed-loop digital servo system used in an actual NC machine tool, which utilizes a measured hydraulic motor input pressure. The other is a semi-graphic solution method using a describing function on the stability problem of a system which has more than two nonlinearities such as DA conversion nonlinearity, nonlinear friction, and nonlinearities between spool displacement in servo valve hydraulic motor input pressure and flow rate. Using these methods, it has been shown, the nature of stability and the mechanism of self-excited oscillations observed in an actual system can be clearly explained.
01 May 1974
TL;DR: In this article, a nonlinear stationary homogeneous digital filter DIRSIT (derivative information recovery by a selective integration technique) is investigated and the spectrum of a quasi-linear discrete describing function (DDF) is obtained by a digital measuring scheme.
Abstract: A nonlinear stationary homogeneous digital filter DIRSIT (derivative information recovery by a selective integration technique) is investigated. The spectrum of a quasi-linear discrete describing function (DDF) to DIRSIT is obtained by a digital measuring scheme. A finite impulse response (FIR) approximation to the quasi-linearization is then obtained. Finally, DIRSIT is compared with its quasi-linear approximation and with a standard digital differentiating technique. Results indicate the effects of DIRSIT on a wide variety of practical signals.
TL;DR: In this article, the problem of designing a closed-loop system containing a constrained linear minimum-phase plant, preceded by a non-linear element whose describing function is known, is studied.
Abstract: In this paper we study the problem of designing a closed-loop system containing a constrained linear minimum-phase plant, preceded by a non-linear element whose describing function is known. The system is to be designed such that its frequency response |T(jw)| lies within specified boundaries, over the range of plant parameter uncertainty, and over a specified sinusoidal command input amplitude r max ≥ r ≥ r min-Subject to the above, the design should be such as to minimize the effect of sensor white noise at the input to the plant.