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20 Dec 2017 Full-text (PDF) | This paper analyzes the dynamical properties of systems with backlashand impact phenomena based on the describing function method. It isshown that this type of nonlinearity can be analyzed in the perspectiveof the fractional calculus theory. The fractional-order dynamics isillust
Of the various describing functions discussed throughout this text, the sinusoidal-input describing function is by far the most widely known and used. In the following discussion the abbreviation DF is reserved for reference to this describing function. As the name implies, the DF is a linearization of a nonlinear element.
In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation
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
Describing Function analysis of nonlinear systems – Prof Elio USAI – March 2008. System definition and problem statement. In many cases the system presents a nonlinear phenomenon which is fully characterised by its static characteristics, i.e., its dynamics can be neglected. ? Saturated actuators. ? Relay control.
Multiple-input describing functions and nonlinear system design. GILL Introduction to the theory of finite-state machines. HANCOCK AND WINTZ Signal detection theory. HUELSMAN Circuits, matrices, and linear vector spaces. KELSO Radio ray propagation in the ionosphere. MERRIAM. Optimization theory and the design
Modelling and basic phenomena. (linearization, phase plane, limit cycles). Lecture 2-6. Analysis methods. (Lyapunov, circle criterion, describing functions). Lecture 7-8. Common nonlinearities. (Saturation, friction, backlash, quantization). Lecture 9-13 Design methods. (Lyapunov methods, Backstepping, Optimal control).
Abstract: In this paper, describing function method is used to analyze the characteristics and parameters selection of differentiators. Nonlinear differentiator is an effective compensation to linear differentiator, and hybrid differentiator consisting of linear and nonlinear parts is the combination of both advantages of linear and
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
combines MATLAB and Simulink to compute the describing function. The describing function is then encapsulated in a frequency response object that is combined with the transfer functions of the pendulum and the escapement to allow a classical Bode plot analysis. The result of the analysis is a feedback gain for the
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