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Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.


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TL;DR: Experimental results obtained showed that GCACO technique developed here for controller design of nonlinear multivariable feedback control systems was capable to produce optimal and practical controllers that meet the design requirement in an efficient manner and computationally acceptable amount of time.
Abstract: In the present study, a swarm intelligent algorithm called gradient-based continuous ant colony optimisation (GCACO) was utilised for controller design in multi-variable nonlinear control systems. The time domain objectives subject to the frequency domain constraints were considered in the proposed procedure. In order to be able to incorporate the time domain requirements in an overall controller design technique, the appropriate linearisation techniques utilised here was the exponential input describing function (EIDF). Experimental results obtained showed that GCACO technique developed here for controller design of nonlinear multivariable feedback control systems was capable to produce optimal and practical controllers that meet the design requirement in an efficient manner and computationally acceptable amount of time.

2 citations

Journal ArticleDOI
TL;DR: An exact analysis of a mutually coupled relay oscillator based on a method orignated by Tsypkin is presented, and limit-cycle frequencies and phases can be determined exactly using this method, unlike other approximate methods based on describing functions and harmonic balance techniques.

2 citations

Journal ArticleDOI
18 Jan 2021-Symmetry
TL;DR: In this article, a non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe the cardiovascular conduction process's dynamics, as the signal generated from the cardiovascular muscle is non-deterministic and random.
Abstract: In this paper, a complete non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe the cardiovascular conduction process’s dynamics, as the signal generated from the cardiovascular muscle is non-deterministic and random. Electrocardiogram (ECG) signal is a significant factor in the cardiovascular system as most of the medical diagnoses can be well understood by observing the ECG signal’s amplitude. A non-linear cardiovascular muscle model has been proposed in this study, where a modified vanderPol symmetric oscillator-based equation is used. Gone are the days whena non-linear system had been designed using the describing function technique. It is better to design a non-linear model using the Hamiltonian dynamical equation for its high accuracy and flexibility. Varying a non-linear spring constant using this type of approach is more comfortable than the traditional describing function technique. Not only that but different initial conditions can also be taken for experimental purposes. It never affects the overall modeling. The Hamiltonian approach provides the energy of an asymmetric oscillatory system of that cardiovascular conduction system. A non-linear symmetric oscillator was initially depicted by the non-linear mass-spring (two degrees of freedom) model. The motion of an uncertain non-linear cardiovascular system has been solved considering second-order approximation, which also demonstrates the possibility of introducing spatial dimensions. Finally, the model’s natural frequency expression has also been simulated and is composed of the previously published result.

2 citations

01 Jan 2011
TL;DR: In this article, the experimental validation of the bifurcation behavior of an EMVA controlled via a so-called "key-on" feedback controller is presented, where the experimental results are validated via an appropriate mathematical model and the existence of limit cycles proved analytically by using a describing function approach.
Abstract: Summary. Electromechanical Valve Actuators (EMVA) are fundamental components of camless engines. This work is concerned with the experimental validation of the bifurcation behaviour of an EMVA controlled via a so-called "key-on" feedback controller. The experimental results are validated via an appropriate mathematical model and the existence of limit cycles proved analytically by using a describing function approach. The numerical and theoretical analysis are shown to capture the observed experimental behaviour. Introduction and motivation Double magnet Electromechanical Valve Actuators (EMVA) (7) are essential components in camless engines (14). They consist of an armature linked to the valve, mounted between two symmetric high-stiffness springs. The valve is operated by means of a magnetic force produced by two magnetic coils so as to be open or closed. In so doing, it is essential for a feedback control action to be present in order to ensure acceptable performance. As shown in (5), to design such a controller it is essential to keep into account the many nonlinear terms affecting the valve operation such as the presence of friction, magnetic forces and the nonlinear behaviour of the springs (10). Here we consider the mathematical model of the valve developed in (5) where a nonlinear Stribeck friction model (2) is used. The proposed control is a switched control action aimed at compensating friction so as to move the valve during the key-on maneuver away from its stable equilibrium position at rest (9). When the controller operates the EMVA, the rigid body (armature and valve body) alternately sticks and slips with the constraints. This is caused by the fact that friction var ies as a function of velocity, i.e., loosely speaking, in certai n velocity range, the friction force is larger at rest than du ring motion. Note that during operation, high and varying temperatures can produce important variations in the parameters of the EMVA, that can affect strongly the controller performance. Therefore, the study of such parameters variation and their effect on system behaviour becomes a key point during controller design in order to tune the controller and increase the robustness range where the system performance is acceptable. In this paper, we validate experimentally the nonlinear behavior of the controlled valve proposing bifurcation analysis as an invaluable tool to tune the controller gains. We also show that the coexistence of limit cycles detected experimental ly can be accounted for by using a describing function approach (3, 13).

2 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847