The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Electric power systems are physically some of the largest and most complex nonlinear systems in the world. Bifurcations are rather mundane phenomena in power systems. The pioneer work on the local bifurcation analysis of power systems can be dated back to the 1970’s and earlier. Within the last 20 years or so nonlinear dynamical theory has become a subject of great interest to researchers and engineers...
The problem of sudden loss of stability (more precisely, sudden change of operating behaviour) is frequently encountered in power electronics. A classic example is the current-mode controlled dc/dc converter which suffers from unwanted subharmonic operations when some parameters are not properly chosen. For this problem, power electronics engineers have derived an effective solution approach, known...
The problem of operating or designing a system with robust stability with respect to many parameters can be viewed as a geometric problem in multidimensional parameter space of finding the position of nominal parameters λ0 relative to hypersurfaces at which stability is lost in a bifurcation. The position of λ0 relative to these hypersurfaces may be quantified by numerically...
Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems is linked to degeneracies in the system zero dynamics. Accordingly, the obvious remedy is to change the system input-output structure, but there are other possibilities as well. In this paper we summarize the main results connecting bifurcation behavior...
This chapter is to give the bifurcation analysis and the verification of chaotic dynamics in nonlinear feedback control systems based on numerical continuation techniques and the Shil’nikov theorem. The studied system is a low-order linear autonomous system with a simple nonlinear controller of the form g(ν)$=\nu|\nu|$. The chaotic dynamics generated in this kind of systems are demonstrated by both...
This chapter deals with bifurcation dynamics in control systems, which are described by ordinary differential equations, partial differential equations and delayed differential equations. In particular, bifurcations related to double Hopf, combination of double zero and Hopf, and chaos are studied in detail. Center manifold theory and normal form theory are applied to simplify the analysis. Explicit...
The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis in a suitable frequency band. Moreover, due to the existing connection between limit cycle bifurcations and routes...
This chapter presents an overview of recent results on an approach to total control of power systems. It is upwards compatible from any conventional or prior advanced control and provides a framework for coordinated development of control to address all major dynamical problems. The approach appears applicable to complex systems generally where behaviour is influenced by nonlinearity, large-scale,...
In this chapter we present a controlling method which allows the preservation of transient chaotic evolution in the desired region of the phase space. The concept of practical stability for the perturbed chaotic attractors and the connection between practical and asymptotic stability is described. Our controlling procedure allows asymptotically unstable chaotic attractors to become practically stable...
In this chapter the mathematical tools from bifurcation theory are used within the framework of feedback control systems. The first part deals with a simple example where the amplitude of limit cycles and the appearance of period-doubling bifurcations are controlled using a method derived from the frequency domain approach. In the second part, bifurcation theory is used to analyze the dynamical behavior...
In this chapter, we present some emerging directions in bifurcation control in continuous-time dynamical systems. Specifically we discuss two unconventional bifurcation control problems: anti-control of bifurcations and nonsmooth bifurcation control. Anti-control of bifurcation means introducing a new bifurcation at desired location with preferred properties by appropriate control. Nonsmooth bifurcation...
In this chapter, the role that bifurcation analysis can play for control systems applications is discussed. It is proposed that bifurcation tools can be used to (i) obtain better models of the system of interest; (ii) design novel control strategies aimed at controlling the bifurcation diagram of a given system rather than its trajectories for a specified parameter value; (iii) assist with the synthesis...
We describe a feedback control method for stabilizing some pathological behaviors of a nonlinear heartbeat model, with and without additive random noise. The controller is discretized to demonstrate how it might be implemented in a practical pacemaker design. Comparisons with some other control methods are discussed.
Local robustness of bifurcation stabilization is studied for parameterized nonlinear systems of which the linearized system possesses either a simple zero eigenvalue or a pair of imaginary eigenvalues and the bifurcated solution is unstable at the critical value of the parameter. It is assumed that the unstable mode corresponding to the critical eigenvalue of the linearized system is not linearly...
The turbo decoding algorithm is a high-dimensional dynamical system parameterized by a large number of parameters (for a practical realization the turbo decoding algorithm has more than 103 variables and is parameterized by more than 103 parameters). In this chapter we treat the turbo decoding algorithm as a dynamical system parameterized by a single parameter that closely approximates the signal-to-noise...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.