10-01-2014, 12:22 PM
Analysis and Control of Chaos in a Current Mode Controlled Buck Boost Converter Using Weak Periodic Perturbation Method
Abstract
This paper presents the investigation of the non linear phenomena in the current mode controlled buck-boost converter. The results shows that converter shifts between period one, period two, higher periods and chaos as parameter(Iref) is varied. The proposed control strategy weak periodic perturbation (WPP) method tries to stabilize one unstable trajectory from a chaotic attractor. The result of this method is the transformation from a chaotic trajectory to a periodic one.
Introduction
Switched mode dc-dc converters may be thought of as non-linear and time varying dynamical systems. They contain switches that cause the topological structure of the converter to vary with time, energy storage components and diodes with non-linear voltage current characteristics. It has been shown that the operation of power converters can easily become chaotic when they fail to maintain their normal periodic operation. A current mode controlled dc-dc buck-boost converter in continuous conduction mode gives rise to a great variety of behavior depending on the parameters of the circuits. With current reference as the bifurcation parameter, the behavior of the buck-boost converter has been analyzed. The converter goes through period-1, period-2, period-4 operations and eventually exhibit chaos. Thus, the ability to avoid chaos is almost a basic feature of all existing practical control strategies, although practicing engineers may not aware of such a perspective. Various methods for the control of chaos have been proposed. Their objectives fall into two general categories namely feedback method and non feedback method. Examples of feedback method is Ott-Grebogi-Yorke(OGY),Time-delayed frequency control etc. In these methods system variable is measured, a control law is implemented and some parameters is varied to achieve the control objective. On the other hand, for non feedback method, no system variables need to be measured and no specific periodic orbit has to be identified as the control target. In this paper, the weak periodic perturbation method is applied to control chaos in a current programmed buck boost converter.
DISCRETE MODEL OF THE CONVERTER
To explore the nonlinear phenomena which may appear across a wide spectrum of frequency, the exact discrete–time maps must be derived. The stroboscopic map, the most widely used type of discrete-time map for modeling dc-dc converters, is used to obtain the Poincare section i.e. the system states, the inductor current and capacitor voltage, are periodically sampled at time instants, t=nT.
Assume in and vn to be instantaneous inductor current and capacitor voltage at time instants t=nT at which the switch starts to close. The control of the switch is that the switch S is turned off when the inductor current reaches reference current Iref. The on-state time tn of S can be obtained by simple integration.
d) BIFURCATION DIAGRAM
If the system is periodic, all the points would fall at the same position and we would see just one point for that parameter value. Higher periodicities would appear as the number of dots equal to the periodicity of the system. And for chaos (period infinity) we would get a smudge of dots, none of them falling on the other. In such a bifurcation diagram, one can clearly see the change of behavior as a parameter is varied. There are six major parameters in the system: the input voltage, load resistance, inductance, capacitance, reference current, and clock frequency.
CONCLUSION
PE designers prefer controllers having scope of easy implementation and simple logical operations. The perturbations in a system parameter or the switching instant are very small, leading to minimal disturbance to the current controlled operation of the converter. The chaotic behavior of dc-dc current mode controlled buck boost converter has been analyzed. The simulated results using MATLAB are presented. The bifurcation diagrams are drawn for the bifurcation parameters namely reference current and input voltage. The results obtained reveal that the current mode controlled buck boost converter enters into chaotic regime with Iref = 3A. It was shown that as the reference current is varied the nominal periodic orbit undergoes a flip bifurcation and finally enters into the chaotic regime. The chaotic behavior has been controlled using weak periodic perturbation. It has also been realized in hardware and the results have been verified with the simulation results.