By Guanrong Chen, David John Hill, Xinghuo Yu
Bifurcation regulate refers back to the activity of designing a controller that could adjust the bifurcation homes of a given nonlinear procedure, so that it will in achieving a few fascinating dynamical behaviors. There exists no comparable regulate theory-oriented ebook out there that's dedicated to the topic of bifurcation regulate, written by means of keep watch over engineers for keep watch over engineers. World-renowned best specialists within the box offer their state of the art survey concerning the large study that has been performed during the last few years during this topic. The booklet is not just aimed toward lively researchers within the box of bifurcation keep an eye on and its purposes, but in addition at a basic viewers in comparable fields.
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Additional info for Bifurcation Control: Theory and Applications
In fact, the so-called boost rectifier or power-factor-correction (PFC) converter is effectively a current-mode controlled boost converter . The circuit schematic is shown in Fig. 12. In this case, instead of setting Iref constant for a fixed load, we let Iref vary according to the input voltage waveform. Thus, the input current is being directly programmed to track the waveform of the input voltage. The result is a nearly unity power factor. 1 Bifurcation analysis The bifurcation analysis described earlier is directly applicable to the case of the PFC boost converter.
In addition, the index provides useful information as to how to derive effective load-shedding schemes to avoid voltage instability. We note that the parameter-space-based performance indices can not take into account the physical limitations of typical control devices such as generator VAR limits and ULTC tap ratio limits; such that their computed load/generation margins may bear some ‘distance’ from the exact margins. Hence, the function of these performance indices is mainly for ranking the severity of a list of credible contingencies or for ranking the effectiveness of different control devices.
By inspecting the slopes of the inductor current in Fig. 2 (a), we get Iref − in+1 v − Vin = (1 − D)T L and Iref − in Vin = DT L (1) where D is the duty ratio which is defined as the fractional duration of a switching period when switch S is closed. Combining the above equations, we have the following iterative function: in+1 = 1− v Vin in + (v − Vin )T Iref v − Vin L (2) If we are interested in the inner current loop dynamics near the steady state, we may write −D 1−D δin+1 = δin + O(δi2n ) (3) Clearly, the characteristic multiplier or eignenvalue, λ, is given by λ= −D 1−D (4) which must fall between –1 and 1 for stable operation.